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 analyzed near the singularity and we find that for alpha is an element of ]1/2, 1[, quantum effects are dominant and the big rip may be avoided whereas for alpha is an element of 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 = n+1/2n+6, n being the space dimension, corresponding to the situation in which the big rip cannot be avoided.