Bianchi type cosmological models in f(R, T) theory with quadratic functional form

Abstract

The spatially homogeneous and anisotropic Bianchi type-III, V and VI$$_{0}$$ cosmological models have been investigated in f(R, T) gravity by choosing the function f(R, T) of the form $$R+\alpha R^2+\lambda T$$. Here, R is the Ricci scalar, T is the trace of the energy momentum tensor and $$\alpha $$, $$\lambda $$ are constants. Exact solutions to the field equations of three models are obtained with the help of hybrid scale factor and the proportionality of shear scalar with expansion scalar (i.e., $$\sigma \propto \theta $$). We have calculated some physical and geometrical properties of the models and their behavior is thoroughly studied with the help of their plots with respect to redshift (z). It is observed that for all three models, pressure (p) is negative and energy density ($$\rho $$) is positive. In case of Bianchi type-V, VI$$_{0}$$ models, the EoS parameter exhibits quintom-like behavior. Also, by using $$f(R,T)=R+\alpha R^2+\lambda T$$ functional form, we have studied all energy conditions for three models. At present ($$z=0$$), the energy conditions particularly NEC and DEC are fulfilled, and SEC is violated for all three models which supports the accelerating expansion of the universe. The advantage of choosing this functional form is that it gives the asymptotically exact de Sitter solution and also the obtained values of physical parameters matches with the current observational data.