Energy–momentum-squared gravity model-ℱ(ℛ,𝒯2) coupled with perfect fluid admitting solitonic-type symmetries

In this research paper, we discuss the energy–momentum-squared gravity model [Formula: see text] coupled with perfect fluid. We obtain the equation of state for the perfect fluid in [Formula: see text]-gravity model. Furthermore, we deal with the energy–momentum-squared gravity model [Formula: see text] coupled with perfect fluid, which admits the Ricci solitons with a conformal vector field. We provide a clue in this series to determine the density and pressure in the radiation and phantom barrier periods, respectively. In addition, we investigate the different energy conditions, black holes and singularity conditions for perfect fluid attached to [Formula: see text]-gravity in terms of Ricci soliton. Finally, we derive the Schrödinger equation for energy–momentum-squared gravity model [Formula: see text] coupled with perfect fluid.