Chapter 4: Critical Energy Density
Why is there a universe? Why does it exist? Why has it arisen? Why does it not collapse under its own weight? Why does it not fly apart in a huge chaotic explosion? Why has it always expanded at just the right speed, so that the galaxies, with their stars and planets, were able to arise? And why has also our planet Earth arisen, as the beautiful home of mankind? - Physicists around the world are trying to solve now this mystery. What have they found out?
Michael Riordan is working at the Stanford Linear Accelerator Center. And David N. Schramm is a renowned theoretical astrophysicist, Professor of Physics at the University of Chicago. What have they found out now about the universe and its origin? They report in their book The Shadows of Creation (1990:19-23):
"The temperature of the Universe 1 second into its evolution was about 10 billion degrees (or 1010°K, in scientific notation), which is the temperature at which atomic nuclei disintegrate. This is about a thousand times hotter than the core of the sun, and a million times hotter than its surface. The density of the universe - the total amount of matter and energy packed into a given unit volume - at that moment was about 10 kilograms per cubic centimeter. For comparison, water has a density of 1 gram (a thousandth of a kilogram), and lead about 10 grams, per cubic centimeter. Thus, the Universe at an age of 1 second was about a thousand times denser than lead. A chunk of it about the size of a tennis ball would have weighed as much as an automobile. ...
"The visible Universe today has a temperature of 3°K and an average density of about a hundred billionth of a trillionth of a trillionth of a gram per cubic centimeter (10-31 g/cm³). An earth-sized balloon full of this stuff would weigh less than a flea! Most of this matter is concentrated in lumps where the density is extremely high, relative to the universal average - in galaxies, stars, and planets. In between them are vast expanses of the most perfect vacuum imaginable, with hardly a single, solitary atom inhabiting every cubic meter.
"The boundary line between these two scenarios, the Big Crunch and the Big Chill, is marked by what cosmologists call the ‘critical density’. This is the average density of matter, needed, about a 5 millionths of the trillionth of a trillionth of a gram per cubic centimeter (or 5 x 10-30 g/cm³), to arrest the expansion of the Universe but never quite turn it around. This is very little matter - about one hydrogen atom in every 10 cubic meters. ... If the average density of the Universe today is greater than this critical value, then gravity is strong enough to force the Big Crunch. If it is less than or equal to the critical density, we get the Big Chill.
"Cosmologists use an important parameter, called ‘omega,’ the last letter of the Greek alphabet, to describe the density of the Universe. Omega is the ratio of the actual density to the critical value. If it turns out to be greater than 1, the Universe will eventually end in the Big Crunch; if it is less than or equal to 1, we get the Big Chill. In the special case where omega equals 1 exactly, we say the Universe is a ‘critical’ universe. The value of omega determines the fate of the Universe.
"Between the open and the closed universes there is a universe with omega equal to 1 - a universe having exactly the critical density. ... Such a flat universe, with omega exactly equal to 1, seems necessary if we wish to understand how it has managed to continue expanding for billions of years without yet reaching a Big Crunch or Big Chill. And if Alan Guth’s inflation scenario is correct, omega must equal 1 exactly." - Riordan and Schramm (1990:25, 27).
Upper and Lower Limit
What is the upper and the lower limit of the energy density of the Universe?
Riordan and Schramm: "Using the observed present-day abundance of deuterium, which is about 20 parts per million, astrophysicists therefore established an upper limit on the density of matter in the Universe today. It must be smaller than 5 x 10-31 grams per cubic centimeter. Any greater , and there would be less deuterium remaining today than actually found.
"By contrast with deuterium, nuclei of helium-3 are created in stars, not destroyed. Therefore, its present abundance in the interstellar medium - also around 20 parts per million - represents at least the amount of primordial helium-3 that was created in the Big Bang. Stellar processes can only have increased the total. This observation allowed a group of astrophysicists to establish a lower limit on the density of matter in the Universe. It must be greater than 2 x 10-31 grams per cubic centimeter. Any lower, and there would be more helium-3 around than we witness today.
"What is truly remarkable about these two independent limits - based on the abundances of deuterium and helium-3 - was the fact that, taken together, they permitted only a narrow range of possible densities. These limits tightly constrained the density of the Universe during the era of nucleosynthesis. So by straightforward extrapolation, we can conclude that the average density of matter in the Universe is no more than 10 percent of the critical density.
"These density limits have been gradually refined over the past decade, getting tighter and more convincing almost every year. During the early 1980s, measurements of the lithium-7 abundance in old stars (less than a part per billion) became accurate enough to confirm the conclusions reached earlier using deuterium and helium-3. The amount of lithium-7 that could have been produced in the Big Bang was consistent with these observations, if and only if the density of the Universe fell into the same narrow range as the one discussed above." (1990:81-83).
Cosmic Background Radiation
The cosmic background radiation is closely connected with the critical energy density of the universe, with its changing energy density, and its expanding speed. - How warm is this cosmic background radiation now?
Riordan and Schramm report: "Recent very accurate measurements by the Cosmic Background Explorer (or COBE) satellite have determined this temperature to be 2.735°K. The exact temperature is determined from the position and shape of the microwave spectrum; a lower temperature means the spectrum peaks at longer wavelengths or lower frequencies. ... In all likelihood, the smooth background radiation witnessed today means that matter was spread out very uniformly at the time it decoupled from radiation 15 billion years ago. Any ripples in this vast ocean must have been extremely small then - assuming, of course, that they were adiabatic fluctuations, in which matter and radiation traced one another.
"Because the average temperature is about 3°K today and was 3000°K at the moment of decoupling, this means a density enhancement can have grown by only a factor of 1000, at the very utmost, during this linear growth period." (1990:122-130).
Cosmic Inflation
The denser the energy of the universe, the faster it must expand. How fast was the universe expanding, when it was young, when it was born?
Riordan and Schramm: "Although the Universe today appears extremely lumpy, with visible structures stretching across millions of light-years, it clearly began as an extremely smooth and homogeneous medium. The nearly perfect uniformity of the cosmic microwave radiation testifies to this inescapable fact. Much the same uniformity is seen today if we look only at the very largest distance scales - in the billions of light-years. ... It is natural therefore to wonder how the Universe ever became so smooth in the first place. Did it simply begin that way, or was there some sort of process that generated the overall uniformity from a state of primordial chaos?
"Cosmological inflation is an extraordinary vigorous growth spurt that may have occurred in the first split second of existence - during the GUTs epoch, which would have ended about 10-34 second. Such a stupendous explosion would have been far, far, faster, than the more leisurely Big Bang explosion, whose efforts we can still see today in the redshifts of galaxies.
"In addition to solving several key cosmological problems in one grand sweep, inflation has another extremely important consequence. It requires that our Universe be an open universe with exactly the critical density - that is, with omega = 1. No other value of this parameter, which we discussed at length ... is possible if inflation occurred.
"The cosmic background radiation seems to be absolutely uniform, as best we can determine, coming with equal intensity from all directions and revealing the same effective temperature no matter where we look. The more one ponders the fact of this uniformity, the more unsettling it becomes. Remember that this radiation was emitted (or perhaps ‘released’ is a better word) about15 billion years ago, when the universe was about 100,000 years old. The photons arriving now from two opposite directions, say north and south, began their long journey to our radio antennas in two regions of the universe that today are almost 30 billion light-years apart due to the Hubble expansion.
"Because the Universe is only 15 billion years old, there is absolutely no possibility these two regions could have transmitted any kind of signal from one to the other. Information cannot travel faster than the speed of light. Scientists say that such regions are ‘causally disconnected.’ What occurs in one should be completely independent of what is happening in the other. In fact, the cosmic background radiation coming from any two points in the sky separated by a few degrees or more must have originated in two such distinct, causally disconnected regions. Light could never have traveled from one region to the other in the 15 or so billion years since the Big Bang. So how could they possibly have obtained enough information about one another to be at almost exactly the same temperature - to better than 1 part in 10,000?
"When we think about the matter further, the mystery deepens. When this relict radiation was first emitted, the Universe was far more compact. The amount of mass within a given horizon (the distance light can travel since time began) was then but a tiny fraction of what it is today. The horizon distance was only about 100,000 light-years instead of 15 billion. When the photons reaching two antennas today from two opposite directions were emitted, however, they must have originated at two points separated by10 million light-years - almost 100 times as far as information could have traveled by that moment.
"Our problem is to understand how any two such causally disconnected regions can possibly have one and the same temperature. Cosmologists have traditionally just assumed an arbitrary initial condition: the Universe simply began smooth. Such a glib answer, however, merely begs the questions: How did this almost perfect smoothness arise in the first place? ... A related mystery is the origin of structure. Although the Universe is extraordinarily smooth at the largest distances, at smaller scales it is extremely bumpy. Most of this visible matter is found compressed into tiny pockets of great density - galaxies, stars, and planets - relative to the universal average. How did this graininess arise?" - Riordan and Schramm (1990:154-157).
"Only in the very special case where omega is exactly equal to 1 does this parameter remain unchanged forever. Here the actual and critical densities are exactly matched, so they continue to evolve at exactly the same rate. In a critical-density universe, in other words, omega must always be 1.00000000000... If, for any imaginable reason, it was nudged higher by the slightest, tiniest amount, omega would grow to infinity as the Universe subsequently collapsed. If it ever fell below 1, it would eventually drop to zero. The only way omega can be 1 forever is to equal 1 exactly.
"In the very early Universe, when it emerged from a spacetime foam with an absolutely stupendous density, the dynamical time was exceedingly brief - 10-43 second (or less than one-millionth of a trillionth of a trillionth of a second). At that very instant, the density (and omega) was changing extremely rapidly, taking only 10-43 second to fall by a factor of 3. Even by the end of the GUTs epoch a bit later, the moment of matter creation, such a change would have taken only 10-34 second. By the end of nucleosynthesis, where we have the abundance of light elements to verify our understanding of this evolution, omega was changing on a timescale measured in seconds.
"In its earliest stages, therefore, the Universe was evolving extremely rapidly. Had it ever been slightly greater than or less than 1 at any moment of those times, omega would have zoomed to infinity or plummeted to zero in a fraction of an eyeblinck. Only in the special case where omega equaled 1 exactly could it have ever remained constant and not have changed with time. Unity, it seems, is a very unstable equilibrium point. Go even the slightest bit off 1, and omega rises or falls with absolutely blinding speed.
"As mentioned above, the Universe is about 15 billion years old, which is over 60 orders of magnitude greater than 10-43 second. If the Universe had emerged from the space-time foam with omega differing from 1 by even the tiniest amount, say in the sixtieth decimal place, this parameter would have evolved significantly by now and be well on its way to zero or infinity. At present, although we cannot say for sure that omega = 1 exactly, we do know that it is greater than 0.1 and less than 3 - or within an order of magnitude of 1. To be so close today, omega must have been extremely near 1 during the earliest instant (at 10-43 second). Any possible difference had to be near the sixtieth decimal place or beyond.
"How did such a fine tuning of omega, to an initial value so extraordinarily close to 1, ever occur? Or, equivalently, how did the Universe become so incredibly old, without ever having evolved to an infinite or zero density? This mystery is known to cosmologists as the ‘age problem.’ And as omega = 1 corresponds to a Universe in which a flat, Euclidean geometry is the norm, it is also referred to as the ‘flatness problem.’" - Riordan and Schramm (1990:159-161).
High Energy Density - Fast Expansion
The denser the energy of the universe, the faster it is expanding, inflating the volume of the Universe. - Why?
Riordan and Schramm: "To understand how this revolutionary process of inflation works, remember that the expansion rate of the Universe is determined by its total energy density -the sum of matter and radiation per unit volume - at any instant. The greater the energy density, the faster the Universe will expand. Because the early Universe was extremely hot and dense, almost beyond our comprehension, it was expanding extremely rapidly. But as time elapsed and this expansion continued, as more space was added to the Universe but no more matter or radiation, the energy density necessarily dropped, and with it the rate of expansion. The existing energy total had to be distributed throughout the ever-growing volume, lowering the universal energy density and slowing the overall outrush." (1990:163, 164).
Why do the electromagnetic waves of the cosmic background radiation coming from different directions, all have the same temperature of about 2.735°K? How can that be, since they are some 15 billion years old?
Riordan and Schramm: "The smoothness of the observable Universe is no such a perplexing mystery anymore because the region from which it originated (before 10-34 second) was a very, very tiny realm where everything was completely in touch with everything else. In fact, it was less than 10-34 light-second (or about 10-24 centimeter) across before inflation, the distance light travels in 10-34 second. That’s about a trillionth the diameter of a proton! During the inflation that tiny region swelled tremendously, to a domain at least the size of a grapefruit and perhaps even more than a billion billion kilometers across. All the matter we can see in the Universe today had to originate inside such a tiny region, where everything would have been in thermal equilibrium before inflation." (1990)
Cosmic Order: Decreasing and Increasing
The order of the universe is steadily decreasing, while at the same time it is increasing. How is that possible? How does that fit together?
Physicist Wolfram Knapp reports about this in the German scientific journal bild der wissenschaft 9/1992 pp. 64, 65: "For the more or less even distribution of energy in thermodynamics, physicists have coined the term entropy. The more even, that is, the ‘less ordered’ energy is, when distributed in a room, the larger will be its entropy. When left to itself, each system will strive toward its most probable state: the even distribution, toward the highest state of entropy. The temperature in a closed room will be after a while evened out... A basic law of thermodynamics says that the total entropy of the world is slowly, but steadily increasing, and that its order is decreasing - it becomes more and more monotonous.
"Contrary to thermodynamics, the material order in the world is not being forced, to strive toward a greater disorder. The gases in a huge cloud in space are never completely evenly distributed. As soon, as somewhere even only a tiny higher density appears, it will not adapt itself anymore to its environment: At this place, gravity has become stronger and is drawing still more gas toward itself. So the density differences are increasing. Gravitation is the motor, which causes matter in the world to strive toward a higher order."
How dense is the universe as a whole? And what is the critical energy density of the universe?
Wolfram Knapp: "The mean density of the universe can easily be estimated, by searching for all the different forms of matter, namely all the shining stars and gas-clouds, all dark fogs, dark bodies and dust-clouds. So we get a density of 10-30 gram per cubic centimeter, that is, one proton per cubic centimeter. But that is by at least the factor of 10 too little, so that the universe will have a strong enough force of attraction: It is not expanding forever, but will sooner or later stop and then collapse again into itself. The density of 10-29 grams per cubic centimeter is the critical size, which determines, whether the universe is open or closed." (1992:65).
Critical Energy Density
How large is the critical energy density of the universe? What is its numerical value? What have other physicists found out about this?
Prof. Hugh D. Young reports in his Physics-textbook about the critical density of the universe: "We’ve mentioned that the law of gravitation isn’t consistent with a static universe. We need to look at the role of gravity in an expanding universe. Gravitational attractions should slow the initial expansion, but by how much? If they are strong enough, the universe should expand more and more slowly, eventually stop... Whether the universe continues to expand indefinitely depends on the average density of matter. If matter is relatively dense, there is a lot of gravitational attraction to slow and eventually stop the expansion and make the universe contract again. If not, the expansion continues indefinitely. ... This is the critical density = 5.8 x 10-27 kg/m³. The mass of a hydrogen atom is 1.67 x 10-27 kg. So this corresponds to about three hydrogen atoms per cubic meter." - Young, H. D. (1992:1310, 1311).
Result
According to new findings, the critical energy density of the universe is now about 2∙10-29 g/cm³. The present-day abundance of deuterium can only have arisen during the era of nucleosynthesis (when the universe was 1 second old), when the energy density of the universe was smaller than 5∙10-31 g/cm³. And helium-3 can only have been made in its present abundance, when the energy density of the universe was larger than 2∙10-31 g/cm³. This allows only a narrow range of possible densities during the era of nucleosynthesis. Also the synthesis of lithium-7 falls into this narrow range (Riordan and Schramm). In other words: The present amount of lithium-7 can only have been made during the "Big Bang", if the energy density of the universe then lay between 5∙10-31 and 2∙10-31 g/cm³.
But during the "Big Bang", at Planck-time, when the universe was 10-43 s old, the energy density of the universe was much larger. So, how can the energy density of the universe then always have been just as large as its critical energy density? That does not fit at all together. There must be something seriously wrong in this whole line of reasoning. We shall find out more about this later on. The critical energy density of the universe, with its fundamental constants, contains information and high mathematics, existing independently of mankind. Information, code, and mathematics always come from an intelligent person. They cannot evolve by themselves, because they are spiritual, non-material.