Gravitationally induced matter creation in scalar-tensor $f(R,T_{\mu\nu}T^{\mu\nu})$ gravity

In this work, we analyze the possibility of gravitationally induced matter creation in the so-called Energy-Momentum-Squared gravity (EMSG), i.e. $f(R,T_{\mu\nu}T^{\mu\nu})$ gravity, in its dynamically equivalent scalar-tensor representation. Given the explicit nonminimal coupling between matter and geometry in this theory, the energy-momentum tensor is not generally covariantly conserved, which motivates the study of cosmological scenarios by resorting to the formalism of irreversible thermodynamics of open systems. We start by deriving the universe matter creation rates and subsequent thermodynamical properties, such as, the creation pressure, temperature evolution, and entropy evolution, in the framework of $f(R,T_{\mu\nu}T^{\mu\nu})$ gravity. These quantities are then analyzed for a Friedmann-Lema\^itre-Robertson-Walker (FLRW) background with a scale factor described by the de Sitter solution, under different assumptions for the mater distribution, namely a vacuum universe, a constant density universe, and a time-varying density universe. Finally, we explore cosmological solutions with varying Hubble parameters and provide a comparison with the standard cosmological model. Our results indicate that the cosmological evolution in the framework of EMSG are in close agreement with the observational cosmological data for low redshift.