Cosmological dynamics in R2 gravity with logarithmic trace term

arXiv:1907.05223v2
A novel function for modified gravity is proposed, f(R,T)=R+λR2+2βln(T), with constants λ and β, scalar curvature R, and the trace of stress energy tensor T, satisfying T=ρ−3p>0. Subsequently, two equations of state (EoS) parameters, namely ω 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 red shift z within the range 0.07≤z≤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 thebouncing point t=0, what shows that the necessary condition for violation of the null energycondition, within a neighborhood of the bouncing point in general relativity, could be avoided bymodifying 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.
This work was partially supported by MINECO (Spain), FIS2016-76363-P, by the CPAN Consolider Ingenio 2010 Project, and by AGAUR (Catalan Government), Spain, project 2017-SGR-247. The work of author GCS is supported by CSIR, India Grant No. 25(0260)/17/EMR-II.