Figure references are to the second edition of Modern Physics by Serway, Moses and Moyer (1997)

unless otherwise stated.

Cosmology deals with the past, present and future state of the universe as a whole. To a large extent, it is a branch of theoretical physics, based on Einstein's General Theory of Relativity for example. However, some of the predictions of cosmological theories can be tested against observations from optical and radio telescopes, supplemented nowadays by measurements in other regions of the electromagnetic spectrum (e.g. gamma rays) made by orbiting spacecraft. As we will see, cosmological theories are closely linked to the ideas of particle physics, so they derive some of their validity from the results of accelerator-physics experiments.

We know that the sun is only one of about 100 billion (10^11) stars within the Milky Way galaxy, which is visible as a diffuse band of light in the night sky. This is a spiral galaxy (about 30000 light years in radius) and we are located in the outer part of one of the spiral arms. Our galaxy part of the so-called local group of galaxies, which includes the Andromeda Nebula (visible to the naked eye as a small fuzzy patch in the sky) about 2 million light-years (10^19 km) away. We are on the edge of a much larger supercluster of galaxies, known as the Virgo cluster, which contains about 1000 galaxies.

There are an estimated 100 billion (10^11) galaxies in the knowable universe, whose light could have reached us during the life of the universe (about 15 billion years). These galaxies do not appear to be distributed uniformly or randomly, but form patterns containing filaments, sheets and bubbles.

Although it is not obvious just looking at the night sky, the universe is expanding. The evidence for this comes mainly from determinations of the Doppler redshift of light from galaxies, as measured by optical spectroscopy in the visible region of the electromagnetic spectrum. Such measurements (Fig. 15.22) show that the speed of recession v (relative to the earth) of an object at a distance R obeys the following relation, known as Hubble's law:

v = H R ................ (1)

H is the Hubble constant; a modern value is H = 65 km/s per megaparsec (1 megaparsec is approximately 3 million light-years) but this value could be in error by as much as 30%.

Although the measurement of v is fairly straightforward, knowing the distance R poses a considerable problem. Stars vary in their apparent brightness both because they are at different distances from us and because their luminosity (light output) varies. However, a certain type of pulsating star (whose light output varies cyclically with time) called a Cepheid variable is found to have period of oscillation which depends on its luminosity in a reproducible way, as first determined by measurements on many Cepheids (in the Magellenic clouds, the nearest galaxies to us) by Henrietta Leavitt in 1912. This property allows the distances of Cepheid stars within our own galaxy to be determined (from their periods), even if they are too far away to be measured by parallax methods. Beginning in 1923, Edwin Hubble (at Mount Wilson observatory) identified Cepheid stars in numerous other galaxies, determined their distances away and (from the slope of the v - R plot) obtained a value for H (initially 500 km/s/megaparsec).

Eq.(1) does not imply that the earth is the centre of a universe which is "exploding" away from us. A modern interpretation is that space itself is expanding (or being created) everywhere, rather than that the galaxies are moving apart through space. The expansion would look the same from any other vantage point in the universe, thereby satisfying what is referred to as the cosmological principle, which postulates that the universe is approximately isotropic (same in all directions) and homogeneous (same number of objects per unit volume, if averaged over a reasonable number of objects).

If we suppose that the velocity of recession has always had the same value v , Eq.(1) would imply R = v/H, which is the equation for the displacement R acquired in a time (1/H) . We could then interpret 1/H = 15 billion years as the age of the universe. Because of the gravitational attraction between matter, v is likely to decrease with time, so this value ought to be an overestimate. However, it is consistent with measurements of the age of the earth, 4.6 billion years as determined from radioactive decay of uranium-238 (half-life = 4 billion years) in the oldest rocks. (With Hubble's original value of H, the universe appeared younger than the earth, a contradiction since the earth is believed to have formed at a relatively late stage in the life of the universe).

A reasonable conclusion from this body of evidence is that the universe began a definite time ago with a (sort-of) "explosion" known as the big bang. Modern theories of cosmology are based on this premise. A steady-state theory (in which one hydrogen atom/m^3/10^10yr is created out of the vacuum) gained some respect for a while. This theory would conform to a perfect cosmological principle, which specifies a universe which appears the same from all points at all times. However, the theory would predict an equal creation of antimatter, for which there is no evidence (in the form of gamma rays resulting from pair annihilation), although the theory was later modified by supposing the creation of matter to occur in dense cores of galaxies (which are intense sources of radio waves).

Decisive data in favour of the big-bang model (and against the steady-state theory) came in 1964, when two scientists (Arno Penzias and Robert Wilson) at Bell Laboratories (New Jersey) detected microwaves with wavelength around 7 cm, coming from all directions in the sky. Later rocket and satellite measurements, particularly those of the Cosmic Background Explorer (COBE) satellite launched in 1989, showed that the spectrum of this cosmic microwave background closely matches that of the radiation emitted by a black body at about 3 K (see Fig. 15.18). COBE measurements have also shown that this radiation is very isotropic; the effective temperature of the radiation from different points in the sky is the same to with 1 part in 10^5. This isotropy is in conformity with the cosmological principle. But after very careful data processing, there appears to be a nonuniformity in the intensity of the radiation from different regions of the sky, of about 6 (+/- 2) parts per million. This observation has been a key factor in shaping theories of the evolution of the universe.

An expanding universe also solves the problem of Olber's paradox, first posed by the German astonomer Heinrich Olbers in 1823. If the universe is infinite or very large, a line drawn from the earth to any point in the sky must intersect a star or galaxy. Therefore the night sky might be expected to be as bright as the surface of the average star, a conclusion which is obviously false. Even the presence of interstellar gas or dust does not alter the conclusion, since the gas (dust) would re-radiate as much radiation as it absorbs (in an equilibrium situation). In an expanding universe, stars radiate their energy into an ever-expanding volume of space, so the implied state of thermodynamic equilibrium is not present. Other resolutions of Olber's paradox could be that the universe has only a limited age, such that distant stars have been radiating light for less time than it takes light to reach us, or that the universe is of finite (limited) size.

A generally accepted modern view of the history of the universe is as follows. At the instant of the big bang (about 15 billion years ago), all matter in the universe probably existed as a singularity, essentially a gigantic black hole with infinite density. This represents a backward extrapolation of physical theory, since at times less than 10^-43 seconds ABB (after big bang), known as the Planck time, the known laws of physics (and spacetime) break down.

At times earlier than 10^-43 s ABB, the four fundamental forces of nature would have been unified in the form of a single type of force, as a result of the enormous temperatures involved (of the order of 10^32 K); see Fig. LS.160 (Lederman & Schramm, p.160) and Fig. 13.14 (Beiser, Concepts of Modern Physics, 5th Edition, McGraw Hill). To understand this state, we would need a theory of quantum gravity, possibly based on superstring theory in which 10 or more dimensions exist at the level of the Planck length (10^-35 m). This period is therefore referred to as the era of quantum gravity or the Planck epoch. The situation has been described as a quantum foam of Planck-mass (10^-5 g) black holes, continuously being created and annihilated, where time would have no meaning. A chance fluctuation may have triggered the expansion of the big bang.

Between 10^-43 s and 10^-32 s ABB, time begins to have a meaning. This is the so-called grand unification era, in which gravity separated out as a distinct force but the strong and electroweak forces remained joined. The universe then consisted of quarks, leptons and massive particles, with energies exceeding 10^16 GeV, corresponding to a temperature of the order of 10^29 K.

One of the observations which any cosmological theory has to explain is that the universe is very smooth (isotropic) on a large scale, although it is lumpy on the scale of stars and galaxies. This smoothness suggests that different parts of the universe initially maintained contact (equilibrium) with each other, through the exchange of energy. However, it would take light about 30 billion years to travel between diametrically opposite points in our knowable universe, whereas the age of the universe is only about 15 billion years, so communication between these points is currently impossible. Moreover, calculations show that when light which we now receive from these regions was emitted, they would have been separated by a distance 100 times larger than light could have travelled (during the prior history of the universe).

In 1980, Alan Guth proposed a solution to this problem (and other ones) called inflation. According to the General Theory of Relativity, the rate of expansion of the universe is related to its energy (strictly mass-energy) density; as the energy is spread out over a larger volume of space, the energy density decreases and so does the rate of expansion. The process of inflation maintains the energy density constant for a while, resulting in a much higher rate of expansion. This allows the early universe to be much smaller (and causally connected), thereby solving the smoothness problem.

According to Guth's theory: when the temperature of the universe fell below a certain value, a Higgs field emerged and filled all space, creating a so-called false vacuum containing an energy density from which particles (quarks and leptons) could be created. This inflationary phase continued until field particles (weak-force bosons) acquired a mass, thereby differentiating the strong and electroweak forces, after which the vacuum energy returned to zero. These changes are referred to as phase changes, by analogy with ordinary matter. During inflation, the size of the universe probably increased by a factor of over 10^43 (rather than 10^26 without inflation) and has since increased by a further factor of 10^26, making it far larger than the knowable universe which we observe.

At 10^-6 s ABB, the universe had cooled to about 10^13 K (particle energy 1 GeV) allowing quarks to condense into baryons and mesons. At about 1 s ABB, the weak and electromagnetic interactions split apart and atomic nuclei formed. Electron-positron pairs were formed and neutrinos ceased interacting with the rest of the universe. At about 3 min ABB, nuclear reactions began, creating deuterium, helium and lithium in amounts which are consistent with current measurements.

At about 100,000 years ABB, when the temperature had fallen to 10,000 K (1 eV particle energy) the plasma of nuclei and electrons began to condense into nuetral atoms. Photons began to propagate freely, forming cosmic background radiation. From this time onwards, the universe was dominated by matter (not radiation), which eventually began to condense under it own gravity into stars and galaxies (at about 10^9 yr ABB). Nucleosynthesis could then occur within stars, creating additional helium-4 (which now accounts for 25% of the mass of the visible universe) and heavier elements.

Will the universe continue to expand forever, or will it later begin to contract (perhaps ending up as a primordial black hole) ? The answer to this question is believed to depend on whether the density of the universe achieves a value known as the critical density. If so, we have a closed universe which will eventually contract; if not, ours is an open universe which will expand forever. Inflation theory predicts that the density of matter should be just sufficient to give a closed universe, but the question is not regarded as settled.

Energy considerations allow the critical density Dc to be estimated. We can argue that a galaxy will just escape the gravitational pull of its neighbours if its total energy is zero. In other words,

(1/2)mv^2 - GmM/R = 0 ................ (2)

where M is the mass of the universe contained within a sphere of large radius R (see Fig.15.24). Setting M = (4p /3)R^3 Dc and using Eq.(1) gives:

Dc = (3/8p ) H^2 / G = 5.8 x 10^-27 kg/m^3 ................ (3)

corresponding to about 4 hydrogen atoms per m^3.

Observations of stars and galaxies indicates that the average density of visible (light-emitting) matter is about 5 x 10^-30 kg/m^3, not nearly enough to close the universe. Including the mass equivalent of the radiation in the universe adds only 2% of the visible mass. However, measurements of the relative abundance of isotopes and of the rotational behaviours of galaxies indicates the presence of dark matter, perhaps twenty to thirty times as much as visible matter. The nature of this dark matter is unknown; it might be ordinary matter whose form and location we have yet to discover, or might be exotic matter quite different to the baryonic matter with which we are familiar.

Candidates for normal (baryonic) dark matter include planets, black holes and brown dwarfs (small "stars" whose internal temperature has not risen sufficiently to start nuclear fusion). They are given the collective name MACHO's (massive compact halo objects), since they are probably located in the dark outer halos of galaxies. Some evidence for their existence comes from the observation of microlensing, a change in apparent brightness of a star whose light passes close to a MACHO.

Measurements of the abundance of deuterium suggest that 90% of the matter in the universe would have to be exotic (nonbaryonic) in order to achieve critical density. One form of exotic matter might be neutrinos, if they have a rest mass. Big-bang theory predicts that today there should be over 300 neutrinos per cm^3 . If the neutrino mass were 50eV, this would be enough mass to close the universe. From tritium-decay experiments, the electron-neutrino mass is believed to be less than 10 eV, but the two other types of neutrinos might have higher masses. Another exotic type of particle, predicted by certain theories but so far not observed, is the photino, whose mass should be between 10 and 100 times that of a proton. Being uncharged, it would interact very weakly with matter, so it is one example of a weakly interacting massive particle (WIMP) whose existence might be necessary to ensure a closed universe.

Theoretical and observational studies are continuing, with a view to answering many basic questions about the history and future of the universe. However, one goal which has already been achieved is to link the physics of the ultra-small (particle and string theories) with that of the ultra-large (cosmology), a range of 10^60 in terms of spatial dimension.

Useful references:

From Quarks to the Cosmos, by L.M. Lederman and D.M. Schramm (Scientific American Library, 1995)

A Short History of the Universe, by Joseph Silk (Scientific American Library, 1997)