Cosmological eras with the neutrino non-relativistic transition in f(R,T) gravity

Abstract

Theories based on the Ricci and the trace of the energy–momentum tensor, or the short name Ricci-trace-based (RTB) theories, represent a gravitational approach based on the Ricci scalar $R$, and the trace of the energy–momentum tensor $g^{\mu \nu }{T}_{\mu \nu }=T$. This theory fits into gravitational models of the type $f(R,T)=R+f\left(T\right)$, where $f\left(T\right)$ is an arbitrary function of $T$. In this study, we explore a cosmological scenario within the context of RTB models, investigating in detail the cosmological consequences of the coupling between matter and geometry. In order to address this issue, we propose a toy model in which the non-relativistic cosmological neutrino transition plays a role in the cosmic evolution since the effective total energy–momentum tensor trace is affected in this process. We raise questions about the coupling of neutrinos with geometry during this transition, providing a detailed analysis of how RTB gravity deals with this phenomenon and the impact of neutrinos on cosmological dynamics. In summary, we show that the coupling of cosmological neutrinos with $T$ dependent cosmologies is severely challenged.