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In this work, we analyze the possibility of gravitationally induced mattercreation in the so-called Energy-Momentum-Squared gravity (EMSG), i.e.$f(R,T_{\mu\nu}T^{\mu\nu})$ gravity, in its dynamically equivalentscalar-tensor representation. Given the explicit nonminimal coupling betweenmatter and geometry in this theory, the energy-momentum tensor is not generallycovariantly conserved, which motivates the study of cosmological scenarios byresorting to the formalism of irreversible thermodynamics of open systems. Westart by deriving the universe matter creation rates and subsequentthermodynamical properties, such as, the creation pressure, temperatureevolution, and entropy evolution, in the framework of$f(R,T_{\mu\nu}T^{\mu\nu})$ gravity. These quantities are then analyzed for aFriedmann-Lema\^itre-Robertson-Walker (FLRW) background with a scale factordescribed by the de Sitter solution, under different assumptions for the materdistribution, namely a vacuum universe, a constant density universe, and atime-varying density universe. Finally, we explore cosmological solutions withvarying Hubble parameters and provide a comparison with the standardcosmological model. Our results indicate that the cosmological evolution in theframework of EMSG are in close agreement with the observational cosmologicaldata for low redshift.

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