The Study of Kantowski-Sachs Perfect Fluid Cosmological Model in Modified Gravity

Abstract

Kantowski-Sachs perfect fluid cosmological model is explored in modified gravity with functional form f (R, T) = f₁(R) + f₂ (T) where R is Ricci scalar and T is the trace of energymomentum tensor. With this functional form, three different cases have been formulated, namely negative and positive powers of curvature, logarithmic curvature and exponential curvature given by f₁ (R) = R + γ R² – μ⁴ / R, f₁(R) = R+ v ln(τR) and f₁(R) = R+ κe^–ιR respectively, and for all these three cases, f₂ (T) = λT, here γ,λ,μ,v,τ,κ and ι are constants. While solving the field equations, two constraints i) Expansion scalar is proportional to shear scalar ii) Hyperbolic scale factor are used. By using these conditions the required optimum solutions are obtained. The physical parameters are calculated and geometrical parameters of three cases are analysed against redshift z with the help of pictorial representation. In the context of f (R, T) gravity energy conditions are discussed with the help of pressure and energy density. If strong energy condition is positive the gravity should be attractive but in our model it is negative. It means that cosmic acceleration is due to antigravity, whereas NEC and DEC are fulfilled. The perturbation technique is used to test the stability of the background solutions of the obtained models. The inferences obtained from this paper are in persistent with the present cosmological observations and the model represents an accelerating universe.