Abstract

We used the absolute parallelism geometry to obtain a new formula for the Ricci scalar. We consider \(f(R,\Sigma,T)\) modified theories of gravity, where the gravitational Lagrangian is given by three arbitrary functions of the Ricci scalar \(R\), Ricci torsion scalar \(\Sigma\), and the trace of the stress-energy tensor \(T\). We obtain the gravitational field equations in the metric formalism. The evolution of the function \(f(R)\) withr time is studied, and we discuss the parameters that make up the function and impose constraints on these parameters. The solution of the \(f(R,\Sigma,T)\) gravity equations are obtained under a varying polynomial deceleration parameter. The effect of torsion on cosmological models is also discussed. Physical aspects of the energy density, pressure, and energy conditions of the cosmological models proposed in this article are studied, and the evolution of the physical parameters is shown in figures. Evolution of the fluid pressure and energy density parameter as a function of redshift has been obtained. The \(f(R)\) gravity and \(f(R,T)\) gravity theories as special cases could be inferred from \(f(R,\Sigma,T)\) gravity. Several special cases have been studied, with illustrations for each case.