Oscillations During Inflation and the Cosmological Density Perturbations

TL;DR

This paper shows that multi-field inflation induces oscillations between the inflaton perturbation and extra scalar perturbations via a non-diagonal mass matrix $M^2$, with mixing angle theta and horizon-crossing resonance that generates a calculable cross-correlation between adiabatic and isocurvature modes. By formulating perturbations with Sasaki–Mukhanov variables and rotating to adiabatic and entropy components, the authors derive explicit expressions for the cross-correlation $C_{Q_A delta_s}$ and connect inflationary perturbations to radiation-era initial conditions, enabling predictions for CMB signatures. The results imply that correlated adiabatic/isocurvature perturbations can persist even when the extra-field energy density is subdominant and may leave observable imprints on the CMB and large-scale structure, offering a robust alternative to strictly single-field inflation. The work also highlights potential transfers of non-Gaussian features from isocurvature to adiabatic modes and motivates further exploration with upcoming CMB data.

Abstract

Adiabatic (curvature) perturbations are produced during a period of cosmological inflation that is driven by a single scalar field, the inflaton. On particle physics grounds -- though -- it is natural to expect that this scalar field is coupled to other scalar degrees of freedom. This gives rise to oscillations between the perturbation of the inflaton field and the perturbations of the other scalar degrees of freedom, similar to the phenomenon of neutrino oscillations. Since the degree of the mixing is governed by the squared mass matrix of the scalar fields, the oscillations can occur even if the energy density of the extra scalar fields is much smaller than the energy density of the inflaton field. The probability of oscillation is resonantly amplified when perturbations cross the horizon and the perturbations in the inflaton field may disappear at horizon crossing giving rise to perturbations in scalar fields other than the inflaton. Adiabatic and isocurvature perturbations are inevitably correlated at the end of inflation and we provide a simple expression for the cross-correlation in terms of the slow-roll parameters.