Attempt to determine the largest scale of primordial density perturbations in the universe

The principle of causality requires that a pure power-law spectrum of cosmological density perturbations possess a super-Hubble suppression scale. We search for evidence of such suppression by performing a three parameter likelihood analysis of the COBE-DMR 4-year sky maps with respect to the amplitude, the spectral index, and the suppression scale. It is found that all suppression scales larger than ${c/H}_0$ are consistent with the data, but that scales of order ${c/H}_0$ are slightly preferred, at roughly the one-sigma level. Super-Hubble density fluctuations on very large scales $\left(\gg {c/H}_0\right)$ can only be explained in the context of present theory by a de Sitter expansion phase, whereas those that are “small” $\left(\sim {c/H}_0\right)$ can also be explained within the standard hot big-bang model. Density perturbations originating after any conceivable de Sitter expansion phase or during non-isentropic de Sitter expansion have natural kinematic constraints which could explain a small super-Hubble suppression scale. Standard inflationary cosmology, which is characterized by isentropic de Sitter expansion, generically predicts that the particle horizon should be much larger than the present-day Hubble radius, ${c/H}_0$. For such scenarios, a small super-Hubble suppression scale would require the duration of the inflation epoch to be fairly short. Suppression scales smaller than ${c/H}_0$ are strongly excluded by the COBE data.