On the agreement between COBE anisotropy results and specific predictions from clusters of galaxies

Abstract

The recent results from the first year of data from the COBE DMR experiment (Smoot et al. 1992) detect a large angle anisotropy in the Cosmic Microwave Background [CMB]. This first set of data seems to indicate that the scale-invariant (n = 1) spec­ trum is preferred, with an amplitude at the horizon crossing of 'H = (5.4 ± 1.6) .10- 6 (Wright et al. 1992). This level is in remarkable agreement with the value of 'H ~ (1.5/b) (6 ± 2.5) . 10- 6 , which was predicted to be the relevant one from a study of the distribution of Abell clusters which sampled large scales which correspond to angles up to twice the COBE FWHM (Scaramella 1992), where the value b - 1.5 was suggested by agreement with the observed large scale peculiar velocities. This observational agreement indicates that on the very large scales the peculiar gravitational potential has kept nearly constant from the epoch of last scattering to the present. This fact, together with the presence of large scale flows, suggests that we live in a spatially flat Universe of critical density, where optical galaxies are mildly biased with respect to the matter distribution, and with a power spectrum which, depending on the spectral index on small scales, has a turnover to n =1 in the 100 - 200 h-1 Mpc scale range. We also considered a tilted (n < 1) CDM model, and find that this model would need a small spectral index (n - 0.3) to match the cluster normalization. However, such an index would yield a too large CMB anisotropy, even without the the possible additional anisotropy due teJ the presence of a significant background of primordial gravitational waves.