Strong energy condition in R+R2 gravity.

In this paper, we study Raychaudhuri's equation in the background of R + βR 2 gravity with a phenomenological matter (ρ ∝ a(t) −n). We conclude that even though the Strong Energy Condition (S.E.C.) for Einstein's gravity, which guarantees singularity, is n ≥ 2 for ρ ∝ a(t) −n , a perturbative analysis of Raychaudhuri's equation in the background of R+βR 2 gravity reveals that the big bang singularity may not be guaranteed for n > 4. We derive the following Strong Energy Conditions for R + βR 2 (β = 0):