An Attempt to Determine the Largest Scale of Primordial Density Perturbations in the Universe

Inflationary cosmology predicts that the particle horizon should be generically much bigger than the present-day Hubble radius, $1/H_0$. This implies a special regime of super-Hubble scale energy density fluctuations imprinted on the cosmic microwave background radiation (CMBR), which from present theory could only be explained by inflation Causality constraints are used to determine models for the power spectrum that accommodate a suppression scale. A three parameter likelihood analysis is performed of the COBE-DMR 4-year data with respect to the amplitude, spectral index, and suppression scale. It is found that all suppression length scales larger than $1/H_0$ are consistent with the data, but that scales of order $1/H_0$ are slightly preferred, at roughly the one-sigma level. Many non-inflation models would be consistent with a small suppression length scale, whereas for standard inflation models, the duration of the inflation epoch would have to be bounded by a fairly small upper limit. Suppression scales smaller than $1/H_0$ are strongly excluded by the anisotrophy data.