Selecting energy–momentum trace dependent gravity theories with LSS

We study scalar cosmological perturbations in $f(R,T)$ modified gravity theories, where $T$ represents the trace of the energy–momentum tensor. We provide detailed equations for the matter energy density contrast. We solve them numerically to facilitate a comparison with available large-scale structure (LSS) formation observational data on $f{\sigma }_8$, while also addressing the $S_8$ tension. We identify $f(R,T)$ models that either lead to growth enhancement or suppression. Since recent results in the literature indicate a preference for the latter feature, this type of analysis is quite useful for selecting viable modifications of gravity. The studied class of such $f(R,T)$ models are either ruled out or severely restricted. After selecting the surviving $f(R,T)$ models we show how they deal with the $S_8$ tension.