On Particles Creation and Renormalization in a Cosmological Model with a Big Rip

TL;DR

This paper derives an exact solution for a scalar field in a cosmological model with a Big Rip, analyzing particle creation, renormalization, and quantum backreaction effects near the singularity.

Contribution

It provides an exact solution for particle creation and renormalization in a Big Rip cosmology with a conformally coupled scalar field, highlighting conditions where quantum backreaction is negligible.

Findings

Number density of created particles is computed and analyzed near the Big Rip.

Renormalization of the energy-momentum tensor shows quantum effects can be neglected under certain conditions.

Quantum backreaction is insignificant if the field mass is small and the Big Rip is sufficiently far away.

Abstract

An exact solution is obtained for a massive scalar field conformally coupled with the curvature in a cosmological model with the scale factor $a(t) = a_0 / |t|$, corresponding to background matter with the equation of state $ p = - 5 \varepsilon /3 $. An expression for the number density of created particles is obtained, and its behavior is studies as the model approached the instant of a Big Rip. Renormalization of the energy-momentum tensor is considered, and it is shown that back reaction of the quantum effects of a conformally coupled scalar field on the space-time metric can be neglected if the field mass is much smaller than the Planck mass and if the time left to the Big Rip is greater than the Planck time.