The study of Kantowski-Sachs perfect fluid cosmological model in modified gravity

Kantowski-Sachs perfect fluid cosmological model is explored in modified gravity with functional form $f(R, T)$=$f_1(R)$+$f_2(T)$ where $R$ is Ricci scalar, and $T$ is the trace of the energy-momentum 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 $f_1(R)=R+\gamma R^2-\frac{\mu^4}{R}$, $f_1(R)=R+\nu ln(\tau R)$ and $f_1(R)=R+\kappa e^{-\iota R}$ respectively. For all these three cases, $f_2(T)=\lambda T$, here $\gamma$, $\lambda$, $\mu$, $\nu$, $\tau$, $\kappa$ and $\iota$ are constants. While solving the field equations, two constraints i) the Expansion scalar is proportional to shear scalar ii) the Hyperbolic scale factor is used. By using these conditions, the required optimum solutions are obtained. The physical parameters are calculated, and the geometrical parameters of three cases are analyzed 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 a strong energy condition is positive, gravity should be attractive but in our model, it shows negative, which 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 persistent with the present cosmological observations, and the model represents an accelerating universe.