R+R2gravity asR+ back reaction

Abstract

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 (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 + OR2 theory coupled to matter with a characteristic p oc a(t)-" dependence on the scale factor. We show that for n > 4 (i.e., p > i p ) and for a particular sign of P, 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 PR2 as a perturbation. We conclude that the potential W(a), in the Wheeler-DeWitt equation [-a2/6'a2 + 2~( a ) ] $(a) = 0, develops a repulsive barrier near a --0 again for n > 4 (i.e., p > i p ) and for the sign of P that corresponds to the nontachyon case. Since a % 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 IPl. It is also shown that, to first order in p, the PR' term has no effect during the radiation (p = Sp) and inflationary (p = -p) era. Therefore, a de Sitter phase can be readily generated by incorporating a scalar field.PACS number(s): 04.50.+h, 98.80.H~

Energy conditions in modified f(G) gravity

“…Similarly, the cosmic acceleration followed by matter era could also be explained by means of some viable models in f (G) gravity [34,35]. Different consistent f (G) models were proposed in order to pass certain solar system constraints [34,35] which are discussed in [38] and additional bounds on f (G) models may arise from the analysis of energy conditions (ECs) [39][40][41]. Nojiri et al [42] have discussed some fundamental cosmic issues, like inflation, late-time acceleration, bouncing cosmology and claimed that some modified theories of gravity, like f (R), f (G) and f (T ) theories (where T is the torsion scalar) could be used as a viable mathematical tool for analyzing the clear picture of our universe.…”

“…There has been an interested results found on the exploration of dark source terms on the dynamical evolution of stellar systems in Einstein-Λ [26], f (R) [27], f (R, T ) [28] (T is the trace of energy momentum tensor) and f (R, T, R µν T µν ) gravity [29]. Among MGTs, available in the literature, the one is Gauss Bonnet (GB) gravity which has received great attraction [30][31][32][33][34][35][36][37][38][39][40] and is named as f (G) gravity, where…”

Energy conditions in modified Gauss-Bonnet gravity

“…The energy conditions have been extensively analyzed in the literature, such as in the cosmology settings and f (R) gravity and we refer the reader to Refs. [14,15] for more details.…”

Modified f(G) gravity models with curvature–matter coupling

“…The energy conditions arise when one refers to the Raychaudhuri equation for the expansion [21]. Under these energy conditions, one allows not only to establish gravity which remains attractive, but also to keep the demands that the energy density is positive and cannot flow faster than light.…”