Future singularities if the universe underwent Starobinsky inflation in the past

TL;DR

This paper examines how quantum fields and an $\alpha_0 R^2$ term influence future cosmological singularities, especially in models consistent with past Starobinsky inflation, revealing their effects on the stability and nature of these singularities.

Contribution

It provides a detailed analysis of the impact of quantum fields and higher curvature terms on future singularities in cosmology, focusing on models compatible with Starobinsky inflation.

Findings

Massive conformally coupled scalar fields approach conformally invariant behavior near singularities.

Solutions with $\alpha_0 R^2$ term can stabilize or alter the nature of future singularities.

Analytic and numerical methods confirm behaviors of semiclassical backreaction solutions.

Abstract

The effects which quantum fields and an $\alpha_0 R^2$ term in the gravitational Lagrangian have on future singularities are investigated. While all values of $\alpha_0$ are considered, an emphasis is placed on those values which are compatible with the universe having undergone Starobinsky inflation in the past. These are also values which lead to stable solutions to the semiclassical backreaction equations in the present universe. The dark energy is modeled as a perfect fluid, and the focus is on type I-IV singularities and little rips which result when the classical Einstein equations are solved with various types of dark energy as a source. First, evidence is provided that the energy densities of massive conformally coupled scalar fields approach that of the conformally invariant scalar field as a type III singularity is approached. Then, solutions to the semiclassical backreaction equations are investigated when conformally invariant fields and the $ \alpha_0 R^2$ term in the gravitational Lagrangian are present. General proofs regarding the behaviors of the solutions are given. The proofs are illustrated by analytic and numerical calculations in specific cases.