Isocurvature Perturbations in Multiple Inflationary Models
D. Polarski, A. A. Starobinsky
TL;DR
Isocurvature Perturbations in Multiple Inflationary Models analyzes long-wavelength isocurvature perturbations in multi-field inflation where scalar fields interact only through gravity. The authors develop an analytic treatment of the inflationary stage, obtaining exact $k\to0$ solutions that yield a growing adiabatic mode and $N-1$ isocurvature modes, with amplitudes fixed by quantum fluctuations via vacuum initial conditions. They then match these solutions to a post-inflationary CDM+radiation era in a two-field scenario, distinguishing heavy and light relics (uncoupled after inflation) and predicting that isocurvature power can be suppressed near the spectrum break but may rise sharply on small scales, potentially producing primordial black holes. The results constrain the observational impact of surviving isocurvature modes and inform model-building in scenarios with relic scalar fields.
Abstract
Dynamics of long-wave isocurvature perturbations during an inflationary stage in multiple (multi-component) inflationary models is calculated analytically for the case where scalar fields producing this stage interact between themselves through gravity only. This enables to determine correct amplitudes of such perturbations produced by vacuum quantum fluctuations of the scalar fields during the multiple inflationary stage. Exact matching to a post-inflationary evolution that gives the amplitude of isocurvature perturbations in the cold dark matter model with radiation is performed in the case where a massive inflaton field remains uncoupled from usual matter up to the present time. For this model, isocurvature perturbations are smaller than adiabatic ones in the region of the break in the perturbation spectrum which arises due to a transition between the two phases of inflation, but they may be much bigger and have a maximum at much shorter scales. The case of an inflaton with a quartic coupling which remains uncoupled after inflation is considered, too.