J. H. Kung | Searcharxiv

arXiv1995

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

In this paper, we study Raychaudhuri's equation in the background of $R + βR^2$ gravity with a phenomenological matter ($ρ\propto a(t)^{-n}$). We conclude that even though the Strong Energy Condition (S.E.C.) for Einstein's gravity, which guarantees singularity, is $n\geq 2$ for $ρ\propto a(t)^{-n}$, 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 $R + βR^2$ ($β\not= 0$): 1) For $k<0$ FRW metric, S.E.C. is ($0\leq n\leq 4$) i.e., $-ρ_n \leq p_n \leq {1\over 3}ρ_n$. 2) For $k=0$ FRW metric, S.E.C. is ( $1\leq n\leq 4$) i.e., $-{2\over 3}ρ_n \leq p_n \leq {1\over 3}ρ_n$. 3) For $k>0$ FRW metric, S.E.C. is ($2\leq n\leq 4$) i.e., $-{1\over 3}ρ_n \leq p_n \leq {1\over 3}ρ_n$.

gr-qc↗

arXiv1995

$R + R^2$ Gravity as $R +$ Backreaction

Quadratic theory of gravity is a complicated constraint system. We investigate some consequences of treating quadratic terms perturbatively (higher derivative version of backreaction effects). This approach is shown to overcome some well known problems associated with higher derivative theories, i.e., the physical gravitational degree of freedom remains unchanged from those of Einstein gravity. Using such an interpretation of $R + βR^2$ gravity, we investigate a classical and Wheeler DeWitt evolution of $R + βR^2$ gravity for a particular sign of $β$, corresponding to non- tachyon case. Matter is described by a phenomenological $ρ\propto a(t)^{-n}$. It is concluded that both the Friedmann potential $U(a)$ ($ {\dot a}^2 + 2U(a) = 0 $) and the Wheeler DeWitt potential $W(a)$ ($\left[-{\partial^2\over \partial a^2} + 2W(a)\right]ψ(a) =0 $) develop repulsive barriers near $a\approx 0$ for $n>4$ (i.e., $ p > {1\over 3}ρ$). The interpretations is clear. Repulsive barrier in $U(a)$ implies that a contracting FRW universe ($k>0, k=0, k<0$) will bounce to an expansion phase without a total gravitational collapse. Repulsive barrier in $W(a)$ means that $a \approx 0$ is a classically forbidden region. Therefore, probability of finding a universe with the big bang singularity ($a=0$ ) is exponentially suppressed.

gr-qc↗