Space-time correlations in inflationary spectra, a wave packet analysis

TL;DR

This paper investigates the nonlocal space-time correlations in inflationary spectra using wave packet analysis, revealing that density fluctuations originate in pairs near reheating, with implications for cosmic microwave background anisotropies.

Contribution

It introduces a wave packet transformation and coherent state analysis to study mode correlations in inflationary spectra, providing a detailed understanding of their spatial properties.

Findings

Density fluctuations originate in pairs near reheating

Local density fluctuations are paired with oppositely moving partners

Wave packet and coherent state methods reveal detailed correlation structures

Abstract

The inflationary mechanism of mode amplification predicts that the state of each mode with a given wave vector is correlated to that of its partner mode with the opposite vector. This implies nonlocal correlations which leave their imprint on temperature anisotropies in the cosmic microwave background. Their spatial properties are best revealed by using local wave packets. This analysis shows that all density fluctuations giving rise the large scale structures originate in pairs which are born near the reheating. In fact each local density fluctuation is paired with an oppositely moving partner with opposite amplitude. To obtain these results we first apply a ``wave packet transformation'' with respect to one argument of the two point correlation function. A finer understanding of the correlations is then reached by making use of coherent states. The knowledge of the velocity field is required to extract the contribution of a single pair of wave packets. Otherwise, there is a two-folded degeneracy which gives three aligned wave packets arising from two pairs. The applicability of these methods to observational data is briefly discussed.