Locally rotationally symmetric Bianchi type-II cosmological model in f(R, T) gravity

Abstract

The present work is focused on the study of locally rotationally symmetric Bianchi type-II model with perfect fluid in f(R, T) gravity. Three types of f(R, T) gravity models are proposed (Harko et al. in Phys Rev D 84:024020, 2011). According to the first model, the function $$f(R,T)=R+2f(T)$$ , where R is Ricci scalar and f(T) is an arbitrary function of trace of stress energy tensor T. In this paper, the function $$f(T) = \alpha T + \beta T^2$$ is considered, where $$\alpha$$ and $$\beta$$ are real numbers. The physical parameters are determined with respect to cosmic time as well as red shift by using the equation of state $$p=\epsilon \rho$$ and the scale factor $$a(t) = (\sinh (\phi t))^{\frac{1}{k}}$$ , where $$k>0$$ & $$\phi \ne 0$$ . The energy density is compared for dust and radiation-dominated models. The present values of deceleration parameter, Hubble parameter and age of the universe are determined and compared with the results of $$\Lambda$$ CDM model. Further, the theoretical and experimental values of luminosity distance and apparent magnitude are compared.