Box 1. Big Bang Basics

The expansion of the universe is described by the cosmic linear-scale factor R(t). The expansion rate H ≡ (dR/d t)/R is gradually slowed down by gravitational attraction: H_o denotes its present value. If the average mass density p is greater than the critical density p_c, the universe will eventually recollapse. (The density parameter Ω = p/p_c.) Otherwise the expansion continues forever. A critical universe(Ω =1) is spatially flat; a high-density universe (Ω > 1) curves back on itself like the surface of a finite ball; a low-density universe (Ω l < 1), is negatively curved like a saddle.

As the universe expands, photons have their wavelengths stretched (redshifted) in proportion to R(t). The measured redshift z of a photon of known wavelength at emission tells us that universe has expanded by a factor z + 1 since it was emitted, as well as the time t since the Big Bang:

t(z) ≈ 13Gyr/(1+z)^3/2,

assuming a matter-dominated, flat universe with H₀ = 50 km/(s Mpc). The most distant object yet seen is a galaxy with a redshift of 4.92, which means the universe was 5.92 times smaller and about 0.9 Gyr old when the light we see was emitted.

The expanding universe cools adiabatically, with tempera­ture falling like 1/R(t). At a temperature of around 3000 K (equivalent to 0.25 eV) the thermodynamic transition from ionized matter to neutral matter occurred. This "recombina­tion" drastically and suddenly reduced the Thomson-scattering opacity. That's when the CMB photons experienced their last scattering. It was about 300 000 years after the Big Bang, and the cosmic photon background, now in the microwave regime, then had wavelengths in the visible.

When the universe was only 10 000 years old and the temperature was about 1 eV, the energy density in the thermal radiation was comparable to that of matter. Before that, density perturbations could not grow, because radiation domi­nated the energy density. During the time between matter-ra­diation equality and recombination, only perturbations in the nonbaryonic dark matter grow, because the baryons are sup­ported against collapse by radiation pressure. (The putative nonbaryonic matter is presumed to be impervious to electro­magnetic interactions.) But once the baryons are safely ensconsed in neutral atoms, the photon background no longer keeps them from falling into the gravitational potential wells already formed by the dark matter.

This extra early growth of density perturbations in a uni­verse with nonbaryonic dark matter means that less initial irregularity is needed to produce the structure seen today. That's why one expects to see less CMB anisotropy if the bulk of the dark matter is nonbaryonic.