Reconstructed f (R) Gravity and Its Cosmological Consequences in theChameleon Scalar Field with a Scale Factor Describing the Pre-Bounce Ekpyrotic Contraction

Abstract

The present study reports a reconstruction scheme for f(R) gravity with the scale factor a(t) ∝ (t∗ − t) 2 c 2 describing the pre-bounce ekpyrotic contraction, where t∗ is the big crunch time. The reconstructed f(R) is used to derive expressions for density and pressure contributions, and the equation of state parameter resulting from this reconstruction is found to behave like “quintom”. It has also been observed that the reconstructed f(R) has satisfied a sufficient condition for a realistic model. In the subsequent phase, the reconstructed f(R) is applied to the model of the chameleon scalar field, and the scalar field φ and the potential V(φ) are tested for quasi-exponential expansion. It has been observed that although the reconstructed f(R) satisfies one of the sufficient conditions for realistic model, the quasi-exponential expansion is not available due to this reconstruction. Finally, the consequences of pre-bounce ekpyrotic inflation in f(R) gravity are compared to the background solution for f(R) matter bounce.