Cosmic Acceleration:
Hounding the White Whale of Cosmology
Philip Petersen, Phd
Empyrean Quest Publishers
P. O Box 628
Byron CA 94514
www.empyreanquest.com
©2004 by Philip Petersen
Library of Congress Cataloging-in-Publication Data
Petersen, P. Stephen
Cosmic Acceleration/Philip Petersen, PhD
ISBN 1-890711-19-5
First Empyrean Quest Edition 2004
Printed in the United States of America
TABLE OF CONTENTS
PREFACE
Ishmael: the Mask of the Universe - 5
INTRODUCTION
Chapter 1
Captain Ahab: Cosmology With A Vengeance - 14
The open sea: Newton’s infinite universe - 14
How Ahab lost his leg: Einstein’s greatest blunder - 18
Maps: is the universe closed, open, or flat? - 20
Chapter 2
Starbuck: the Voice of Reason–
Standard Big Bang Theory - 22
The sameness of the voyage:
homogeneous and isotropic - 22
The origin of the ocean: the Big Bang - 24
Symbolism of the ocean: there is no ether--
Einstein himself - 26
Starbuck warns of the Moby Dick obsession: LeMaitre’s Universe - 27
Chapter 3
The Lost Boat: Steady State Theory capsizes - 30
First sighting of a School of Whales:
the DeSitter Universe - 30
Rescued crew members:
Hoyle, Gold, and Bondi rescue Einstein - 32
A School of whales:
Quasars signal doom for continuous creation - 33
Fedallah--the subordinate phantom:
Cosmic Microwave Background - 34
Chapter 4
The Captain of the British Ship and his lost arm:
other failed theories - 37
How dangerous is Moby Dick?
Conflict over The Hubble Constant - 37
Is Moby Dick immortal?
The age of the universe in doubt - 40
The legend lives on: the Virgo Infall - 42
Chapter 5
Pip goes missing: Missing Matter - 44
Where is that black boy?
Do galaxies have missing mass? - 44
He could be anywhere: galactic clusters - 46
The ocean appears calm:
Is the universe flat? - 47
Pip becomes schizophrenic:
many possibilities for dark matter - 49
Baryonic Dark Matter - 49
Non-baryonic Matter
and Other Possibilities - 53
Chapter 6
Ahab’s ivory leg breaks:
Inflation in the Early Universe - 57
A new course: Linde and Steinhard’s Revised Inflation - 62
The track of the whales–the immortal ocean:
Chaotic and Eternal Inflation - 65
Chapter 7
The Chase: The nature of the ‘White Whale’–
the Cosmological Constant - 68
The Ship, the Ocean, and the Whale--
Matter, Curvature, and the Cosmological Constant - 68
The inferred existence of the ‘White Whale’,
the Cosmological Constant - 70
The wake of the ‘White Whale’:
the effects of a Cosmological Constant - 73
Former observations of the ‘White Whale’:
Truth or Fiction - 77
How to ‘kill’ the ‘White Whale’:
Theory and the Cosmological Constant - 80
Chapter 8
Starbuck almost kills Ahab:
the Universal Expansion is Accelerating
Ahab will not give up:
Supernova Observations and Cosmic Repulsion - 85
The Pequod and the Rachel:
The Two Supernova Teams Provide the First Equation - 89
Ahab is forever Ahab:
The Cosmic Background Provides the Second Equation - 93
Chapter 9
The Hidden Terrors of Moby Dick: Quintessence - 100
The Harpoon is not yet forged:
Time variable cosmological constant? - 102
Ahab as Prometheus:
Does the Fire of Space Expand the Universe? - 105
Explanations for Saint Elmo’s Fire--
conservation: the energy of space and matter - 106
All fired up to hunt Moby Dick:
Andrei Sakharov: is space spongy? - 110
Chapter 10
The High Velocity of the Breach: Variable Speed of Light Theories
Chapter 11
The Sphinx in the Desert–The Earliest Stages in the Universe and How We Know ThemParticles and Light–the Flesh and Blood of the Universe
Astronomer Talk about the Epochs.
Chapter 12
Fate’s Lieutenant: The Destiny of the Universe
Chapter 13
Harborless Immensities:
Extra Dimensions
Chapter 14
The final pursuit and demise of the Pequod crew: Repulsion Kills Cosmology
The ship sinks: old views of cosmology fall - 113
A sequel to ‘Moby Dick’?
what is next for cosmology? - 114
PREFACE
“All visible objects, man, are but as pasteboard masks. But in each event--in the living act, the undoubted deed--there, some unknown but still reasoning thing puts forth the mouldings of its features from behind the unreasoning mask.”
Captain Ahab
The Mask of the Universe
Though not a social creature, I attended a few parties with fellow graduate students and faculty at the University of California, San Diego. I recall a non-academic young lady at one of the parties approached me and asked what I did.
“I am a cosmologist,” I replied with some pomp, proud that I had initiated a journey of great peril and scope.
“Great!” she said, “would you do my face sometime?”
Had I been in full possession of my faculties, I might have replied:
“I don’t make up faces, I make up the Universe!”
The face the universe presents taunts us. As the white whale, ‘Moby Dick’, taunted Ahab and his crew, the facts we gather about the large scale structure and evolution of the universe have led us to one disappointing plateau of false understanding to another. From the comfort of Einstein’s Static Homogeneous Universe, we moved to an expanding one as the data demanded. Hoyle and Bondi imitated sameness over space with sameness over time: their Steady State theory of continuous creation. It went down with observations that the universe had indeed evolved. We then confronted the non-Newtonian behavior of galaxies and galactic clusters and proposed it to be explained by matter which does not shine--dark matter. This seemed to be corroborated by Guth’s Inflationary Theory of a short-lived accelerated expansion which required the universe to have more matter than we see.
Now it seems this type of cosmic acceleration is happening once again. Data from ancient exploding stars--supernovae--reveal a force of cosmic repulsion. This is not what most cosmologists expected.
If God were a NASCAR driver piloting the car of the universe, here’s what would happen with time. At about 10-35 seconds, it’s pedal to the metal. He puts his foot down hard on the accelerator. This inflationary acceleration expands the universe about 1060 times. This has the effect of smoothing out space and time and its energy content.
An instant later, at about 10-30 seconds, he takes his foot off the accelerator and puts it gently on the brake for about 7 billion years. The deceleration that results is the result of the gravity of the matter part of the universe. A baseball thrown straight up into the air slows down. In a way the deceleration period is like rounding a sharp turn in a NASCAR turn where the brake must be applied.
About 7 billion years ago we reach the next phase. As if coming out of a turn, God puts his foot back on the accelerator, not as hard this time. This is the moment astronomers now call ‘the big jerk’. The speeding up process is more gentle this second time. A small, nearly constant acceleration is maintained. As the matter is diluted by universal expansion, the matter component’s gravitational effect lowers until it is negligible, and the funny energy in space continues the acceleration.
Synopsis of Moby Dick
The story of cosmology is presented in parallel to Herman Melville’s Moby Dick. Here is the plot of that book.
A schoolteacher named Ishmael decides to take a break from his teaching and spend a year at sea aboard a whaling ship. He arrives at the whaling port, where at the inn he is made to room with a ferocious and superstitious south sea island harpooner by the name of Queequeg. They become friends, and Queequeg’s talent as a harpooner lands the teacher a berth as a novice aboard the whaler, the Pequod.
The ship is captained by the obsessed Ahab who has lost a leg to the white whale he calls ‘Moby Dick’. The white whale is known for his elusive intelligence and strength.
The obsession of Ahab to retaliate against the white whale grows as the search for ordinary whales goes on. He diverts the ship’s focus toward finding and ending the life of the white whale. Always on the lookout for clues as to the whale’s whereabouts, they follow those clues until a sighting is made. In fact, they follow the whale to the ends of the earth, suffering the cold of the arctic and the storms of the tropics.
On the journey, the ship’s first mate, Starbuck, realizes that Ahab’s obsession is preventing them from making a living, and leading them to ultimate destruction. Starbuck chides the captain for leading them astray, but Ahab is firm in his resolve.
When they encounter a British ship, the captain, who lost his arm to Moby Dick, reveals that he has seen the whale recently.
The chase is on. On the way the black cabin boy, Pip, is temporarily lost at sea, and when found, he seems to have lost his mind, ranting on incoherently about the whale. Queequeg, the nobel savage, becomes ill and blames it on the whale. During his illness, he sleeps in a coffin.
The white whale is eventually sighted and the battle is on. Ahab eventually rides the back of the leviathon. The whale capsizes the ship and the Captain and the entire crew are lost, with the exception of the schoolteacher, Ishmael, who lives to tell the tale.
Why Moby Dick and Cosmology?
The encounter with the supernova Ia observations and the realization of a dominating energy component to the universal expansion has devastated our prior beliefs regarding the history of the cosmos. We have encountered the white whale and it has sunk our ‘Pequod’, the 20th century cosmological ship of thought.
In this book we chronicle the journey of this ‘Pequod’. In a way, the characters in this story are not so much individuals like Einstein, Lemaitre, Hoyle, Bondi, and Guth. Rather, they are the different personalities which live in the psyche of a cosmologist--and perhaps each one of us.
There is ‘Captain Ahab’, the compulsive self which inordinately longs to solve the mystery of the origin and evolution of the cosmos. The dedicated cosmologist strives to wrest the mystery ‘from the hands of God’ with a vigor which can become obsessive. I gave up a spiritual vocation to go on my personal cosmological quest.
There is ‘Queequeg’, the savage mystical part, which longs to intuit the true nature of the cosmos by directly experiencing its relationship to the ‘inner cosmos’ of a man or woman. Drugs, near death experiences, fasting, contemplation of omens (all used by Melville’s South Sea island harpooner), all may be considered products of the desire of the soul to reunite with its source. Again, as in my case, some cosmologists might take up their ‘calling’ in response to a mystical, or at least transforming experience.
Certainly, all scientists can recognize ‘Starbuck’ in themselves--the voice of responsibility and reason: conservative, careful science. He tempers the ‘Ahab’ in us by reminding us our models must tow in to the observational data. Otherwise we will be abandoning our reason and perhaps our ‘living’ and our families. Being a theorist, however, I have often gone on flights of mathematical fancy, ignoring the voice of the ‘Starbuck’ in me.
My own story began much as Ishmael’s in ‘Moby Dick’. A schoolteacher, going back to graduate school, saunters into ‘port’. The goal is to “sail about a little and see the watery part of the world.” In my case, this was a journey into the sea of space, the domain of astronomy and astrophysics, rather than whaling and charting.
In telling this tale, I will relate it to the order of events and appearances of characters in Melville’s story. Chapters and subheadings will be headed by major characters or events in ‘Moby Dick’ and their similarity to cosmologists’ personalities and the events which shaped them.
If the metaphors and similes become strained, forgive me. Hopefully the drama and adventure of the quest for the ‘White Whale’ of Cosmology will compensate the reader. Perhaps we both might understand a little better the “little lower layer” of the mask, the “makeup” of the universe.
INTRODUCTION
This book divides neatly in two. Just as the story of Moby Dick is halved by the first sighting of the white whale by the Pequod., our story of cosmology nicely separates into what was known before the discovery of the accelerating universe in 1998, and what has happened since. There are seven chapters exploring each of the two halves. They are thus divided in time by this watershed revelation.
The supernova observations published in 1998 by Harvard and Berkeley teams brought about a revolution in cosmology unparalleled in the history of science. Before that time, it was thought that gravity dominated the current current expansion of the universe and was in the process of slowing it down. In fact, an important quantity in the theory of the cosmos was named the ‘deceleration parameter’ in honor of gravity’s role.
However, the theory was entirely wrong. Though gravity still appears to have some sway, our new view of the universe includes a ‘funny energy’ in space which currently dominates gravity as a cause of motion. This ‘dark energy’, as it is sometimes called, is responsible for an overall acceleration of galactic super-clusters away from each other.
The first seven chapters present cosmology before 1998. Because many people are acquainted with many of the principles of the ‘Old Cosmology’ and because they are more accessible, most readers will find the first half easy going. The second half is necessarily a bit tougher.
We begin with Chapter 1 and Newton’s infinite universe, pioneered a century earlier by the Italian monk Giordano Bruno.
We proceed to give a view of Einstein’s General Theory of Relativity and how the Russian, Friedmann, showed it provided for two versions of the cosmos: one infinite and saddle-shaped and the other finite and spherical.
Explored also is Einstein’s realization that if the universe were finite and static, as astronomer’s believed before the discovery of the Big Bang, then a repulsive force would be necessary to keep the matter from falling together as a result of gravitational attraction. The repulsion was provided for by a constant in Einstein’s Field equations somewhat like a spring constant in Hooke’s law. This is Einstein’s cosmological constant.
As Captain Ahab loses his leg to the white whale, Einstein loses his credibility in proposing the cosmological constant, when the universe is found to be expanding.
In alignment with the character of Starbuck, the first mate who is always practical and reasoned, Chapter 2 gives a sound basis for the Big Bang, ruled by gravity. First we lay out the principles of Homogeneity and Isotropy for a ‘dust’ inhabited universe. Then the characteristics of an expanding universe are sketched in terms of motion and temperature for the three possible cases: open, closed, and flat.
In this second chapter we also explore very fundamental reasons scientists (up until 1998) believed space should be empty, then explore LeMaitre’s 1930 model in which it is not. The possibilities multiply if we include a cosmological constant in an expanding universe, as he suggested.
Relevant to the history leading up to the acceleration discovery is the Steady State Universe of Hoyle, Bondi, and Gold. This is a lost theory like the rowboat first lost after leaving the home ship of the Pequod to chase a school of whales. Chapter 3 outlines DeSitter expansion and that theory, which proposed a universe uniform in time, perpetuated by continuous creation. Though observations eventually showed that the universe has evolved, Steady State prepared the way for an understanding of an energy in space which may not have evolved. We also discuss the Cosmic Microwave Background: a manifestation of the evolution.
As Ahab confronts a British Captain who also lost his arm to the white whale, so also Chapter 4 confronts other failed theories and observations that change. One side of the conflict over the rate of expansion of the universe we call the Hubble Constant is particularly prescient with regard to a possible energy content in space. When it is discovered that we are falling into the Virgo cluster of galaxies at a certain rate, a cosmological constant seems to be implicated, but is rejected by the mainstream.
Chapter 5 talks of Pip, the ‘black boy, lost in the black night, on the black sea’. Just as hard to find is the dark matter–matter not in stars--which is necessary to explain why stars move the way they do in galaxies, and why galaxies move the way they do in galactic clusters. At this point in the history, most of the matter universe is thought to be dark matter.
Then Ahab’s ivory leg breaks, and his carpenter must make a new one. Similarly, the standard Big Bang must be revised to include an early rapid inflation to handle observations. The inflationary theory is the topic of Chapter 6. We also explore the difficulty in finding a reasonable theory of inflation.
In Chapter 7 we explore the Cosmological Constant up close–theory and observations suggestive of it. We will be finally giving chase to the ‘white whale’.
The half of the book beyond Chapter 7 takes us beyond the Supernova discovery of the accelerating universe in 1998.
Chapter 8 details the observations of the ‘whale’ up close. How did we determine that there is about 70% dark energy and 30% matter? This mystery and the Supernova observations will be explained.
Chapter 9 reveals the hidden terrors of our ‘Moby Dick’. Einstein’s revision of General Relativity may not have been right. A cosmological constant representing the ‘funny energy in space’ may have to vary with time. It also may vary throughout space. Theories explaining it may have to be more complex. These we call ‘quintessence’ theories, relating to the fifth element beyond earth air fire and water.
In Chapter 10 the whale moves rapidly. We consider variable speed of light theories providing not only inflation, but also possible variable energy in space.
Chapter 11 talks of the epochs in cosmology. How do we know how the universe came to be the way it is? The past of the universe haunts us like the face of the Sphinx. Can we understand how particles making up matter came about?
The future of the universe is the topic of Chapter 12. Fate plays a great role in the story of Moby Dick. Is the fate of the universe a whimper or a cosmic rip?
Extra dimensions play a role in superstring theory. Is it possible that they relate to the nature of the recent acceleration of the universe? M Theory, the Randall-Sundrum Model, and Ed Witten’s great ideas are discussed in Chapter 13.
Chapter 14 ties the threads of the story of our ‘white whale’ together. Our ship of cosmology has been devastated, nay destroyed! In the end, all theories will be lost but one. What will it be? New observations via planned projects--the Planck observatory and the James Webb Space Telescope--may tell the entire story of our ‘Moby Dick’ from beginning to end.
Chapter 1
Captain Ahab: Cosmology With A Vengeance
“Already we are boldly launched upon the deep, but soon we shall be lost in its unshored, harbourless immensities.”
The Open Sea--An Infinite Universe?
We head out to sea, the Pequod, our ship of Cosmology, full of sailors--parts of ourselves who relate to the adventure ahead. What is the nature of the sea of space? The world was once thought to be flat, and sailors feared falling off the edge of a finite plane. Colombus had discovered once again that the world was spherical long before Melville wrote ‘Moby Dick’.
The spherical nature of the planet was understood by Pythagoras nearly 2,000 years earlier. Though we don’t know if he was the first to have this knowledge, we do know that he noticed ships appear to sink as they went out to sea, and the circular nature of the earth’s shadow in a partial lunar eclipse. These facts led him to conclude the earth was ‘round’.
What of space? Pythagoras thought of the stars as embedded on a celestial sphere. After all, didn’t they have circular tracks in the sky at night? Simplicity would demand that the stars occupy a surface reflective of the earth itself: a sphere. That meant that all objects in the heavens were less than that distance away. The planets--Greek for ‘wandering stars’--turned on imaginary spheres inside the sphere of the fiery element of the stars. Aristotle, two generations down the line, carried on and expanded this earth-centered, finite universe picture.
Even Copernicus, who in 1543 AD ‘changed the world forever’ with his picture of planets revolving around the sun, still had the stars pasted on a finite sphere. Though he increased their distance so as to conform with observational facts, such as the size of Saturn’s orbit, his universe was still finite.
Aristarchus in the second century BC first lent reasonable support to a sun-centered universe, infinite in extent. However, observations seemed to contradict his great intuitive glimpse. Aristotle, two centuries before him, pointed out that if the sun were at the center of the universe, the angular location of the stars would change with the seasons as the earth orbited the sun. This ‘stellar parallax’ was not observed, so when Aristarchus asserted the universe to be heliocentric, reasonable scientists dismissed it. The problem was with Aristotle’s small distance to the stellar sphere. If stars were much further away, they would shift by too small an amount to be seen as the earth shifted its position.
The universe seemed ‘made for man’ instead of the modern idea of man evolving from the universe. This stigma still clung to the picture of Copernicus. Fifty years after Copernicus passed, the infinite universe was again proclaimed. The monk, Giordano Bruno gave us a vast, untrammeled view:
“The stars are suns like our own and there are countless suns freely suspended in limitless space, all of them surrounded by planets like our own earth, peopled with living beings. The sun is only one star among many, singled out because it is so close to us. The sun has no central position in the boundless infinite.”
Such a profound, revolutionary set of hypotheses has no comparison in the history of science. In 1997, we found evidence of the first planets around other stars. Bruno spoke that hypothesis over 400 years before it was proven. Though many believe UFO’s are evidence of extraterrestrial life, the hypothesis of ‘living beings’ still remains to be openly verified. In addition, cosmologists are still contending over whether the universe is finite or infinite. However, the results of early 1998 dealing with supernova-implied expansion and the WMAP results from 2003 seem to favor a universe which is at least very, very large--much larger than the portion we can see.
Giordano Bruno, arguably the first claimant to the infinite universe, was burned at the stake as a heretic.
Isaac Newton, with Ahabian abandon, also supported the ‘infinite universe’ theory.
Newton was attending Cambridge University, when a version of the plague swept the countryside. His school was shut down, but this didn’t deter his studies. He retreated to his mother’s care at Woolsthorpe, and discovered the laws of motion, but more important to our discussion is his discovery of the nature of gravity.
I often ask my students what they would do if an epidemic of the proportion of the plague were to shut down all colleges. It could be AIDS, ebola virus, or something else. Would they have the initiative to follow their search for knowledge anyway? Would their dream just languish, or perish?
Newton’s contribution to the understanding of gravity was penultimately profound. His famous second law of motion was really the definition of mass, the source of gravity. No one before him had quantified matter, made it amenable to experiment. He defined mass as the ratio of the total applied force on an object to it’s acceleration.
Second, Newton realized that gravity acted from the center of a symmetric spherical object like the earth. It generated an attractive pull he deduced from Kepler’s laws of planetary motion, to be proportional to the masses of the two objects involved. Gravity was found to be a very weak force. It takes the entire earth to produce a pull on your body with a force equal to your weight.
Here is another way of demonstrating how weak gravity is. Take a blown-up balloon and hold it against the wall. Newton said that wall should attract the balloon in proportion to its mass and that of the wall. This is the ‘Universal’ of the ‘Universal Law of Gravitation’--all bodies attract this way.
However, the gravity of the earth overpowers that attraction and the balloon falls to the floor. Nevertheless, if you charge the balloon by rubbing it against your clothing, it will stick to the wall by inducing an opposite charge in it. That is, with a little bit of charge in the balloon and wall, electricity has exerted a force much stronger than the gravity between the balloon and wall. Gravity is weaker than the electric force.
The third thing Newton realized, again by deriving it from Kepler’s laws, was that gravity falls off as square of the distance between centers of symmetric spherical objects. This r-squared law of falloff holds, strangely enough, for light intensity from a spherical source, and for electrical force as well. It is as if gravity is an emanation like light--a field, if you will. The fall-off was discovered around the same time by an English contemporary of Newton’s: Robert Hooke. Newton and Hooke had a bitter dispute about the discovery of gravity. However, Newton won out, as Hooke had only discovered that one fact about gravity, whereas Newton had attained more profound knowledge.
Newton used his grasp of gravity to reason that the universe must be infinite. He assumed stars to be distributed somewhat uniformly throughout space. Each star attracted each other by gravity. If such a universe were finite, the stars would fall together, attracted by the force. This could be stopped by assuming an infinite universe, since each star would have equal pull to all sides. Milne and McCrea in the 1930's discovered that Newton’s laws of motion and gravity could be used to describe the universe, giving the same results as the more profound General Theory of Relativity of Einstein. Only when observing very distant objects must we use Einstein’s theory.
How Ahab Lost His Leg--Einstein’s Greatest Blunder
It was this static, infinite ‘Ahabian’ universe to which Einstein and most physicists clung before the era of the First World War. This was shortly before Edwin Hubble and his assistant Milton Humason discovered the galaxies were flying apart. After all, when we look at the sky, the stars appear to hang there motionless except for the motion related to the earth turning under them. Also, observations on the then new 100 inch Mount Wilson telescope indicated a universe orders of magnitude more vast than previous instruments. For all intents and purposes, it seemed as if it would all go on forever.
Having just formulated his new theory of gravity, General Relativity, in 1915, a static universe was puzzling to Einstein. In this theory of gravity it was possible for the universe to be finite. If the matter in it were dense enough, space and time would bend in response--into a closed form. This is analogous to the surface of a sphere, but in an extra dimension. In this ‘spherical’ closed finite universe, gravity would collapse it. Being static like in Newton’s example, there would be nothing to prevent the force from drawing all the stars together. However, we don’t see this, Einstein surmised.
He concluded that gravity must be countered by a repulsive force. He also included this as an addendum to his General Theory of Relativity. There are many ways of thinking of this force, but perhaps the most graphic is to compare space to a compressed sponge when you let it expand. An ideal gas has a similar outward pressure. It is sort of like having compressed springs between the galaxies. In fact, our friend Robert Hooke would have been pleased to find that the force necessary is proportional to the expansion scale as in his famous ‘Hooke’s Law’ of spring extension. However, instead of being attractive, like for a spring, it is repulsive. As for a spring, the force is imputed a strength by a constant. This universal ‘spring’ constant is lambda (Λ), the ‘cosmological constant’.
There are very convincing mathematical reasons why the force must be represented by a lambda term in Einstein’s Field Equations, but for many years, scientists thought there were observational and theoretical reasons that force should be zero (Λ = 0). We will discuss that later in the book.
When the expanding universe was discovered, the need for a force to balance gravity was done away with. Einstein began to think of the cosmological constant as his ‘Greatest Blunder’. ‘Ahab’ lost his leg in the first encounter with the ‘white whale’.
It was thought that the universe would slow down as it expanded, much like a ball slows down when thrown straight up from the earth. It was believed that gravity was the only force acting on the galaxies and tended to decelerate them. A term was devised as a measure for the amount of deceleration. Thus was born what cosmologists call the ‘deceleration parameter’, q . We will later see, however, that observations of the rate of supernova expansion do not match a state of deceleration. Rather we must hypothesize a force similar to Einstein’s to explain the universal acceleration, and q must be a negative number at present.
Maps: Is the Universe Closed or Open?
Ahab consulted detailed maps and was familiar with the lay of the oceans. Einstein’s General Theory of Relativity gives us possible maps of the universe. It says that the gravitational nature of matter is equivalent to curved space-time. The more matter is in space-time the more curved it is. Generally in cosmology we assume that the matter density at the largest scale is uniform throughout space. Later we will see just how uniform it really is. But for now, consider adding matter uniformly a little at a time to originally flat space-time. The more we add the more curved it is.
Note that for the meantime, we are leaving out any additional components, like the cosmological constant, contributing to the curvature of space. Though we now know that this is probably not valid, such a discussion is at least simple, and will give us ideas which will be useful later.
The addition of mass increasing curvature is analogous to trying to bend a thin rod of steel by applying increasing force on two ends. Such a tensile force will be uniformly distributed. The more pressure (gravity due to mass), the more the rod will bend. A critical amount of pressure (mass) may be reached where the steel bends into a circle.
In a similar way, if a critical mass density is exceeded for models of the universe in Einstein’s theory, space-time is bent into a hyper-sphere. This is one dimension up from the surface of a sphere like the earth, and the universe is finite in extent, a finite hyper-spherical surface. We call this a ‘closed universe’. The Soviet, Friedmann, found the first General Relativistic solutions for the expanding universe. His equations implied that the universe, if only the force of gravity were important, would expand for a time, then recollapse into what we now call ‘the Big Crunch’.
If the present mass density is less than the critical amount, space-time is saddle-shaped and infinite, sort of like an extended ‘Pringle’ potato chip. This is called an ‘open universe’. Friedmann’s mathematics (without cosmological constant) said that this type of universe would expand forever.
The expansion in these models can be grasped if we think of throwing a ball off successively larger asteroids. If your arm can achieve acceleration to a certain velocity, you could throw the ball at that speed straight up in all cases. Newton laws tell us that escape velocity from a gravitational body goes up as the mass goes up.
The gravity of a small asteroid is insufficient to prevent the ball from escaping. In a nearly empty universe, expansion under the influence of gravity only will slow in rate and eventually continue outward at a nearly constant velocity. In fact, this is true for a universe with any density less than the critical amount.
When we try the asteroid with just enough gravity to almost turn the ball around, this is like critical mass density for the universe. All larger asteroids return the ball because escape velocity exceeds the velocity thrown. Thus a universe with enough density doesn’t originally have escape velocity from itself, and recollapses.
However, what if gravity is not the only force important to changes in expansion? Then the entire picture must be modified. LeMaitre, the Catholic priest, did calculations in the late 1920s for a repulsive force added to gravity, and found the behavior to be more complex. We will talk about these possibilities later, in our next encounter with the ‘white whale’ of cosmology.
Chapter 2
Starbuck: the Voice of Reason--
Standard Big Bang Theory
“Vengeance on a dumb brute!” cried Starbuck, “that simply smote thee from blindest instinct! Madness! To be enraged with a dumb thing, Captain Ahab, seems blasphemous.”
The Sameness of the Voyage: Homogeneous and Isotropic
As we look out at the expanse of stars, the band of stars we call the Milky Way takes on the character of an imaginatively semi-uniform veil. Thus it was that early cosmologists assumed the universe to be uniformly sprinkled with matter at the largest scale. Perhaps the assumption was also constrained by the fact that calculations for a non-uniform universe were outrageously difficult in Einstein’s General Theory. Though knowing that proof of such a sweeping generalization was not attainable with the telescopes of the 20's and 30's, Robertson and Walker obtained in that epoch a description of the curvature of a universe which was not only looked the same everywhere, but the same in any direction. They called it ‘homogeneous and isotropic’.
A homogenous universe is invariant under translation from one position in space to another. The density in one locality is identical to that in another locality. How can this be if the universe contains lumps like stars, galaxies, galactic clusters, galactic superclusters, and perhaps complexes of superclusters? Evidence now indicates that beyond the scale of superclusters this is nearly true. Although the universe has not been thoroughly mapped, the overall picture in our locality is that the universe is smooth at the very largest scale.
An Australian based group called the 2-Degree Field Galaxy Redshift Survey, announced in June of 2000, the mapping of 100,000 galaxies surrounding us in space. This allowed us, for the first time, to get a good look at the largest structures and beyond. This is filigree inhomogeneity at the level of structure we call superclusters, and perhaps one level of clumping some call ‘continents’ at a larger scale. However, beyond that, galactic clustering reaches the ‘end of greatness” and is smooth.
The Sloan Digital Sky Survey has finished a survey of a million galaxies. This has pinned down the nature of the smoothness even further. Nevertheless, this is a drop in the bucket of the 50 billion estimated galaxies in the visible universe.
‘Largest scale’ is like looking at the lights of Los Angeles at night from a helicopter at a great height. They all blend into a smooth glow.
There is at least one exception to this smoothness called the Great Attractor, a mass at least a thousand times larger than that of the largest galaxy observed. Hidden by the dust in our galaxy, behind its center, this large gravity source is drawing thousands of galaxies toward it in ‘violation’ of the expanding universe. However, even the Great Attractor pales to insignificance as a lump, if the scale imagined is large enough. This is particularly so if the universe is Open and infinite.
The universe is also isotropic, invariant under rotations. The density we observe at a given distance is the same no matter what direction we look. Maps of the universe at the largest scale look the same wherever we turn.
Thus these two assumptions, very much ad hoc at first, are now fairly firmly founded in observations. They are as rational as Starbuck’s goal to hunt whales without risking the unknown in an encounter with the leviathon, Moby Dick. And, as with Starbuck, one’s livelihood as a cosmologist may be dependent on these realizable conditions.
The Origin of the Ocean: the Big Bang
The discovery of the expanding universe began with Vesto Slipher’s measurements of what we call the ‘redshifts; of galaxies in 1914. Working at Lowell Observatory in Arizona, he noticed the Doppler shifting of spectral lines in 11 out of 15 galaxies was toward the red end of the rainbow, indicating that they were moving away from us. This motion indicated that what was thought to be gas clouds called ‘nebula’ in some cases were not caught up in the motion of the galaxy. Curtis used this fact to try to convince the scientific world that this ‘island universe’ of the Milky Way was not the only one--that there were other galaxies of stars besides our own. His 1920 debate on this issue with Harlow Shapley, who first proved we don’t inhabit the center of the universe, was inconclusive, however.
Obtaining spectra of galaxies at that time was an all night, six hour time-exposure affair, so the sample was limited. This small sample was by no means proof that the universe was expanding. Four out of the 15 galaxies had blueshifts, indicating motion towards the observer.
Edwin Hubble, a law student turned astronomer, was the first to have opportunity to take a larger sample on the Mt. Wilson observatory scope. The actual all night vigils were accomplished by his assistant, Milton Humason. This is sort of like having a crew member up in the crows nest searching for spouting whales.
Humason was a mule team driver who carted the telescope parts up the narrow mountain roads to Mt. Wilson. He had only elementary school education, and was an addicted gambler who was hired on as a janitor in the observatory. His curiosity led Hubble to teach him how to operate the telescope and photographic equipment.
They noticed a trend in the spectra of the more distant of their sample. A little over thirty galaxies seemed to lie along a line in a plot of Doppler shift-implied recession velocity versus distance. The Doppler shift in frequency can be experienced when a fire engine races away from us. The greater its speed, the greater the shift. Shift implies speed. Blue light from a receding source will be shifted toward the red end of the rainbow. This astronomers call a ‘red shift’.
Using distances derived from other sources, they concluded that the farther away a distant galaxy was, the faster it was moving away from us. The exact proportionality of distance and recession velocity meant something absolutely astounding. It meant that the universe was expanding uniformly. Wherever in the universe an observer would view moderately distant galaxies, they would all lay along the same Hubble’s Law straight line. If one thinks backwards, considering gravity as a retarding force to this expansion, the universe must have come from a ball of matter and energy in an explosion named by Fred Hoyle thirty years later--‘The Big Bang’.
The exact mathematical relationship of Hubble’s Law--and its implications--was worked out by Robertson, a theoretical cosmologist. He then took this uniform expansion and made up what is called a ‘metric’ or scaling geometry for it in Einstein’s General Theory of Relativity. The Soviet Friedmann also had solved Einstein’s equations, without understanding they were consistent with an expanding universe.
Since Hubble, Humason, Robertson, and Friedmann were all responsible for understanding the data, we probably should call Hubble’s Law, the Hubble-Humason-Robertson-Friedmann Law. :>)
Symbolism of the ocean: there is no ether--Einstein himself
One key to Friedmann’s Gravitational theory was that gravity was the only force involved in regulating the expansion. Certain discoveries over twenty years earlier made this assumption at least temporarily reasonable.
Nineteenth Century physicists tried to understand the nature of the propagation of light. Light had been discovered to be an electromagnetic wave by the theory of Maxwell and the light-generating circuits of Hertz. The thinking was that all waves require a medium for the transmission of energy.
If that medium were still with respect to the ‘fixed stars’ the earth moving through it should have created a substantial ether wind. Using a device accurate enough by twice to detect such a wind, Michelson and Morley in 1900 bounced light off mirrors in different directions, but noticed no change in the speed of light with direction. This meant that the earth was not ploughing through some ‘stationary’ stuff in space, and that the speed of light could not be ‘boosted’ or retarded.
Albert Einstein was developing a theory which harmonized with the Michelson-Morley experiment. In 1905, as a clerk in the Patent Office in Germany, he published a theory that would transform our understanding of motion forever. His special relativity required that the speed of light would be the same for all observers, no matter how fast they were moving. This required that there could be no motion through a medium that would add or subtract from that speed.
This began to cement the idea in physicists minds that space was indeed empty. Light required no medium, it was thought, for its transmission. Could there be a medium for light that did not behave like an ordinary fluid? Is there something in empty space? Is there something that is spongy that could act as a repulsive force? We will explore these questions later in this book.
This blanket denial of stuff in space was reasonable. It was like the rational Starbuck observing that Ahab’s obsession with white whale hunting was interfering with making a living made by killing the much more abundant darker whales (like the dark matter hypothesis, we will see later). As Starbuck thought it absurd to strike out after the white leviathon, physicists and astronomers for nine decades, for the most part, had thought it folly to search for a compressible ether in space.
Starbuck warns of the Moby Dick obsession:
LeMaitre’s Universe
Friedmann’s three expanding universes: open, closed, and flat--are obtained by setting the cosmological constant, Λ = 0. However, many more possibilities for expanding universes open up with the possibility of a non-zero cosmological constant. Georges LeMaitre, a priest in the Catholic Church obtained a PhD in Physics from the Massachusetts Institute of Technology in 1927. His thesis involved the first understanding of the Big Bang from a theoretical point of view, utilizing Einstein’s General Relativity. He was the first to state that the universe may have emanated from a hot dense state. His cosmological equations yielded, however, a bewildering variety of universes behaving in response to gravity and the cosmic ‘spring’ force. Those with expansion periods could be classified by the following adaptation of Edward R. Harrison:
‘Bang’--an expansion period, with space-time emanating from a point,
‘Static’--a finite period with no expansion or contraction.
‘Whimper’--a period of expansion to infinity.
‘Crunch’--a period of contraction ending in a point. (My addition to Harrison’s treatment.)
Possible Universal Behaviors
(if Λ is allowed to be positive, negative, or zero):
The first three were the only allowed in Friedmann’s picture with Λ = 0, although still possible for Λ≠0.
1. Bang-Crunch (closed universe--universe recollapses in finite time)
2. Bang-Static (flat universe--asymptotic--gradually approaches a halt)
3. Bang-Whimper (open universe--universe expands forever)
4. Bang-Static (universe comes to a dead halt non- asymptotically)
5. Bang-Static-Crunch (universe expands, stays static a while, then contracts)
6. Bang-Static-Whimper (LeMaitre’s Universe)
7. Static-Whimper (Eddington’s Universe)
8. Whimper (Desitter Universe, gravity ignorable, in the usual way of thinking)
9. Crunch-Whimper (universe contracts to a finite size, then expands)
10. Crunch-Static-Whimper
Each of these 10 possibilities have a period of expansion. However, if the universe is presently accelerating, as recent supernova data indicate, this narrows the field to leave only models 3 and 6-10. All of these models extend to more possibilities for the universe’s age from the limiting nature of the Friedmann models.
Lemaitre’s Universe (6) has a long quasi-stationary period, which was first thought to explain an epoch where Quasars were formed. Many of them were found clustering at a certain distance which corresponded to several billion years ago. (That was at a redshift of z = 2. Note, redshift, the relative change in wavelength/wavelength, relates to look-back time.) Later, though, the need for this stable epoch evaporated as more Quasars were discovered at much greater distances.
Eddington’s Universe (7) did away with the need for a beginning, a creation event, with an early static phase extending into the infinite past. During the static phase, no galaxies could have formed. It lasted until about 10 billion years ago. Thus this model also is not viable, since we have observed galaxies as much as 13 billion years old.
‘Crunch-whimper’ (9) is only allowed for a cosmological constant much smaller than Einstein’s original value.
‘Crunch-Static-Whimper’ (10), like LeMaitre’s universe, has a long stable static period, for which we see no evidence.
Though it will take more evidence to motivate it, we will argue that with the latest supernova observations, it would seem that all that is left is the Bang-Whimper (3) and the DeSitter Universe (8). Most cosmologists rule out a currently DeSitter Universe, however, because it is an ‘empty’ universe with no matter in it, and the universe seems to had a phase where it decelerated, a phase when matter dominated.
Chapter 3
The Lost Boat: Steady State Theory capsizes.
“There are certain times and occasions in this strange mixed affair we call life when a man takes this whole universe for a vast practical joke, though the wit thereof he but dimly discerns, and more than suspects that the joke is at nobody’s expense but his own.”
Melville’s comments after a whale chase in Moby Dick resulted in the temporary loss of a boat.
“The Steady State Theory has a sweep and beauty that for some unaccountable reason the architect of the universe appears to have overlooked. The universe is in fact a botched job, but I suppose we shall have to make the best of it.”
Dennis Sciama, 1967
First sighting of a School of Whales: the DeSitter Universe
“ As he stood hovering over you half suspended in air, so wildly and eagerly peering toward the horizon, you would have thought him some prophet or seer beholding the shadows of Fate, and by those wild cries announcing their coming.”
“‘There she blows! there! there! there! she blows! she blows!’”
A friend of Einstein’s, a Dutch theoretician by the name of DeSitter, in 1917 proposed a surprising cosmology. He showed that the universe could expand ever more rapidly--exponentially--if it had no matter in it, only ‘funny energy’ in space described by Einstein’s cosmological constant. Hubble had not discovered the expanding universe yet. That came nearly 10 years later.
DeSitter’s suggestion was a wild stab in the dark with no evidence to back it up. However, if one believes in intuition, it was a great signet of what was to come. Not only was it the first proposed expanding universe, but the expansion paved the way for an important phase in cosmological wandering--the Steady State Universe.
The emptiness of the De Sitter universe could be justified by saying that the ‘funny energy’ of the Cosmological Constant dominated over the effects of gravity, and it just may be what our universe will end up like. So his theory is very likely an asymptotic description of our present cosmological knowledge. At least in the future, the universe will probably break free of its gravitational bonds, and expand under the influence of the cosmological ‘funny energy’ in space itself. That is, as long as the funny energy obeys Einstein’s requirement that its density remain constant, a cosmological constant. We will see later that other types of ‘funny energy’ have been proposed which would accelerate universal expansion, but none of them at this point seem as likely as a cosmological constant, simply for the reason that they would violate Einstein’s General Theory of Relativity–the comfort zone of many physicists.
DeSitter’s universe is a flat universe. The curvature constant, k, is zero, and the mass density is zero in the Friedman equations. The Hubble constant is proportional to the square root of the Cosmological Constant, Λ, implying the scale of distances increases as an exponential function of time. An important measure is the deceleration parameter, q, describing how fast the universe is slowing down. This remains constant at q = - 1. The negative value means the universe is speeding up, not decelerating. This is the very value which the Adam Riess group from Berkeley Labs reported with the first big batch of redshifts of moderately distant supernovae, and the current WMAP value of q < -0.8. Could it be that the universe--at least currently--behaves as if it is empty... even though it has matter in it?
In a way, the DeSitter Universe is a steady state universe. In the conventional way of looking at it, the density of matter remains constant at zero, even though two observers will drift apart exponentially. The universe always looks the same. This is all mathematical and hypothetical--don’t ask me how two observers get to exist in a universe without matter.
The Rescued Crew Members:
Hoyle, Gold, and Bondi rescue Einstein
One of the fascinating features of a pure DeSitter universe is that it has no beginning. It is a way of putting off the question, ‘where does the universe come from’. It never was infinitesimally small, so there is no cause required. At least that was the argument Gold and Bondi gave for the first De Sitter-like cosmological model which proposed to match the evidence--the Steady State Universe with matter in it.
To produce such a universe, Gold and Bondi proposed not only that the universe should look the same throughout all space, but throughout all time. Sameness throughout all space had been tagged ‘The Cosmological Principle’. Space-time sameness they called the ‘Perfect Cosmological Principle’. In the form they gave it, however, it was not so perfect. We have found that the universe does evolve. Nevertheless, the concept prompted the search for cosmic evolution, and gave us some mathematical tools which may help us to model possible objects called ‘white holes’, for example.
To maintain a constant matter density, the Steady State Universe had to involve continuous creation of matter in space at a rate too small to be detected. The rate of matter creation in the theory had to exactly fill in the empty space left by the expansion of the universe. This assumption was completely ad hoc, and thought by some to be a flaw in the theory.
Pascal Jordan in 1933 had modified General Relativity with new mathematical objects called scalar-tensors which he said would produce ‘drops’ of created matter in space. However, there was no evidence indicating that Einstein’s theory needed to be modified.
Fred Hoyle created new objects within Einstein’s General Relativity called C operators which did the job. He is thus credited with inventing the theoretical equipment to make Steady State work. However, his theory gave no indication of what form the created matter would take.
The Steady State universe doubles its matter content in one third of the Hubble time (1/Ho). It expands exponentially as in the DeSitter Universe, and the deceleration parameter is q = - 1. One third the Hubble time is about 4 or 5 billion years, and is indicative of the average age of galaxies in the theory. The Milky Way galaxy is most likely about 12-13.5 billion years old, making it quite out of the ordinary. In the regular big bang universe, most galaxies are the age of the Milky Way, more or less. This was not clear at the time the theory was proposed, however.
A School of whales:
quasars signal doom for continuous creation.
There are two stronger reasons the Steady State Universe has been rejected. First, there are more strong radio sources in the past than in the present. Many of these radio sources are quasars, cores of nuclei of ancient galaxies exploding vast amounts of energy. In fact we see no quasars nearby, but many as we look out in space, and thus back in time. At least some large spiral galaxies’ cores may even evolve from powerful gushers (quasars) in the distant past, through active galaxies (less potent gushers) in the median past, to normal present day spirals (not as bright in the core). The first glimpses of this evolution was discovered in the mid ‘60s, and meant it was time to move on from Steady State Cosmological theories.
Fedallah--the subordinate phantom:
Cosmic Microwave Background
Fedallah, the turbaned assistant of Captain Ahab, came from one of “those insulated, immemorial, unalterable countries, which even in these modern days still preserve much of the ghostly aboriginalness of earth’s primal generations.”
The second reason for the rejection of Steady State theories came in the late ‘60s with the discovery of the Cosmic Microwave Background (CMB) by Penzias and Wilson. They were working on microwave communications at Bell Labs, utilizing a horn-shaped antenna. They noticed they were receiving a mysterious noise, no matter what direction they pointed it.
Thinking it was caused by pigeon droppings, they cleared the horn--to no avail. They soon realized that the wavelength of this radiation corresponded closely to the energy predicted by McKellar and Gamow 20 years earlier as a remnant of the fireball of the Big Bang. They had discovered the cosmic microwave background.
280,000 years after the Big Bang, in most theories, the universe was a soup composed mainly of light, protons, and electrons. Enough space had evolved so that the energy of the light couldn’t keep the electrons from going into ‘orbit’ about the protons. As the electrons fell into orbit, they released ultraviolet photons of a specific energy. The universe expanded, and space with it, increasing the wavelength of the light from ultraviolet to microwaves. Ultraviolet has wavelength of a few billionths of a meter, and microwaves a few centimeters, so this was a substantial stretch. I usually illustrate this in my classes by pulling on the ends of a coat-hanger wire I have bent into a sine wave.
The era that generated the background is called the ‘Recombination Era’ because electrons are recombining with protons. The light radiation released is also sometimes called ‘recombination radiation’.
The CMB is thus one of the great proofs of the Big Bang. The microwave background is difficult to explain in a universe that is never dense enough in the past to prevent electrons and protons from being together. Thus the Steady State Universe requires some special circumstance to explain the background: super-massive stars or masses varying with time, for example.
CMB has so many implications that it really deserves a chapter by itself. It is actually a spread of wavelengths with a peak at a specific wavelength. We call this a Black Body Spectrum because a black body, a star, a hole in an electromagnetic cavity resonator, all give off this characteristic spread of photon energies. A dense cloud of gas in equilibrium with itself produces it, and leaves a clue as to its temperature. Wien’s law tells us that the peak wavelength is related to that temperature. For CMB the corresponding temperature is 2.7 Kelvin above absolute zero--very low indeed.
One of the first things that was done was to identify the shape of the black body curve which would be expected if the radiation was a remnant of the Big Bang. That was done, and remarkably the radiation was coming from all over the sky with very close to the same temperature, betraying a uniformity reminiscent of the primordial gas.
In the early ‘80s, however, George Smoot and his team from UC Berkeley investigated the microwave background with COBE, the Cosmic Background Explorer satellite. They found something even more remarkable. There were small variations of temperature of a few parts in ten thousand, just large enough to be tracers of the original lumpiness of the matter at the Recombination Era. These are just the right size, under the influence of long-term gravity, to become galaxies, clusters of galaxies, and stars. In addition the spread of lump sizes were just those expected in the Inflationary Theory of the quantum generation of the universe. We will have much to say about this later.
The important fact now is that CMB is a nearly indigestible fact for most Steady State Theories, though some, including Philip Peebles, don’t consider it to be a devastating blow to the theory. Cosmic evolution is.
Chapter 4
The Captain of the British Ship and his lost arm: other failed theories
“The White Whale, said the Englishman, pointing his ivory arm toward the east, and taking a rueful sight along it, as if it had been a telescope; “there I saw him on the Line, last season.”
“And he took that arm off didn’t he?”asked Ahab.
How dangerous is Moby Dick? Conflict over The Hubble Constant
There are 10 numbers now reputed by some to be necessary to determine Cosmology. Cosmologists call it the ‘ten parameter’ theory. We have talked about the mass density of the universe, the size of the cosmological constant energy density, Λ, and the current deceleration constant, q0, but the first number we expected to pin down was the Hubble Constant, H0. This is because it can be determined using fairly nearby galaxies.
The Hubble Constant is the slope of the Hubble’s Law plot, the ratio of recession velocity and distance. We get recession velocity from the redshift of a galactic spectrum, so if we can find a galaxy’s distance accurately we get a good value for H0. This tells us how fast the universe is expanding in the present epoch. This is the first approximation for the lower redshift or distance end of the Hubble plot, which is as far as Hubble got. It is of prime importance because it starts our quest for cosmology, being essential for the first approximation of how the universe has expanded. It answers the question: how is the universe expanding now?
If we could get qo, the current deceleration parameter, we would get the second approximation, or how the universe expanded in the moderately recent past. It tells us how the Hubble plot is shaped in moderate redshift regions. However, up until a decade ago there was much dispute over both constants.
Let’s consider H0. Some history is in order, to give us a clear perspective of how difficult the task of determining it is.
Hubble found the distance to the nearby Andromeda galaxy by observing what are called Cepheid Variable stars in that conglomeration. In about 1912, Henrietta Leavitt from Harvard gave us one of our most powerful distance-determining techniques. Cepheid Variables oscillate in brightness over a period of 1 to 50 days, but each star dims and brightens with regularity. Leavitt found that the longer the period of variation the greater the star’s luminosity--power output at the source. From luminosity and apparent brightness at earth (called flux) one can obtain their distance (now called Luminosity distance, dL).
By using other methods to obtain the luminosity of closer Cepheids, she hoped to be able to determine distance to more distant ones. Harlow Shapley did just that. However, his research and that which followed was flawed by the fatal distance factor, because intervening dust was obscuring and lowering the intensity of light from the clusters she used to calibrate these stars. There was also confusion, because Cepheid variable stars in globular clusters turned out to have a different distance scale than those in spiral arms of spiral galaxies.
Up until the late forties, early fifties, it was thought that the time since the Big Bang was much shorter than it is now. This was because the Cepheid variable star scale for luminosity was off by about a factor of 5. Astronomers were using type II Cepheid standards for observing Type I Cepheids. This made the related distances off by about a factor of 3. The main yardstick for close by galaxies was off by that factor, and thus more distant galactic distances were off too, because those distances were based on the nearby measuring technique.
Thus for 20 or 30 years it was thought that the universe was only about 3 billion years old, which was fine because we hadn’t encountered anything older. Then in the early ‘50s, we radioactively dated rocks on the earth at 4.5 billion years old. This ‘time conflict’ was another factor which led Bondi and Gold to their infinite-universal-age Steady State theories. Ordinary Friedmann cosmology wouldn’t allow such antiquity.
More accurate determinations of the Hubble constant were made, implying the universe was also about 5 times larger than once thought–distance scales were up by 5. Alan Sandage, Hubble’s replacement at the Mt. Wilson Observatory, managed this refinement. However, the confidence in the Sandage value of H0 eroded in the 1980's when new determinations of the Hubble Constant emerged which were higher by about 50%. In the mid 1990's the debate heated up with Wendy Friedman and her group using what is thought to be the most accurate method of scaling the universe–Cepheid variables.
Before the Hubble Space Telescope (HST) was fully operational, it was impossible to see Cepheid variable stars in nearby galaxies outside the Local Group. However, HST allowed Wendy and her Harvard-based group to work with Cepheids in the nearby Virgo Cluster of galaxies.
Since Cepheid variables are thought to be accurate to within about 5%, we now have most astronomers settling on a Hubble Constant of about 70 km/s/Megaparsec. This is much larger than Sandage’s stubborn claim of 55. However, cosmologists drifted into the Friedman camp, and later supernova Ia data was closer to Friedman’s value.
Is Moby Dick Immortal? The Age of the Universe In Doubt
“‘Whom call ye Moby Dick?’ ‘A very white, and famous, and most deadly immortal monster...’”
Friedman’s large Hubble Constant makes the age of the universe problematic, if one ignores a cosmological constant. In standard General Relativistic cosmological models, the new H0 means the universe cannot have been much older than 13 billion years, and that’s really stretching it. When Friedman first announced her results, the age was forced under 11 billion years, but under pressure and supposed ‘closer examination’, H0 was given a smaller value--a good thing too, as WMAP Microwave Background measurements in 2003 were announced to give an age of the universe of 13.7 Billion years.
When the 11 billion year age figure was announced, all hell broke loose in the cosmological world. After all, the stars in the globular clusters of the Milky Way were at the very least 12 billion years old, a figure difficult to fudge. Additionally, the oldest galaxy we have found is at minimum 13 billion years, and some suggest there are quasars as old as 14 billion years!! We may still have a problem as we look for older objects. We call this the ‘time problem’ in cosmology.
The time problem was made even worse if one accepted theoretical demands that the density of the universe be as large as the critical value necessary for the Inflationary Scenario of Alan Guth and others. 9 Billion years was incredibly small for those espousing a particle physics-driven early period of exponential expansion. It seemed that the ‘inner space–outer space’ connection--relating particle physics to Cosmology was absurd.
It was at that point that the particle physics cosmologists like Michael Turner from the University of Chicago began to seriously consider the return of Einstein’s ‘greatest blunder’, the cosmological constant. Michael Turner’s lectures had become very popular, with humor and entertaining graphical illustrations, and he became the spokesman for the ‘inner space’ connection. The reemerging cosmological constant was required by observations to be very small. This was still an embarrassment for particle theory. Theorists had calculated that empty space should have an absurdly large cosmological constant or none at all. Nevertheless, they swallowed their pride in the face of necessity.
It’s like the old man who bought a pair of shoes (time scale) too small to fit in a second hand store. He paid half the price of a new pair to get them stretched, and they didn’t fit. He tried getting them stretched a second time, but found he couldn’t even use a new shoehorn to get his feet in them. In desperation he bought a new pair (with cosmological constant), paying double the price he would have if he had bought the new ones in the beginning.
A new cosmological theory was needed. We had outgrown our cosmological ‘shoes’ several times and we still clung to shoes that didn’t fit. The oldest objects we are seeing now are claimed to be products of a just-born universe, but are they? When the cosmological constant is thrown into the mix, the time problem is not as severe. However, it will be humorous to look back on the difficulty in the paradigm shift if we start discovering we need theories with objects 17, 20, or even 25 billion years old.
The Legend Lives On–The Virgo Infall
“‘Avast’ roared Ahab, ... ‘Man the boat! Which way heading?’
‘Good God!’ cried the English captain... ‘What’s the matter? He was heading east, I think–is your captain crazy?’”
The first fairly recent indication of the sighting of the cosmological constant ‘white whale’ was given by two researchers at the University of Hawaii in about 1985. They were investigating the peculiar velocity of the Milky Way relative to the Hubble flow and found that the local group of galaxies was falling into a nearby rich cluster–the Virgo Cluster.
The Virgo galactic cluster has hundreds of galaxies grouped about a supergiant elliptical galaxy called M87, one of the largest galaxies we have seen. Tully and Shaya from Hawaii were able to plot the motion of the Milky Way and found it falling into that massive cluster. Thus to measure the rate of universal expansion using the redshift of galaxies in the Virgo cluster, it was necessary to add the velocity of infall to the recession velocity to get the speed of Hubble expansion.
With the universe thus expanding faster than was thought before, the flat universe needed for inflationary theories required additional complexity to avoid having too little time. Tully and Shaya claimed the necessity for a cosmological constant to resolve the time problem created by a more rapidly expanding universe. The particle cosmologists felt the bite as clearly as if they had lost their left arm to the leviathon.
I recall the reaction of some inflationary theorists was to go into kind of a denial. They ignored the warning sign for a long time, and still went on looking for extra matter–dark matter–to add to visible matter. They needed to have exactly the critical density to make their theories work, and only about a fifth of the matter required had been sighted or inferred gravitationally. Never mind that this was another weakness to the theory.
The theoretical reasons for inflation, however, were impelling, as we will see in the next and following chapters.
Chapter 5
Pip Goes Missing. Missing Matter.
“Pip jumped again,... and was left behind on the sea... Out from the center of the sea, poor Pip turned his crisp, curling, black head to the sun, another lonely castaway...”
‘Where is that black boy?’ Do Galaxies have missing Mass?
The first indication of dark matter in the Milky Way was encountered by the Dutch astronomer Jan Oort. Oort measured velocities of stars that gravity makes bob up and down through the plane of our galaxy’s disk like horses on a carousel. He could not account for their high bobbing speeds without hypothesizing more matter than was seen in stars. He suggested an amount of invisible matter equal to the visible matter. He would later discover the region beyond Pluto where most comets spend most of their time–the famous Oort Cloud, another dark matter conglomeration.
This suggestion was confirmed by observations of galactic rotation. In about 1970, Vera Rubin and W. Kent Ford at the Carnegie Institute were first able to get some data accurately plotting rotational speeds versus distance from the center in the nearby spiral Andromeda galaxy. To Vera’s surprise, the linear velocity spread did not obey Kepler’s laws of planetary motion. This meant that the gravity of the stars they saw was not causing the rotation of galaxy. The velocities remained fairly constant as one observed further and further out from the center, whereas Keplerian motion would have had them tail off, radically departing from what was seen.
To observe the rotation curve of a galaxy, one has to block all but the portion one is observing and find the component of rotational speed in the line of sight from a Doppler redshift or blueshift. If the galaxy is not seen edge-on, a geometric correction must be made to find the actual rotation speed.
A few years later, Vera Rubin collaborated with David Burstein and Bradley Whitmore and observed and analyzed dozens more spirals inclined toward the earth. They all had an anomalous rotational spread similar to Andromeda’s. The conclusion–not seen right away--was that gravity was acting to produce this. The only reasonable way was to have an enormous amount of ‘dark matter’ interspersed throughout the galaxy. Perhaps 1% of the matter needed to produce a flat universe had been seen in stars at that time. Galaxy rotation curves upped the ante substantially, at least in principle.
More than 200 galaxies have been measured since 1978, firmly establishing the necessity for dark matter within them. This is in a proportion of about ten to one, lifting the matter inferred to occupy the universe to about 10% of the critical density. Since then, we have found some of the dark mass necessary, and although some of still eludes our view, only a radical dissenter like Milgrom (in the early ‘80s) claimed that Newton’s laws (equivalent to Kepler’s for orbital motion) are violated for very large masses like galaxies.
In 1973, however, Jeremy Ostriker and Philip Peebles constructed a computer model of the spiral Milky Way, and found that stars could not remain in a disk of matter alone. Some went flying off, and others went into very eccentric orbits. To maintain the spiral disk, they had to model it as being embedded in a much larger spherical ‘halo’ of matter. Observations have somewhat born out the theory, and it is now thought to be five to ten times the diameter of the visible star disk. So it is likely that a nearly equal amount of dark matter resides in the halo, far outside of the dark matter in the disk.
He could be anywhere: Galactic Clusters.
Call him a rebel, or a stubborn individualist, Fritz Zwicky established one of the most memorable careers at Cal Tech. His work led to the understanding of the neutron star. He was a master of crystal and liquid physics. Along with his collaborator, Walter Baade, supernovae were understood as a source of cosmic rays.
He was able to have a special 18 inch wide-field telescope constructed for him at Palomar by which he scanned the skies for supernovae. He boasted that the only two who knew how to use such a small telescope were he and Galileo. In the process, he produced two catalogs of galaxies: one of 30,000 galaxies in the northern hemisphere, and one of active galaxies with bright cores.
He rightfully, however, holds the claim to being the first discoverer of the necessity for dark matter. In the early 1930's he studied the motion of galaxies in the Coma Cluster about 300 million light years away. This rich cluster was found to have its hundreds of members swarming around each other much faster than the masses of its members and Newtonian gravity would indicate. To understand this, one merely has to note that to remain in orbit around a larger planet than the earth requires a higher orbital velocity.
It didn’t take Zwicky long to realize that there was extra matter in that galactic cluster. In a Swiss physics journal he called it ‘dunkle materie’ (dark matter). That was 1933, many decades before Vera Rubin’s encounter with extra matter in spiral galaxies.
Not long after that, Sinclair Smith at Mt. Wilson Observatory applied Zwicky’s techniques and dark matter conclusion to the rich Virgo cluster of galaxies, somewhat closer than Coma. He concluded that there was “a great mass of internebular material within the cluster”.
We now know that if we use Rubin’s masses, including the dark matter internal to galaxies including the halos, it is still necessary to postulate about an equal amount of dark matter between the galaxies, that is, if we wish to rescue Newton’s Laws. This brings the tally of inferred dark matter--at most--to about 20% of the critical density.
Zwicky also paved the way to an independent way of assessing intergalactic dark matter. In 1937, he suggested for the first time that a galaxy might be weighed by noting its effect as a ‘gravitational lens’. Later he made the seemingly outrageous claim, 40 years ahead of the actual observation, that galaxies and large masses could create multiple images or even a ring of images by the gravitational bending of light. This was identically similar to the way General Relativity says light bends around the sun.
Looking at pictures of how light from distant galaxies passes through a large cluster of galaxies, J. Anthony Tyson and his colleagues from Bell Labs were able to map the dark matter in the cluster, Abell 1689. A photograph, taken in the early 90's, shows the distant galaxies as small circular arcs around the center of the cluster. Utilizing this gravitational lensing effect, Tyson was able to map the dark matter in the cluster. All told, then, there is 10-20 times more material acting gravitationally, internal and external to galaxies than exists in stars.
The ocean appears calm. Is the Universe Flat?
Is there more dark matter than the 10-20% of critical mass accounted for? Even considering the missing mass of galaxies and galactic clusters, is it possible that this is not an effect of matter at all?
The argument for even more dark matter is theoretical in the main. As the universe expands, any deviation from flat, Euclidean space-time is magnified by the expansion. The fact that we are at about 20% of critical mass is very close, considering that if we work this backward the universe must have been within 100 trillionth of critical mass away from this critical value in the beginning. Such a finely tuned initial state of the universe is highly improbable. So why not postulate that things were simple–exactly critical density for all time? Or at least a long time after a brief, rapid inflationary period?
The inflationary theory, explained in the next chapter, does just that. It resolves this dilemma, called the ‘flatness problem’, by postulating a nearly eternally flat universe: zero curvature.
In a way, however, without additional arguments, this is much like learning that someone shot a powerful bow and arrow 5 miles. You are able to see the target was hit through powerful binoculars, but not which part of the target. You then conclude that since it’s so unlikely the target was hit, that there must have been a way of aiming the arrow perfectly–that the arrow hit the exact center. This is absurd. In other words, it is more reasonable to conclude that the ‘arrow’ did not hit the center of the target. Similarly, reason suggests that it is possible there is no more than about 30% of critical density in matter, and modern observations confirm that.
Philip Peebles, the Princeton author of the standard book on the evidence–Physical Cosmology--went through earlier phases where he doubted the flatness argument for dark matter. It is however, because of other impelling theoretical arguments that this flatness resolution makes more sense, as we will see in the next chapter.
Pip becomes schizophrenic: many possibilities for dark matter.
When models are computed for the maximum amount of normal matter formed in the Big Bang, theorists can account for about 20% of critical density. This normal matter, sometimes called ‘baryonic matter’ is made up primarily of baryons: protons and neutrons. Electrons make up a negligible portion by mass. Thus normal objects we know and love, which are composed of atoms, could conceivably be all there is. And the majority of it might be hidden. I joke with my students, saying that ‘God put most of the matter in the universe where the sun don’t shine’.
It is usually roughly assumed that when we look for the matter accounting for the gravitational anomalies in galaxies and clusters that we are looking for baryonic matter. However, ‘it ain’t necessarily so’. Some of the baryonic matter may be distributed in realms between the galactic clusters. It is reasonably certain, though, that to justify critical density, we must look for exotic, non-baryonic matter.
Baryonic Dark Matter
Until the cosmic repulsion discovery in 1998, the most conservative among astronomers believed that the only dark matter was to be found internal to galaxies and clusters. Not only did they suggest that it was only in the amount necessary to explain galactic motion, but that all of it was in ordinary, baryonic form.
Think of the many possibilities: dim or obscured galaxies, faint or failed stars, planets and black holes, and interstellar gas and dust. And we keep discovering new forms.
In the late ‘70's, the Einstein X-ray observatory satellite discovered that galactic clusters had globs of x-ray emitting gas in and around them. The Hydrogen gas inhabiting the regions between galaxies and voids between superclusters is visible in the Radio. We also keep seeing more and more stars in galaxies as the light gathering capabilities of our telescopes increase with the area of their apertures and the efficiency of detection technology.
Spiral galactic disks seen before and after increased ability to see look like doughnuts before and after deep frying. There are also dark galaxies, ineffective in producing stars and composed mainly of gas. This decreases the matter needed to explain cluster motions. All of these together, though, make up only a small fraction of the mass needed for galaxies and clusters to be Newtonian.
In addition, IRAS, a 1983 satellite viewing in the infrared, observed gas about newly forming stars. The protoplanetary disks of stars like Vega and Beta Pictoris became visible. These are young stars with pre-planetary dust and rock surrounding them in doughnut-shaped disks. These disks were estimated to be a factor contributing to dark matter for 50% of young stars.
However, we can do a rough calculation. One thousandth of the mass of our solar system is in planets and debris. So that makes one half of one thousandth of a percent of critical mass in planets and protoplanetary disks. That is tiny enough to make dark matter scavenger hunters go stark raving mad.
Speculative forms of dark matter often don’t stand theoretical tests. Cold gas in a halo around galaxies, would have fallen in since the Big Bang, and hot gas would radiate and be seen. Enough dust to make up a goodly amount of dark matter would obscure the stars. So if there is something in the halo surrounding a spiral galaxy (of which there are many, especially early on), it must be in a more condensed form.
The most likely candidate for this condensed matter up until the year 2000 was MACHOS (massive compact halo objects).
In the formation of stars it is reasonable some clumps of matter will not have sufficient gravity to have the 0.08 solar masses necessary to kindle nuclear fusion at 10 million Kelvin degrees. We know now that gas clouds come in all sizes, and like watery dough dropped into rapidly boiling oil, they break up into a spectrum of sizes. It is reasonable to assume that some gas lumps will not quite be large enough to kindle Hydrogen burning. These failed stars may exist in an abundance comparable to ordinary stars. However, since their mass is much smaller than the average star, we cannot hope to make up a substantial fraction of the missing mass in the disk or even core of a galaxy.
Nevertheless, halo matter is probably much more sparse, and some astronomers say that failed stars called brown dwarfs exist in the halo in the trillions and thus could make up as much as half of the missing matter in galaxies. This hope is fading somewhat, however, as the search for brown dwarfs progresses. Several such objects have been found. Gliesse 229B, for example, is 30-55 times the mass of Jupiter, has a surface temperature of 1200 K, and its luminosity is six millionths that of the sun. First viewed at Palomar, this object has no metal spectral lines.
The brown dwarf search also goes on, utilizing the gravitational lens effect. When a brown dwarf passes in front of a more distant star it acts like a magnifying glass focusing that sun and makes the star behind appear much brighter. The duration of the lensing event might give us the mass of the MACHO. They act on one star in a million a year, and the bright stars in the halo are very sparse to begin with.
However, estimates from the number of lensing events seen in a year indicate that brown dwarfs are not living up to early expectations. There are probably much less than a trillion in the Milky Way.
And the conclusion of Katherine Freese from the University of Michigan even indicate severe doubts in the lensing observations. Such stars would have to have the signature of large of mass loss, heavy elements and infrared radiation. None of these have been seen. Besides, a large amount of baryons would not be consistent with our present understanding of elements formed in the Big Bang. She concludes “It’s looking very likely that 50-90 percent of our galaxy is non-baryonic.”
We come to a rankling conclusion: that baryonic matter doesn’t even explain the non-Keplerian rotation curves of spiral galaxies. In addition, baryonic matter is even more sparse between galaxies, and thus we are even further away from explaining the ‘Zwicky anomaly’--galaxies zipping around in clusters like they were a swarm of hornets.
I was once stung by such an angry swarm of these creatures over a dozen times on the top of my head. I won’t forget it. In a way, gravitational astrophysics has been stung by the missing matter hypothesis. It is sad for observational astronomers to have to rely on theorists for explanations, but that is apparently what must be done, at least for now.
When I explain the above paucity of baryonic matter in galaxies, my students invariably come back with what they think is a solution: ‘What about black holes, Dr. Petersen?” I sadly have to tell them that stars with three solar masses left after losing a 30-90% of their mass in supergiant phases are very rare. They are the exception, not the rule. “What about the supermassive black holes in the centers of galaxies?” they might retort. I would have to tell them that if they made up a substantial portion, the stars in and near the core would be moving much, much faster than we observe. And what of the tell-tale traces of mini-black holes left over from the Big Bang? They have never been observed. After all, Stephen Hawking has pointed out that the smaller a black hole is the faster it evaporates. Evaporation in a puff of black body radiation of high temperature would be seen in the x-ray, and it hasn’t.
Non-Baryonic Matter and Other Possibilities.
I used to tell my students, somewhat tongue-in-cheek, that the search for dark