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)2c2 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.

A Study on the Various Aspects of Bounce Realisation for Some Choices of Scale Factors

“…After bouncing out of the Hubble radius, the fluctuations re-enter the inner regions of the horizon during the expanding phase. Now, we have thought about the e-folding time scale N [141,142], which is the base-e equivalent of doubling time in physics, is the period of time during which an exponentially expanding quantity rises by a factor of exp, related to the scale factor as given in spite of cosmic time t:…”

A truncated scale factor to realize cosmological bounce under the purview of modified gravity

“…In a very recent study, Chattopadhyay (2023) demonstrated bounce realization in $$$ f(T) $$$ gravity with exponential and power‐law forms of scale factor and indicated the possibility of realization of nonsingular holographic bounce. Pre‐bounce ekpyrotic contraction under $$$ f(R) $$$ gravity and in presence of chameleon scalar field was reported in Karmakar et al (2020) and bounce realization of the universe with a form of Chaplygin gas in modified gravity framework was discussed in Chattopadhyay (2017), where the role of the model parameters of the modified Chaplygin gas was investigated before and after the bounce scenario. Occurrence of type IV singularity at the bouncing point in the context of $$$ F(R) $$$ modified gravity and the evolution of the Hubble radius with the primordial cosmological perturbations were demonstrated in Odintsov & Oikonomou (2017).…”

Cosmological bounce in a modified gravity framework

“…The current advances in cosmology have made it possible to access several cosmological data, including the scalar spectral index and tensor‐to‐scalar ratio that describe the early universe and the late time equation of state parameters s (Odintsov & Oikonomou 2022). Inflation, a cosmological scenario, successfully illustrates the early stage of the universe (Bamba et al 2014, 2015; Karmakar et al 2020; S. Nojiri et al 2017; Odintsov & Paul 2022). It gives a solution to the horizon and flatness problems and it is consistent with the recent Planck data.…”