$f(R)$ Gravity $k$-Essence Late-time Phenomenology

TL;DR

This paper investigates the late-time cosmological behavior of $k$-Essence $f(R)$ gravity models without scalar potential, showing they can avoid dark energy oscillations and align with observational data, unlike standard $f(R)$ gravity.

Contribution

It introduces a $k$-Essence extension to $f(R)$ gravity that suppresses late-time oscillations and matches Planck data, offering a novel approach to dark energy modeling.

Findings

Higher order kinetic terms eliminate dark energy oscillations.

Models are compatible with Planck data and resemble $ m{ extLambda CDM}$.

Possible negative dark energy density at certain redshifts.

Abstract

In this work we shall study the late-time behavior of $k$-Essence $f(R)$ gravity without scalar potential, in the presence of matter and radiation perfect fluids. We quantify the late-time study by using the statefinder function $Y_H(z)=\frac{\rho_{DE}}{\rho_m^{(0)}}$, which is a function of the redshift and of the Hubble rate. By appropriately rewriting the Friedmann equation in terms of the redshift and of the function $Y_H(z)$, we numerically solve it using appropriate initial conditions, and we critically examine the effects of the $k$-Essence higher order kinetic terms. As we demonstrate, the effect of the higher order scalar field kinetic terms on the late-time dynamics is radical, since the dark energy oscillations are absent, and in addition, the cosmological physical quantities are compatible with the latest Planck data and also the model is almost indistinguishable from the $\Lambda$ Cold Dark Matter model. This is in contrast to the standard $f(R)$ gravity case, where the oscillations are present. Furthermore, by choosing a different set of values of two of the free parameters of the model, and specifically the coefficient of the higher order kinetic term and of the exponent of $R^{\delta}$ appearing in the $f(R)$ action, we demonstrate that it is possible to obtain $\rho_{DE}<0$ for redshifts $z\sim 2-3.8$, which complies phenomenologically with, and seems to explain, the observational data for the same redshifts, and also to obtain a viable cosmological evolution at $z\sim 0$, at least when the dark energy equation of state parameter and the dark energy density parameters are considered.