On Cross-correlations between Curvature and Isocurvature Perturbations during Inflation

TL;DR

This paper analyzes how couplings between curvature and isocurvature perturbations during inflation influence their correlations, especially when sound speeds differ, revealing conditions for enhanced cross-correlations.

Contribution

It introduces a generalized two-field inflation model with arbitrary sound speeds and calculates the effects of couplings on perturbation spectra using perturbative analysis.

Findings

Cross-correlations are generated and amplified at horizon crossing.

Smaller isocurvature sound speed enhances cross-correlation.

Isocurvature perturbation acts as a source for curvature perturbation.

Abstract

We investigate the effects of couplings between curvature and isocurvature perturbations before and around horizon-crossings during cosmological inflation. We consider a generalized two-field inflation model, in which the non-canonical kinetic term allows us arbitrary sound speeds of curvature and isocurvature perturbations. By using the field-theoretical perturbative analysis, we calculate the cross-spectrum between curvature and isocurvature perturbations and the corrections to curvature and isocurvature power spectra due to the presence of couplings between them. Our analysis confirms previous results that the cross-correlations are generated and amplified when perturbations cross the horizons. Moreover, we find the cross-correlation, which was previously shown to be first-order in slow-roll parameter, can be enhanced when the sound speed of isocurvature perturbation is much smaller than that of the curvature perturbation. This is because in this case the isocurvature perturbation exits its horizon much earlier than the curvature perturbation and acts as a nearly constant source on the curvature perturbation.