Quantum effects from particle production on background evolution and Cardy-Verlinde formula in f(R) gravity

TL;DR

This paper explores quantum particle production effects in f(R) gravity models near big rip singularities, analyzing conditions under which quantum effects can prevent singularities and examining the applicability of the Cardy-Verlinde entropy formula.

Contribution

It introduces the analysis of quantum effects in f(R) gravity with R^α terms near singularities and identifies specific conditions where the Cardy-Verlinde formula aligns with total entropy.

Findings

Quantum effects dominate for α in (1/2, 1), potentially avoiding the big rip.

In Einstein gravity, the Cardy-Verlinde formula always matches the universe's entropy.

In f(R) gravity, the formula holds only for specific α related to space dimension.

Abstract

We investigate particle production in an expanding universe under the assumption that the Lagrangian contains the Einstein term $R$ plus a modified gravity term of the form $R^\alpha$, where $\alpha$ is a constant. Dark fluid is considered as the main content of the universe and the big rip singularity appears. Quantum effects due to particle creation is analysed near the singularity and we find that for $\alpha\in ]1/2, 1[$, quantum effects are dominant and the big rip may be avoided whereas for $\alpha\in J$ the dark fluid is dominant and the singularity remains. The Cardy-Verlinde formula is also introduced and its equivalence with the total entropy of the universe is checked. It is found that this can always occur in Einstein gravity while in f(R) gravity, it holds only for $\alpha=\frac{n+1}{2n+6}$, $n$ being the space dimension, corresponding to the situation in which the big rip cannot be avoided.