Wave asymptotics at a cosmological time-singularity: classical and quantum scalar fields

TL;DR

This paper analyzes scalar wave behavior in various cosmological singularities, providing precise asymptotic descriptions and showing that particle creation remains finite under broad conditions.

Contribution

It offers new sharp asymptotic descriptions for scalar wave solutions in cosmological models with different singularities and establishes finiteness of particle creation in these scenarios.

Findings

Sharp asymptotics for linear Klein-Gordon solutions

Finite cosmological particle creation under general conditions

Results extend to semilinear equations with subcritical exponents

Abstract

We investigate the propagation of the scalar waves in the FLRW universes beginning with a Big Bang and ending with a Big Crunch, a Big Rip, a Big Brake or a Sudden Singularity. We obtain the sharp description of the asymptotics for the solutions of the linear Klein-Gordon equation, and similar results for the semilinear equation with a subcritical exponent. We prove that the number of cosmological particle creation is finite under general assumptions on the initial Big Bang and the final Big Crunch or Big Brake.