Scale-invariant Perturbations from Chaotic Inflation

TL;DR

The paper analyzes density perturbations in chaotic inflation with a symmetric quadratic potential for an $N$-component scalar field, showing that isocurvature perturbations have an almost scale-invariant spectrum with $n\approx 0.9998$ while inflaton perturbations give $n\approx 0.97$. It explores how post-inflation interactions, notably asymmetric instant preheating, can transfer isocurvature fluctuations into curvature perturbations, potentially dominating the primordial spectrum under certain symmetry-breaking conditions. Using the $\delta N$ formalism, it derives the combined power spectrum and identifies regimes where isocurvature contributions can prevail, along with implications for non-Gaussianity and the tensor-to-scalar ratio. If observations favor a nearly scale-invariant scalar spectrum and a smaller gravitational-wave background, an isocurvature-dominated mechanism would be a viable alternative to single-field slow-roll predictions; otherwise, standard inflaton perturbations remain favored.

Abstract

Vacuum fluctuations in the inflaton field driving chaotic inflation with a quadratic potential give a red spectrum of primordial density perturbations, n=0.97. However angular fluctuations in an O(N)-symmetric quadratic potential have a very nearly scale-invariant spectrum, n=0.9998. We investigate the possibility that these isocurvature field perturbations could give the dominant contribution to the primordial density perturbation after inflation.