Revisiting f(R,T)f(R,T) cosmologies

We review the status of $f(R,T)$ theories, where $T$ is the trace of the energy momentum tensor $T^{\mu\nu}$, concerning the evolution of the cosmological flat Friedmann-Lema\^itre-Robertson-Walker (FLRW) background expansion. We start focusing on the modified Friedmann equations for the case of a minimally coupled gravitational Lagrangian of the type $f(R,T)=R +\alpha e^{\beta T} + \gamma_{n} T^{n}$. With this choice one is allowed to cover all existing proposals in the literature via four free parameters and all relevant $f(R,T)$ models as well as the $\Lambda$CDM model can be achieved in the appropriate limit. We show that in such minimally coupled case there exists a useful constraining relation between the effective fractionary total matter density with arbitrary equation of state parameter and the modified gravity parameters. Then, with this association the modified gravity sector can be independently constrained using estimations of the gas mass fraction in galaxy clusters. Using cosmological background data and demanding the universe is old enough to accommodate the existence of Galactic globular clusters with estimated age of at least $\sim 13$ Gyrs we find a narrow range of the modified gravity free parameter space in which this class of theories remains cosmologically viable. As expected, this preferred parameter space region accommodates the $\Lambda$CDM limit of $f(R,T)$ models. We also work out the non-minimally coupled case in the metric-affine formalism and find that there are no viable cosmologies in the latter situation.Comment: 9 pages, 4 figure