Finite-time singularities in f(R, T) gravity and the effect of conformal anomaly

TL;DR

This paper explores how specific $f(R,T)$ gravity models can produce all four types of future finite-time singularities and examines the role of conformal anomaly and matter contributions in avoiding these singularities.

Contribution

It demonstrates that $f(R,T)$ gravity can reproduce all known singularity types and shows how conformal anomaly and matter effects influence their occurrence or avoidance.

Findings

Conformal anomaly cannot remove sudden or type IV singularities.

Big rip and type III singularities can be avoided with certain parameters.

Matter contributions in $f(R,T)$ gravity can prevent some singularities.

Abstract

We investigate $f(R,T)$ gravity models ($R$ is the curvature scalar and $T$ is the trace of the stress-energy tensor of ordinary matter) that are able to reproduce the four known types of future finite-time singularities. We choose a suitable expression for the Hubble parameter in order to realise the cosmic acceleration and we introduce two parameters, $\alpha$ and $H_s$, which characterise each type of singularity. We address conformal anomaly and we observe that it cannot remove the sudden singularity or the type IV one, but, for some values of $\alpha$, the big rip and the type III singularity may be avoided. We also find that, even without taking into account conformal anomaly, the big rip and the type III singularity may be removed thanks to the presence of the $T$ contribution of the $f(R,T)$ theory.