R+R(2) gravity as R+ back reaction

The quadratic theory of gravity is a complicated constraint system. We investigate some consequences of treating quadratic terms perturbatively (higher derivative version of back reaction effects), which is consistent with the way the existence of quadratic terms was originally established (radiactive 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 + beta R(2) theory coupled to matter with a characteristic rho proportional to a(t)(-n) dependence on the scale factor. We show that for n > 4 (i.e., p > 1/3 rho) and for a particular sign of beta, corresponding to the nontachyon 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 minisuperspace model that resulted from treating the beta R(2) as a perturbation. We conclude that the potential W(a), in the Wheeler-DeWitt equation [-partial derivative(2)/partial derivative a(2) + 2W(a)] psi(a) = 0, develops a repulsive barrier near a approximate to 0 again for n > 4 (i.e., p > 1/3 rho) and for the sign of beta that corresponds to the nontachyon case. Since a approximate to 0 is a classically forbidden region, the probability of finding a universe with a singularity (a = 0) is exponentially suppressed. Unlike the quantum cosmology of Einstein's gravity, the formalism has dictated an appropriate boundary (initial) condition. Classical and quantum analyses demonstrate that a minimum radius of collapse increases for a larger value of \beta\. It is also shown that, to first order in beta, the beta R(2) term has no effect during the radiation (p = 1/3 rho) and inflationary (p = -rho) era. Therefore, a de Sitter phase can be readily generated by incorporating a scalar held.