Quantum effects from particle production on background evolution and Cardy-Verlinde formula in f(R) gravity

We investigate particle production in an expanding universe under the assumption that the Lagrangian contains the Einstein term $R$ plus a modified gravity term of the form $R^\alpha$, where $\alpha$ is a constant. Dark fluid is considered as the main content of the universe and the big rip singularity appears. Quantum effects due to particle creation is analysed near the singularity and we find that for $\alpha\in ]1/2, 1[$, quantum effects are dominant and the big rip may be avoided whereas for $\alpha\in J$ the dark fluid is dominant and the singularity remains. The Cardy-Verlinde formula is also introduced and its equivalence with the total entropy of the universe is checked. It is found that this can always occur in Einstein gravity while in f(R) gravity, it holds only for $\alpha=\frac{n+1}{2n+6}$, $n$ being the space dimension, corresponding to the situation in which the big rip cannot be avoided.Comment: 22 pages, 1 figure, accepted for publication in International Journal of Modern Physics D (IJMPD

Testing some f(R,T) gravity models from energy conditions

We consider $f(R, T)$ theory of gravity, where $R$ is the curvature scalar and $T$ the trace of the energy momentum tensor. Attention is attached to the special case, $f(R, T)= R+2f(T)$ and two expressions are assumed for the function $f(T)$, $\frac{a_1T^n+b_1}{a_2T^n+b_2}$ and $a_3\ln^{q}{(b_3T^m)}$, where $a_1$, $a_2$, $b_1$, $b_2$, $n$, $a_3$, $b_3$, $q$ and $m$ are input parameters. We observe that by adjusting suitably these input parameters, energy conditions can be satisfied. Moreover, an analyse of the perturbations and stabilities of de Sitter solutions and power-law solutions is performed with the use of the two models. The results show that for some values of the input parameters, for which energy conditions are satisfied, de Sitter solutions and power-law solutions may be stables.Comment: 25 pages, 6 figures. Accepted for publication in Journal of Modern Physcis (JMP