Cosmology: The Science of the Universe

Francesco Longo

A brief introduction of the recent scientific developments of satellite web site. Some personal consideration are added at the end of the presentation.

1. INTRODUCTION

Cosmology is the scientific study of the large scale properties of the Universe as a whole. It endeavors to use the scientific method to understand the origin, evolution and ultimate fate of the entire Universe. Like any field of science, cosmology involves the formation of theories or hypotheses about the universe which make specific predictions for phenomena that can be tested with observations. Depending on the outcome of the observations, the theories will need to be abandoned, revised or extended to accommodate the data. The prevailing theory about the origin and evolution of our Universe is the so-called Big Bang theory discussed below. This primer in cosmological concepts is organized as follows. The main concepts of the Big Bang theory are introduced in the first section. The second section discusses the classic tests of the Big Bang theory that make it so compelling as an apparently valid description of our universe. The third section discusses observations that highlight limitations of the Big Bang theory and point to a more detailed model of cosmology than the Big Bang theory alone provides. The final section discusses what constraints we can place on the nature of our universe based on current data.

2. BIG BANG COSMOLOGY

The Big Bang Model is a broadly accepted theory for the origin and evolution of our universe. It postulates that 12 to 14 billion years ago, the portion of the universe we can see today was only a few millimeters across. It has since expanded from this hot dense state into the vast and much cooler cosmos we currently inhabit. We can see remnants of this hot dense matter as the now very cold cosmic microwave background radiation which still pervades the universe and is visible to microwave detectors as a uniform glow across the entire sky.

a. Foundations of the Big Bang Model

The Big Bang Model rests on two theoretical pillars: General Relativity and the Cosmological Principle.
The first key idea dates to 1916 when Einstein developed his General Theory of Relativity which he proposed as a new theory of gravity. His theory generalizes Isaac Newton’s original theory of gravity, c. 1680, in that it is supposed to be valid for bodies in motion as well as bodies at rest. Newton’s gravity is only valid for bodies at rest or moving very slowly compared to the speed of light (usually not too restrictive an assumption!). A key concept of General Relativity is that gravity is no longer described by a gravitational “field” but rather it is supposed to be a distortion of space and time itself. Physicist John Wheeler put it well when he said “Matter tells space how to curve, and space tells matter how to move.” Originally, the theory was able to account for peculiarities in the orbit of Mercury and the bending of light by the Sun, both unexplained in Isaac Newton’s theory of gravity. In recent years, the theory has passed a series of rigorous tests.
After the introduction of General Relativity a number of scientists, including Einstein, tried to apply the new gravitational dynamics to the universe as a whole. At the time this required an assumption about how the matter in the universe was distributed. The simplest assumption to make is that if you viewed the contents of the universe with sufficiently poor vision, it would appear roughly the same everywhere and in every direction. That is, the matter in the universe is homogeneous and isotropic when averaged over very large scales. This is called the Cosmological Principle. This assumption is being tested continuously as we actually observe the distribution of galaxies on ever larger scales. In addition the cosmic microwave background radiation, the remnant heat from the Big Bang, has a temperature which is highly uniform over the entire sky. This fact strongly supports the notion that the gas which emitted this radiation long ago was very uniformly distributed.
These two ideas form the entire theoretical basis for Big Bang cosmology and lead to very specific predictions for observable properties of the universe.

b. Concepts of the Big Bang theory

The Big Bang theory makes definite predictions for the structure and evolution of the universe that depend on the nature and amount of matter in the universe.
By assuming that the matter in the universe is distributed uniformly on the largest scales, one can use General Relativity to compute the corresponding gravitational effects of that matter. Since gravity is a property of space-time in General Relativity, this is equivalent to computing the dynamics of space-time itself. Given the assumption that the matter in the universe is homogeneous and isotropic it can be shown that the corresponding distortion of space-time (due to the gravitational effects of this matter) can only have one of three forms. It can be “positively” curved like the surface of a ball and finite in extent; it can be “negatively” curved like a saddle and infinite in extent; or it can be “flat” and infinite in extent – our “ordinary” conception of space.
Matter plays a central role in cosmology. It turns out that the average density of matter uniquely determines the geometry of the universe (up to the limitations noted above). If the density of matter is less than the so- called critical density, the universe is open and infinite. If the density is greater than the critical density the universe is closed and finite. If the density just equals the critical density, the universe is flat, but still presumably infinite. The value of the critical density is very small. One of the key scientific questions in cosmology today is: what is the average density of matter in our universe? While the answer is not yet known for certain, it appears to be tantalizingly close to the critical density.
Given a law of gravity and an assumption about how the matter is distributed, the next step is to work out the dynamics of the universe – how space and the matter in it evolves with time. The details depend on some further information about the matter in the universe, namely its density (mass per unit volume) and its pressure (force it exerts per unit area), but the generic picture that emerges is that the universe started from a very small volume with an initial expansion rate. For the most part this rate of expansion has been slowing down (decelerating) ever since due to the gravitational pull of the matter on itself. A key question for the fate of the universe is whether or not the pull of gravity is strong enough to ultimately reverse the expansion and cause the universe to collapse back on itself. In fact, recent observations have raised the possibility that the expansion of the universe might in fact be speeding up (accelerating), raising the possibility that the evolution of the universe is now dominated by a bizarre form of matter which has a negative pressure. As noted above, the geometry and evolution of the universe are determined by the fractional contribution of various types of matter. Since both energy density and pressure contribute to the strength of gravity in General Relativity, cosmologists classify types of matter by its “equation of state” the relationship between its pressure and energy density. The basic classification scheme is:
* Radiation: composed of massless or nearly massless particles that move at the speed of light. Known examples include photons (light) and neutrinos. This form of matter is characterized by having a large positive pressure.
* Baryonic matter: this is “ordinary matter” composed primarily of protons, neutrons and electrons. This form of matter has essentially no pressure of cosmological importance.
* Dark matter: this generally refers to “exotic” non-baryonic matter that interacts only weakly with ordinary matter. While no such matter has ever been directly observed in the laboratory, its existence has long been suspected for reasons discussed in a subsequent page. This form of matter also has no cosmologically significant pressure.
* Dark energy: this is a truly bizarre form of matter, or perhaps a property of the vacuum itself, that is characterized by a large, negative pressure. This is the only form of matter that can cause the expansion of the universe to accelerate, or speed up.
One of the central challenges in cosmology today is to determine the relative and total densities (energy per unit volume) in each of these forms of matter, since this is essential to understanding the evolution and ultimate fate of our universe.

3. OBSERVATIONAL TESTS OF THE BIG BANG THEORY

a. Expansion of the universe

The Big Bang model was a natural outcome of Einstein’s General Relativity as applied to a homogeneous universe. However, in 1917, the idea that the universe was expanding was thought to be absurd. So Einstein invented the cosmological constant as a term in his General Relativity theory that allowed for a static universe. In 1929, Edwin Hubble announced that his observations of galaxies outside our own Milky Way showed that they were systematically moving away from us with a speed that was proportional to their distance from us. The more distant the galaxy, the faster it was receding from us. The universe was expanding after all, just as General Relativity originally predicted! Hubble observed that the light from a given galaxy was shifted further toward the red end of the light spectrum the further that galaxy was from our galaxy.

b. Abundance of the light elements H, He, Li

The term nucleosynthesis refers to the formation of heavier elements, atomic nuclei with many protons and neutrons, from the fusion of lighter elements. The Big Bang theory predicts that the early universe was a very hot place. One second after the Big Bang, the temperature of the universe was roughly 10 billion degrees and was filled with a sea of neutrons, protons, electrons, anti-electrons (positrons), photons and neutrinos. As the universe cooled, the neutrons either decayed into protons and electrons or combined with protons to make deuterium (an isotope of hydrogen). During the first three minutes of the universe, most of the deuterium combined to make helium. Trace amounts of lithium were also produced at this time. This process of light element formation in the early universe is called Big Bang nucleosynthesis (BBN).
The predicted abundance of deuterium, helium and lithium depends on the density of ordinary matter in the early universe. These results indicate that the yield of helium is relatively insensitive to the abundance of ordinary matter, above a certain threshold. We generically expect about 24% of the ordinary matter in the universe to be helium produced in the Big Bang. This is in very good agreement with observations and is another major triumph for the Big Bang theory.

c. The cosmic microwave background (CMB) radiation

The early universe should have been very hot. The cosmic microwave background radiation is the remnant heat leftover from the Big Bang. The Big Bang theory predicts that the early universe was a very hot place and that as it expands, the gas within it cools. Thus the universe should be filled with radiation that is literally the remnant heat left over from the Big Bang, called the Cosmic Microwave Background radiation, or CMB. The existence of the CMB radiation was first predicted by George Gamow in 1948, and by Ralph Alpher and Robert Herman in 1950. It was first observed inadvertently in 1965 by Arno Penzias and Robert Wilson at the Bell Telephone Laboratories in Murray Hill, New Jersey. The radiation was acting as a source of excess noise in a radio receiver they were building. Penzias and Wilson shared the 1978 Nobel prize in physics for their discovery.
Today, the CMB radiation is very cold, only 2.725 degrees above absolute zero, thus this radiation shines primarily in the microwave portion of the electromagnetic spectrum, and is invisible to the naked eye. However, it fills the universe and can be detected everywhere we look. Since light travels at a finite speed, astronomers observing distant objects are looking into the past. The CMB radiation was emitted only a few hundred thousand years after the Big Bang, long before stars or galaxies ever existed. Thus, by studying the detailed physical properties of the radiation, we can learn about conditions in the universe on very large scales, since the radiation we see today has traveled over such a large distance, and at very early times.

4. SOME QUESTIONS TO THE BIG BANG THEORY

a. Structure in the universe

The Big Bang theory makes no attempt to explain how structures like stars and galaxies came to exist in the universe.
Astronomers observe considerable structure in the universe, from stars to galaxies to clusters and superclusters of galaxies. How did these structures form? The Big Bang theory is widely considered to be a successful theory of cosmology, but the theory is incomplete. It does not account for the needed fluctuations to produce the structure we see. Most cosmologists believe that the galaxies that we observe today grew from the gravitational pull of small fluctuations in the nearly-uniform density of the early universe.

b. Fluctuations in the cosmic microwave background (CMB) radiation

The temperature of the CMB is observed to vary slightly across the sky. What produced these fluctuations and how do they relate to stars and galaxies?
The cosmic microwave background is the afterglow radiation left over from the hot Big Bang. Its temperature is extremely uniform all over the sky. However, tiny temperature variations or fluctuations (at the part per million level) can offer great insight into the origin, evolution, and content of the universe.
These cosmic microwave temperature fluctuations are believed to trace fluctuations in the density of matter in the early universe, as they were imprinted shortly after the Big Bang. This being the case, they reveal a great deal about the early universe and the origin of galaxies and large scale structure in the universe.

c. The accelerating universe

Rather than slowing down, the expansion of our universe appears to be speeding up! One possible source of this acceleration is a form of energy called the “cosmological constant”, or a variant of it called “quintessence”.
Einstein first proposed the cosmological constant (not to be confused with the Hubble Constant) usually symbolized by the greek letter “lambda” (l), as a mathematical fix to the theory of general relativity. In its simplest form, general relativity predicted that the universe must either expand or contract. Einstein thought the universe was static, so he added this new term to stop the expansion. Friedmann, a Russian
mathematician, realized that this was an unstable fix, like balancing a pencil on its point, and proposed an expanding universe model, now called the Big Bang theory. When Hubble’s study of nearby galaxies showed that the universe was in fact expanding, Einstein regretted modifying his elegant theory and viewed the cosmological constant term as his “greatest mistake”.
Very recently it has become practical for astronomers to observe very bright rare stars called supernova in an effort to measure how much the universal expansion has slowed over the last few billion years.
Surprisingly, the results of these observations indicate that the universal expansion is speeding up, or accelerating! While these results should be considered preliminary, they raise the possibility that the universe contains a bizarre form of matter or energy that is, in effect, gravitationally repulsive. The cosmological constant is an example of this type of energy. Much work remains to elucidate this mystery!

5. SOME PERSONAL CONSIDERATIONS

The possibility to investigate the entire Universe, once reserved only to philosophy and theology, since almost 80 years became a real scientific question. An hypothesis on it written with the mathematical language, the General Relativity of Einstein and the possibility of an expanding or a static universe was verified them with the scientific methodology by means of the Hubble’s observations of the receding galaxies. From these first scientific results on the structure of the Universe, the cosmologists, both from the astrophysical and the particle physics community, have done more. Now Cosmology is one of the most promising branches of theoretical and experimental physics. Some questions that are often raised in this field are however according to mine personal view more philosophical than physical. Most of these questions are outside the scope of this short review. But just for completeness, the question of the fluctuations of the CMB is often explained as quantum mechanical perturbations of the primordial Universe. This is a sentence that in principle could be verified and tested by physical techniques. The quantum mechanical description of the primordial Universe, which at the present stage is outside the actual description of physical laws, however for some theorists should postulate the existence of Multiple Universes, each of them with a different choice of physical laws and constants. This sentence is outside the present, and probably forever, possibilities of a scientific verification. For the same question another solution is possible: Affirm that the Universe is contingent, that is that it does not contain in itself the explanation for his existence, a purely philosophical affirmation surely, but an explanation that does not require an infinite multiplication of Universe but a First Cause that provide the existence for the Universe as it is. And even though there could be infinite universes, why this one in which we live is so beautiful? Why is so well tuned to the Human Being? Are we here only by chance? These questions are surely philosophical! To the philosophers the last word…

E-mail:
francesco.longo@ts.infn.it
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