f(R) Gravity with k-essence scaling relation and Cosmic acceleration

TL;DR

This paper explores a modified gravity model with f(R)=R^2 coupled to a k-essence scalar field, demonstrating scenarios of early inflation and late-time acceleration consistent with cosmological observations.

Contribution

It introduces a novel f(R) gravity framework with k-essence coupling and derives conditions for accelerated cosmic expansion, extending previous models with new scalar field dynamics.

Findings

Multiple cosmological scenarios including inflation and acceleration.

Conditions for accelerated expansion based on the power n in f(R)=R^n.

Small-time behavior of the scalar field as an inflaton.

Abstract

A modified gravity theory with $f(R)=R^2$ coupled to a dark energy lagrangian $L=-V(\phi)F(X)$ , $X=\nabla_{\mu}\phi\nabla^{\mu}\phi$, gives plausible cosmological scenarios when the modified Friedman equations are solved subject to the scaling relation $X (\frac{dF}{dX})^{2}=Ca(t)^{-6}$. This relation is already known to be valid, for constant potential $V(\phi)$, when $L$ is coupled to Einstein gravity. $\phi$ is the k-essence scalar field and $a(t)$ is the scale factor. The various scenarios are: (1) Radiation dominated Ricci flat universe with deceleration parameter $Q=1$. The solution for $\phi$ is an inflaton field for small times. (2) $Q$ is always negative and we have accelerated expansion of the universe right from the beginning of time and $\phi$ is an inflaton for small times. (3)The deceleration parameter $Q= -5$, i.e. we have an accelerated expansion of the universe. $\phi$ is an inflaton for small times.(4)A generalisation to $f(R)= R^n$ shows that whenever $n > 1.780$ or $n < - 0.280$ , $Q$ will be negative and we will have accelerated expansion of the universe. At small times $\phi$ is again an inflaton.