4.2. CDM models for structure formation

The elements discussed so far assemble into the CDM cosmological model, which is the simplest possibility that is consistent with current evidence. The overall matter power spectrum is written dimensionlessly as the logarithmic contribution to the fractional density variance, ²:

(91)

which undergoes linear growth

(92)

where the linear growth law is D(a) = a g[(a)] in the matter era, and the growth suppression factor for a density parameter _m 1 is

(93)

The transfer function T_k depends on the dark-matter content as discussed earlier, in particular displaying a horizon-scale break at k 0.06(_m h)^-1 h Mpc^-1. Weak oscillatory features are also expected if the universe has a significant baryon content. Eisenstein & Hu (1998) give an accurate fitting formula that describes these wiggles. This detailed fit of the CDM spectrum is to be preferred to the older notation in which the spectrum was described by the zero-baryon form, but with an effective value of _m h that allowed for the main effects of the baryon content:

(94)

(Sugiyama 1995).