R + R 2 Gravity as R+ Backreaction 1

Quadratic theory of gravity is a complicated constraint system. We investigate some consequences of treating quadratic terms perturbatively (higher derivative version of backre-action effects), which is consistent with the way existence of quadratic terms was originally established (radiative loop effects and renormalization procedures which induced quadratic terms). We show that this approach overcomes 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 approach, we first study the classical cosmology of R + βR 2 theory coupled to matter with a characteristic ρ ∝ a(t) −n dependence on the scale factor. We show that 1 3 ρ) and for a particular sign of β, corresponding to non-tachyon case, there is no big bang in the traditional sense. And therefore, a contracting FRW universe (k > 0, k = 0, k < 0) will rebounce to an expansion phase without a total gravitational collapse. We then quantize the corresponding mini-superspace model that resulted from treating the βR 2 as a perturbation. We conclude that the potential W (a), in the Wheeler DeWitt equation − ∂ 2 ∂a 2 + 2W (a) ψ(a) = 0, develops a repulsive barrier near a ≈ 0 again for n > 1 3 ρ) and for the sign of β that corresponds to non-tachyon case. sign of β. Since a ≈ 0 is a classically forbidden region, the probability of finding a universe with singularity (a = 0) is exponentially suppressed. Unlike quantum cosmology of Einstein's gravity, the formalism has dictated an appropriate boundary (initial) condition. Classical and quantum analysis demonstrate that a minimum radius of collapse increases for a larger value of |β|. It is also shown that, to first order in β, βR 2 term has no effect during the radiation (p = 1 3 ρ) and inflationary (p = −ρ) era. Therefore, a deSitter phase can be readily generated by incorporating a scalar field.