Vacuum Solutions of FRW and Axially Symmetric Space–Time in f(R) Theory of Gravity

Abstract

In the present paper an attempt has been made to study the spatially homogeneous and isotropic FRW model and axially symmetric spacetime in f (R) theory of gravity. We have obtained the solutions of the field equations in vacuum. To find the solutions of axially symmetric space-time we have assumed the relation between scale factor and scalar field and also we considered that scalar expansion (θ) in the model is proportional to shear scalar (σ). The physical behavior for both models have been discussed by using physical parameters. The function of Ricci scalar is investigated for these models.

Stability of Axially Symmetric Cosmological Model in Lyra Geometry

“…The field equations ( 6), (10), and ( 11) are three equations in five unknowns . Hence to get a determinate solution, one has to assume the relation between metric coefficients, i.e., and the condition of stiff fluid gives,…”

“…(2) Agrawal et al [10] studied vacuum solutions of FRW and axially symmetric spacetime in f(R) theory of gravity, Mete et al [11] investigated an axially symmetric non-static space-time in the presence of bulk stress in the scalar-tensor theory formulated by Saez and Ballester, Sahoo et al [12] studied an axially symmetric cosmological model in f(R, T) gravity in the presence of perfect fluid. Vinutha et al [13] studied the Kantowski-Sachs perfect fluid cosmological model in R2-Gravity.…”

Fractal FRW model within domain wall

“…Many researchers studied the FRW model within modified theories of gravitation. Samantha et al [15] have studied the bulk viscous fluid in the formalism of f (R, T) theory of gravitation in the frame of flat FRW space-time, Agrawal and Pawar [16] have studied the spatially homogeneous and isotropic FRW model and axially symmetric spacetime in f(R) theory of gravity. Sezgin Aygun [17] studied the behavior of cosmological parameter for flat FRW universe with scalar potential in f (R, T) theory of gravity.…”