Strong Energy Condition in $R + R^2$ Gravity

Details Strong Energy Condition in $R + R^2$ Gravity Strong Energy Condition in $R + R^2$ Gravity

1995-10-04

arxiv.org/abs/gr-qc/9510008v1

Phys.Rev.D53:3017-3021,1996

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

Submitted to Phy. Rev. D.,15 pages, 2 figures, Latex file

Scientific paper

10.1103/PhysRevD.53.3017

In this paper, we study Raychaudhuri's equation in the background of $R + \beta R^2$ gravity with a phenomenological matter ($\rho \propto a(t)^{-n}$). We conclude that even though the Strong Energy Condition (S.E.C.) for Einstein's gravity, which guarantees singularity, is $n\geq 2$ for $\rho \propto a(t)^{-n}$, a perturbative analysis of Raychaudhuri's equation in the background of $R + \beta R^2$ gravity reveals that the big bang singularity may not be guaranteed for $n > 4$. We derive the following Strong Energy Conditions for $R + \beta R^2$ ($\beta \not= 0$): 1) For $k<0$ FRW metric, S.E.C. is ($0\leq n\leq 4$) i.e., $-\rho_n \leq p_n \leq {1\over 3}\rho_n$. 2) For $k=0$ FRW metric, S.E.C. is ( $1\leq n\leq 4$) i.e., $-{2\over 3}\rho_n \leq p_n \leq {1\over 3}\rho_n$. 3) For $k>0$ FRW metric, S.E.C. is ($2\leq n\leq 4$) i.e., $-{1\over 3}\rho_n \leq p_n \leq {1\over 3}\rho_n$.

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