Cosmological dynamics in $R^2$ gravity with logarithmic trace term

Abstract

A novel function for modified gravity is proposed, $f(R,T)=R+\lambda R^2+2\beta \ln (T)$, with constants $\lambda$ and $\beta$, scalar curvature $R$, and the trace of stress energy tensor $T$, satisfying $T=\rho -3p>0$. Subsequently, two equations of state (EoS) parameters, namely $\omega$ and a parametric form of the Hubble parameter $H$, are employed in order to study the accelerated expansion and initial cosmological bounce of the corresponding universe. Hubble telescope experimental data for redshift $z$ within the range $0.07\le z\le 2.34$ are used to compare the theoretical and observational values of the Hubble parameter. Moreover, it is observed that all the energy conditions are fulfilled within a neighborhood of the bouncing point $t=0$, what shows that the necessary condition for violation of the null energy condition, within a neighborhood of the bouncing point in general relativity, could be avoided by modifying the theory in a reasonable way. Furthermore, a large amount of negative pressure is found, which helps to understand the late time accelerated expansion phase of the universe.

27 pages and 30 figures, accepted in Physics of the Dark Universe