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

Understand

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.