The Big Bang Theory

What has become known as the Big Bang theory originally was an attempt by George Gamow and his coworkers to explain the chemical elements in the universe. In this, the theory was incorrect because elements actually are synthesized in the interiors of stars, but the theory is still successful in explaining many other observed cosmological phenomena. Using the same physical principles for understanding stars, the theory does account for the evolution of the universe after a time of about 30 seconds. Those aspects that the Big Bang theory was developed to address are Olbers' Paradox, the Hubble Relation, the 3 K black body radiation and its present ratio of 10 9 photons for each nucleon, the apparent large‐scale uniformity and homogeneity of the universe, the primordial helium‐to‐hydrogen ratio (even the oldest stars are about 25 percent helium, thus helium must have a prestellar origin), and the existence of clusters of galaxies and individual galaxies (that is, the small‐scale variations in the mass distribution of today's universe).

Cosmological Principle

Two explicit assumptions are made in the Big Bang cosmological model. The first is that the observed shift of features in galaxy spectra to redder wavelengths at greater distances is really due to a motion away from us and not to some other cosmological effect. This is equivalent to saying the redshifts are Doppler shifts and the universe is expanding. The second assumption is a basic principle that the universe looks the same from all observing points. This Cosmological Principle is equivalent to saying the universe is homogeneous (the same everywhere) and isotropic (the same in all directions). This is the ultimate Copernican Principle that the Earth, Sun, and Milky Way Galaxy are not in a special place in the universe.

According to the Big Bang Cosmology, the universe “originated” at infinite temperature and density (not necessarily true, because the conventional rules of physics do not apply to the exceedingly high temperatures and densities at a time before 30 seconds, which was in a state that scientists are only now beginning to understand). Coming out of this early unknown era, the universe was expanding with both temperature and density decreasing. Initially the radiation density exceeded matter density (energy and mass have an equivalency given by E = mc 2), thus the physics of radiation governed the expansion.

For matter, the density relationship with respect to any measure of the size of the universe r is straightforward. Volume increases as length 3 = r 3. A fixed mass within an expanding volume thus has a density ρ = mass/volume, hence proportional to 1/r 3. For electromagnetic radiation, the density of a fixed number of photons in a given volume changes in the same way that mass changes, or photon number density is proportional to 1/r 3. But a second factor must be introduced. The energy E of each photon depends inversely on its wavelength λ. As the universe expands, the wavelengths increase also, λ ∝ r; hence the energy of each photon actually decreases as E ∝ 1/r (this is a consequence of the Hubble Law: a photon moves at the speed of light, hence any photon is observed as having come from a distance and is subjected to a redshift). The evolution of the energy density therefore requires both factors; energy density ρ ≈ (1/r 3)(1/r) = 1/r 4, so it decreases faster than mass density with its 1/r 3 dependence. At some time in the history of the universe, the density of the radiation dropped below the density of the real mass (see Figure ). When this occurred, the gravitation of the real mass began to dominate over the gravitation of the radiation and the Universe became matter dominated.




Figure 1
Density of the evolving unverse.


At extremely high temperatures, normal matter cannot exist because photons are so energetic, the protons are destroyed in interactions with photons. Thus matter came into existence only by a time of about t ≈ 1 minute when the temperature dropped below T ≈ 10 9 K and the average energy of photons was less than what is necessary to break apart protons. Matter began in its simplest form, protons or hydrogen nuclei. As the temperature continued to drop, nuclear reactions occurred, converting protons first into deuterium and subsequently into the two forms of helium nuclei by the same reactions that now occur in stellar interiors: 



Also, a tiny amount of lithium was produced in the reaction 



Heavier elements were not produced because by the time a significant abundance of helium was produced, the temperatures and densities had dropped too low for the triple‐alpha reaction to occur. In fact, by t ≈ 30 minutes, the temperature was too low for any nuclear reactions to continue. By this time, approximately 25 percent of the mass had been converted to helium and 75 percent remained as hydrogen.257

At high temperatures, matter remained ionized, allowing continual interaction between radiation and matter. As a consequence, their temperatures evolved identically. At a time of about 100,000 years, however, when the temperature dropped to T ≈ 10,000 K, recombination occurred. Positively charged nuclei combined with the negatively charged electrons to form neutral atoms that interact poorly with photons. The universe effectively became transparent, and matter and photons no longer strongly interacted (see Figure ). The two decoupled, each subsequently cooling in its own way as the expansion continued. The cosmic black body radiation, about 1 billion photons of light for every nuclear particle, is left over from this era of decoupling.






figure 2
Temperature of the evolving universe


By an age of 100 million years to 1 billion years, matter began to clump under its self‐gravitation to form galaxies and clusters of galaxies, and within the galaxies, stars and clusters of stars began to form. These early galaxies were not like the galaxies of today. Hubble Space Telescope observations show them to have been gassy disk galaxies, but not as regularly structured as true spiral galaxies. As the universe continued to age, galaxies regularized their structures to become the spirals of today. Some merged to form ellipticals. Some galaxies, if not all, underwent spectacular nuclear region events, which we now observe as the distant quasars.

In the Big Bang theory, the present‐day homogeneity of the universe is considered to be the result of the homogeneity of the initial material out of which the universe evolved; but this is now known to be a serious problem. For one region of the universe to be just like another (in terms of all physically measurable properties, as well as the very nature of the laws of physics), the two must have been able to share or mix every physical factor (for example, energy). Physicists express this in terms of communication (sharing of information) between the two, but the only means of communication between any two regions is one receiving electromagnetic radiation from the other and vice‐versa; commication is limited by the speed of light. Throughout the whole history of the universe, regions that today are on opposite sides of the sky have always been farther apart than the communication distance at any era, which is given by the speed of light times the time elapsed since the origin of the universe. In the language of physicists, there is no causal reason for every region of the observable universe to have similar physical properties.

Closed and open universes

Within the context of a Big Bang theory there are three types of cosmologies that are differentiated on the basis of dynamics, density, and geometry, all of which are interrelated. An analogy may be made in the launch of a satellite from Earth. If the initial velocity is too small, the satellite's motion will be reversed by gravitational attraction between Earth and satellite and it will fall back to Earth. If given just enough initial velocity, the spacecraft will go into an orbit of fixed radius. Or if given a velocity larger than the escape velocity, then the satellite will move outward forever. For the real universe with a rate of expansion as observed (Hubble Constant) there are three possibilities. First, a low‐density universe (hence low self‐gravity) will expand forever, at an ever slowing rate. As mass has a relatively weak effect on the expansion rate, the age of such a universe is greater than two‐thirds of the Hubble Time T H. Second, a universe with just the right self‐gravity, for example a critical mass universe, will have its expansion slowed to zero after an infinite amount of time; such a universe has a present age of (2/3)T H. In this case, the density must be the critical density given by


   


where H o is the Hubble constant measured in the present day universe (due to the gravitational deceleration, its value does change over time). In a higher‐density universe, the current expansion at a time of less than (2/3) T H ultimately is reversed and the universe collapses back onto itself in the big crunch.

Each of these three possibilities, via the tenets of Einstein's theory of general relativity, are related to the geometry of space. (General relativity is an alternative description of gravitational phenomena, in which changes in motions are the result of geometry rather than the existence of a real force. For the solar system, general relativity states that a central mass, the Sun, produces a bowl‐shaped geometry. A planet moves around this “bowl” in the same manner that a marble prescribes a circular path within an actual curved bowl. For mass distributed uniformly over vast volumes of space, there will be a similar effect on the geometry of that space.) A low‐density universe corresponds to a negatively curved universe that has infinite extent, hence is considered open. It is difficult to conceptualize a curved geometry in three dimensions, hence two‐dimensional analogs are useful. A negatively curved geometry in two dimensions is a saddle shape, curving upwards in one dimension, but at right angles curving downward. The geometry of a critical mass universe is flat and infinite in extent. Like a two‐dimensional flat plane, such a universe extends without bound in all directions, hence also is open. A high‐density universe is positively curved, with a geometry that is finite in extent, thus considered to be closed. In two dimensions, a spherical surface is a positively curved, closed, finite surface.

Will the universe expand forever?

In principle, observation should allow determination of which model corresponds to the real universe. One observational test is based upon deducing the geometry of the universe, say by number counts of some type of astronomical object whose properties have not changed over time. As a function of distance, in a flat universe, the number of objects should increase in proportion to the volume of space sample, or as N(r) ∝ r 3, with each increase of a factor of 2 in distance producing an increase in the number of objects by 2 3 = 8 times. In a positively curved universe, the number increases at a lesser rate, but in a negatively curved universe, the number increases more rapidly.

Alternatively, because the strength of gravity slowing the expansion of the universe is a direct consequence of the mass density, determination of the rate of deceleration constitutes a second potential test. Greater mass means more deceleration, thus a past expansion is much more rapid than at present. This should be detectable in measurement of Doppler velocities of very distant, young galaxies, in which case the Hubble Law will deviate from being a straight line. A lesser mass density in the universe means less deceleration, and the critical case universe has an intermediate deceleration.

Differing rates of expansion in the past also yields a direct relationship to the ratio of helium‐to‐hydrogen in the universe. An initially rapidly expanding universe (high‐density universe) has a shorter time era for nucleosynthesis, thus there would be less helium in the present day universe. A low‐density universe expands more slowly during the helium‐forming era and would show more helium. A critical case universe has an intermediate helium abundance. Deuterium and lithium abundances also are affected.

The fourth test is to measure directly the mass density of the universe. In essence, astronomers select a large volume of space and compute the sum of the masses of all the objects found in that volume. At best, individual galaxies appear to account for no more than about 2 percent of the critical mass density suggesting an open, forever expanding universe; but the unknown nature of the dark matter makes this conclusion suspect. The other tests suggest a universe that is flat or open, but these tests are also fraught with observational difficulties and technical problems of interpretation, thus none really produces a decisive conclusion.

Is the Big Bang theory correct?

Recent observations of Type I supernovae in distant galaxies suggest that, contrary to a basic assumption of the Big Bang cosmological theory, the expansion may actually be accelerating, not slowing. Scientists always worry that a single suggestion in major conflict with accepted theory may itself be in error. One always wishes confirmation, and in 1999 a second group of astronomers was able to provide confirmation that the expansion is indeed accelerating. How this will force changes in cosmological theory is as yet unclear.