FUNDAMENTAL ISSUES IN COSMOLOGY

Professor Joseph Silk

Cosmological principles

The scientist, although not necessarily the poet or the theologian, commences his study of the universe by assuming that the laws of physics which are locally measured in the laboratory have more general applicability. If experiment proves that this assumption is wrong, one then proceeds to explore generalizations of local physics. In this spirit, cosmology, the science of studies of the universe, is developed by extrapolation of locally verified laws of physics to remote locations in space and time, which can be probed with modern astronomical techniques. In a theory of cosmology, simplicity is sought on sufficiently large scales. The successful theories in physics and mathematics are invariably the simplest, with the least number of arbitrary degrees of freedom. Postulating that Titan held up the heavens (where did he come from? Why didn't he get bored? or sleepy?) requires many more ad hoc assumptions than the realization that the orbits of the planets in the gravity field of the sun suffice to stop them falling onto the earth like so many shooting stars.

Unlike other branches of science, cosmology is unique in that there is only one universe available for study. We cannot tweak one parameter, juggle another, and end up with a different system on which to experiment. We can never know how unique is our universe, for we have no other universe with which to compare. The universe denotes everything that is or ever will be observable, so that we can never hope to glimpse another universe.

Nevertheless, we can imagine other possible universes. One could have a universe containing no galaxies, no stars and no planets. Needless to say, man could not exist in such a universe. The very fact that our species has evolved on the planet Earth sets significant constraints on the possible ways our universe has evolved. Indeed, some cosmologists think that this may be the only way we can ever tackle such questions as why does space have three dimensions, or why does the proton have a mass that is precisely 1836 times larger than the electron? If neither were the case, we certainly would not be here. One can take the argument further: our actual existence requires the universe to have had three space dimensions and the proton mass to be 1836 electron masses. This conclusion is called the anthropic cosmological principle: namely, that the universe must be congenial to the origin and development of intelligent life. Of course, it is not an explanation, and the anthropic principle is devoid of any physical significance. Rather it limits the possibilities. There could be a host of radically different universes that we need not worry about.

It is inevitable that an astronomer studies objects remote in time as well as in space. Light travels a distance of 300,000 kilometers in one second, or ten thousand billion kilometers in a year. The nearest star, Alpha Centauri, is 3 light years from us: we see it as it was three years ago. The nearest galaxy comparable to our own Milky Way is two million light years distance: we are seeing the Andromeda galaxy, a naked eye object in a dark sky, as it was when homo sapiens had not yet evolved. A large telescope is a time-machine that can take us part way to creation, to examine regions from which light emanated more than five billion years ago, before our sun had ever formed. To a cosmologist, the issue of creation is inevitable.

There are three possibilities that one may envisage for the creation of the universe.

  1. The beginning was a singular state, not describable by physical science. A skeptic might ask, what did God do before He created the Universe? The apocryphal answer is that He was preparing Hell for people who might ask such questions (attributed to St. Augustine).
  2. The beginning was the most simple and permanent state imaginable, containing within itself the seeds of future evolution. This is the modern view, and one searches for the correct physical laws that describe this initial state.
  3. There was no creation, and the universe is unchanging and of infinite age. We can try to distinguish between the latter two possibilities, the only two options on which scientific tools can be brought to bear. The earlier considerations about the simplicity of a successful theory are incorporated into a simple principle that serves as a guide for building a model of the universe. There are various versions of such a cosmological principle.
The cosmological principle states that the universe, on the average, looks the same from any point. It is motivated by the Copernican argument that the Earth is not in a central, preferred position. If the universe is locally isotropic, as viewed from any point, hence it is also uniform. So the cosmological principle states that the universe is approximately isotropic and homogeneous, as viewed by any observer at rest. This allows the possibility of very different past and future states of the universe.

A stronger version, the perfect cosmological principle, goes further: the universe appears the same from all points and at all times. In other words, there can have been no evolution: the universe must always have been in the same state, at least as averaged over long times.

Finally, the anthropic cosmological principle argues that the universe must have been constructed so as to have led to the development of intelligence.

The darkness of the night sky.

Olbers' paradox is "Why is the sky dark at night?". Olbers (and before him, others) assumed that both the average space frequency and luminosity of stars (and galaxies) is approximately constant throughout space and over time. Consider any large shell of matter of radius r and thickness dr. The light from this shell is 4Pi r^2 dr n L$ where the number of stars per unit volume is n and the luminosity of a star is L. So the radiation measured at the centre of the shell is n L dr, and does not depend on the radius of the shell. As we add up the contributions of more and more distant concentric shells (each of equal thickness), the radiation measured at the centre seems to increase without limit. This is not quite right, since light from a distant star is intercepted by an intervening star, but we would expect the sky to be about as brilliant as the surface of a star. Any line of sight must sooner or later run into a star. This conclusion applies at any arbitrary point, and hence it applies everywhere.

We have a contradiction with the trivial observation that apart from the Milky Way, our own galaxy, the night sky is remarkably dark. Olbers' paradox is not resolved by allowing for interstellar dust since this absorbs and radiates energy. Possible resolutions are (A) the universe is young, so stars have only been shining for about ten billion years, or (B) the universe is of infinite age but expanding so as to avoid a state of thermodynamic equilibrium. Expansion ``cools off" the universe, due to the Doppler shift (which reddens light or reduces the energy of photons that are received from a receding source). Of course, the universe may be both young and expanding, but only hypothesis B requires expansion.

Steady State Cosmology.

The steady state universe (Bondi, Gold, Hoyle 1949) postulates matter creation out of vacuum, so that the perfect cosmological principle is satisfied (density = const). This postulated was motivated by an apparent time--scale problem. The universe of galaxies was found to be expanding by Hubble at a velocity V=H_0*R that increased systematically with galaxy distance R. This means that if there has been no acceleration or deceleration, all matter must have been piled up at the beginning of the expansion a time R/V or 1/H_0 ago. H_0 is Hubble's constant and was found to be H_0= 500 km/s Mpc in Hubble's original work. This means that 1/H_0= 2 billion yr. is an upper limit on the age of the universe.

One may compare this with radioactive dating technique of old rocks, e.g. U-238 -> Pb-205 with half-life of 4x10^9 yr. Measured for different rock and meteorite samples, the present lead isotope abundances allow an estimate of age. We infer 4.6x10^9 yr for oldest meteoritic, lunar rocks.

Stellar evolution theory with hydrogen fusion to helium as an energy source yields the age of globular clusters, the oldest stars in our galaxy. The main sequence turnoff denotes the duration of the observed era of hydrogen burning, while the horizontal branch (on the HR diagram) indicates the location of helium burning stars. The inferred age to fit the observed HR diagram is 10x10^9 yr. The discrepancy between the universal expansion age, on the one hand, and meteoritic and stellar ages on the other hand, was only removed in the 1950's, when a more accurate value for H_0 emerged. The best modern value is H_0=50 km/s Mpc, or 1/H_0=20x10^9 yr.

Key predictions of steady state cosmology were that:

  1. There was and is creation of one hydrogen atom per cubic metre per 10^10 yr. Creation is assumed to occur out of the vacuum, radically violating their law of conservation of mass and energy: One expects antimatter to also be produced, leading to a gamma ray background that results from occasional annihilations of protons and antiprotons. One does not want to also violate another fundamental law, namely the law of conservation of electric charge. Hence another possible form for newly created matter is neutrons. These decay and leave behind hot x-ray emitting gas pervading the universe. Neither the expected cosmic gamma rays or x-rays were seen, so that the theory was modified to postulated creation only in dense cores which we identified with the nuclei of galaxies.
  2. No evolution at great distance could have occurred. Radio source counts tested this. N(>f) is the number observed brighter than flux f, which for a source at distance d luminosity L is given by f=L/4pi d^2. So the distance to which one can see in a flux-limited survey of sources with identical L is d=(L/4pi f)^1/2. Now the total number measured in all-- sky survey is N=(4/3)pi d^3n, where n is the source density. The steady state model predicts that n=constant, so that N(>f) is proportional to d^3 or (L/f)^3/2, predicting that as the survey sensitivity is increased (or as f is lowered), then N(>f) should increase as f^{-3/2} in Euclidean space. Observations revealed a much stronger increase in source counts. Proponents of the steady state model in the 1950s argued that we might be living in a very local hole. However, subsequent optical identifications and distance determinations have shown the radio sources primarily to be radio galaxies and quasars that are several billions of Mpc away from us, demonstrating that evolution must be occurring over a time--scale of order 10^{10} yr. Luminous radio emitting galaxies were far more frequent in the past than they are seen to be today.
The final blow to the steady state theory came with the discovery of the cosmic microwave background in 1964. This was direct evidence of radiation originating in a dense hot phase of the universe, as predicted by the Big Bang theory. It is characterized by a blackbody spectrum appropriate to a blackbody at 2.75 degrees Kelvin. The intensity of such a cold blackbody peaks at a wavelength of 1 mm, in the microwave band. To explain such radiation in a steady state model requires one to postulate the universal presence of millimeter sized dust grains that would absorb an intense radiation field produced by many exceptionally luminous galaxies and reradiate it at the appropriate temperature. This interpretation is so contrived and requires so many special assumptions that it is generally regarded as being highly implausible.