Evolution of coupled scalar perturbations through smooth reheating. I. Dissipative regime

TL;DR

This paper develops a gauge-invariant formalism for coupled scalar perturbations during smooth reheating, accounting for dissipation and thermal effects, with potential applications in early universe phenomena like phase transitions and gravitational wave production.

Contribution

It introduces a set of coupled equations for scalar perturbations in a dissipative regime, enabling reliable numerical analysis from horizon crossing to acoustic oscillations.

Findings

Numerical solutions are achievable despite singular coefficients.

Perturbations originate quantum-mechanically and dissipate via plasma interactions.

Framework applicable to inhomogeneity-induced nucleations and gravitational wave generation.

Abstract

If the inflaton is a heavy scalar field, it may equilibrate slower than some other degrees of freedom, e.g. non-Abelian gauge bosons. In this case, perturbations in the inflaton field and in a thermal plasma coexist from a given moment onwards. We derive a gauge-invariant set of three coupled equations governing the time evolution of such a system. Despite singular coefficients, a reliable numerical solution can be obtained for a long time period, starting from phase oscillations inside the Hubble horizon, and extending until acoustic oscillations in a radiation-dominated universe. Benchmarks are illustrated from a "weak regime", where perturbations have a quantum-mechanical origin but get dissipated by interactions with the plasma. Among applications of our formalism could be inhomogeneity-induced nucleations in post-inflationary phase transitions, and the production of scalar-induced gravitational waves.