To build a model of large-scale structure, four key ingredients need to be specified: (i) the content of Universe, (ii) the initial conditions, (iii) the growth mechanism, and (iv) the values of fundamental cosmological parameters. I now discuss each of these in turn.
2.1. The content of the Universe
Densities are usually expressed in terms of the cosmological density parameter, = / crit, where the critical density, crit, is the value that makes the geometry of the Universe flat. The main constituents of the Universe and their contribution to are listed in Table 1.
|CMB radiation||r = 4.7 × 10-5|
|massless neutrinos||= 3 × 10-5|
|massive neutrinos||= 6 × 10-2(( < m > ) / (1 ev))|
|baryons||b = 0.037 ± 0.009|
|(of which stars)||s = (0.0023 - 0.0041) ± 0.0004|
|dark matter||dm 0.3|
The main contribution to the extragalactic radiation field today is the cosmic microwave background (CMB), the redshifted radiation left over from the Big Bang. These photons have been propagating freely since the epoch of "recombination", approximately 300,000 years after the Big Bang. The CMB provides a direct observational window to the conditions that prevailed in the early Universe. The Big Bang also produced neutrinos which today have an abundance comparable to that of photons. We do not yet know for certain what, if any, is the mass of the neutrino, but even for the largest masses that seem plausible at present, ~ 0.1eV, neutrinos make a negligible contribution to the total mass budget (although they could be as important as baryons). The abundance of baryons is now known with reasonable precision from comparing the abundance of deuterium predicted by Big Bang theory with observations of the absorption lines produced by intergalactic gas clouds at high redshift seen along the line-of-sight to quasars (Tytler et al. 2000). Baryons, the overwhelming majority of which are not in stars today, are also dynamically unimportant (except, perhaps, in the cores of galaxies).
Dark matter makes up most of the matter content of the Universe today. To the now firm dynamical evidence for its existence in galaxy halos, even more direct evidence has been added by the phenomenon of gravitational lensing which has now been detected around galaxy halos (e.g. Fischer et al. 2000, McKay et al. 2001, Wilson et al. 2001), in galaxy clusters (e.g. Clowe et al. 2000), and in the general mass field (e.g. Van Waerbeke et al. 2001 and references therein). The distribution of dark matter in rich clusters can be reconstructed in fair detail from the weak lensing of distant background galaxies in what amounts virtually to imaging the cluster dark matter. Various dynamical tests are converging on a value of dm 0.3, which is also consistent with independent determinations such as those based on the baryon fraction in clusters (White et al. 1993, Evrard 1997), and on the evolution in the abundance of galaxy clusters (Eke et al. 1998, Borgani et al. 2001). Since dm is much larger than b, it follows that the dark matter cannot be made of baryons. The most popular candidate for the dark matter is a hypothetical elementary particle like those predicted by supersymmetric theories of particle physics. These particles are referred to generically as cold dark matter or CDM. (Hot dark matter is also possible, for example, if the neutrino had a mass of ~ 5 eV. However, early cosmological simulations showed that the galaxy distribution in a universe dominated by hot dark matter would not resemble that observed in our Universe (White, Frenk and Davis 1983).)
A recent addition to the cosmic budget is the dark energy, direct evidence for which was first provided by studies of type Ia supernovae (Riess et al. 1998, Perlmutter et al. 1999) (2). These presumed `standard candles' can now be observed at redshifts between 0.5 and 1 and beyond. The more distant ones are fainter than would be expected if the universal expansion were decelerating today, indicating that the expansion is, in fact, accelerating. Within the standard Friedmann cosmology, there is only one agent that can produce an accelerating expansion. This is nowadays known as dark energy, a generalization of the cosmological constant first introduced by Einstein, which could, in principle, vary with time. The supernova evidence is consistent with the value 0.7. Further, independent evidence for dark energy is provided by a recent joint analysis of CMB data (see next section) and the 2dFGRS (Efstathiou et al. 2002).
Amazingly, when all the components are added together, the data are consistent with a flat universe:
2 The possibility that dark energy might be the dynamically dominant component had been anticipated by theorists from studies of the cosmic large-scale structure (see e.g. Efstathiou et al. 1990), and was considered in the first simulations of structure formation in cold dark matter universes (Davis et al. 1985). Back.