Abstract
We reconstruct F(R) gravity models with exponential and power-law forms of the scale factor in which bounce cosmology can be realized. We explore the stability of the reconstructed models with analyzing the perturbations from the background solutions. Furthermore, we study an F(R) gravity model with a sum of exponentials form of the scale factor, where the bounce in the early universe as well as the late-time cosmic acceleration can be realized in a unified manner. As a result, we build a second order polynomial type model in terms of R and show that it could be stable. Moreover, when the scale factor is expressed by an exponential form, we derive F(R) gravity models of a polynomial type in case of the non-zero spatial curvature and that of a generic type in that of the zero spatial curvature. In addition, for an exponential form of the scale factor, an F(R) bigravity model realizing the bouncing behavior is reconstructed. It is found that in both the physical and reference metrics the bouncing phenomenon can occur, although in general the contraction and expansion rates are different each other.
Highlights
We reconstruct F (R) gravity models with exponential and power-law forms of the scale factor in which bounce cosmology can be realized
We study an F (R) gravity model with a sum of exponentials form of the scale factor, where the bounce in the early universe as well as the late-time cosmic acceleration can be realized in a unified manner
When the scale factor is given by an exponential form in eq (6.6), with the reconstruction method [120,121,122,123], we find F (R) gravity models with realizing the bounce cosmology
Summary
We examine the case that the scale factor is expressed by an exponential form. For instance, we consider a bouncing solution which behaves as a(t) ∼ eαt. It should clearly be mentioned that the metric with the scale factor (3.1) does not have a finite maximum in the Riemann curvature, whereas the Riemann curvature takes its minimum by modulus in the bounce epoch This space-time is irrelevant to the thing necessary to remove a cosmological singularity. Starobinsky inflation occurs, the scale factor at the slow-roll inflationary stage is given by a(t) ∝ exp H1t − M 2t2/12 , where H1 and M are constants with the dimension of mass. We explore the stability with respect to tensor perturbations, namely, the required condition F (R) > 0 It follows from the second relation in (3.5) with the first one in (3.4) and eq (3.8) that we have F (R) = (2/α) (R − 36α) = 48 2αt − .
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