Bottom-up reconstruction of non-singular bounce in F(R) gravity from observational indices

TL;DR

This paper develops a method to reconstruct non-singular bouncing cosmologies in F(R) gravity using observable indices, leveraging conformal transformations to connect with scalar-tensor inflationary models and ensure observational viability.

Contribution

It introduces a bottom-up reconstruction approach for F(R) bouncing models based on observable indices, utilizing conformal correspondence with scalar-tensor theories.

Findings

Constructed a viable non-singular bounce in F(R) gravity.

Demonstrated the invariance of perturbations under conformal transformation.

Linked bouncing models to inflationary observables through scalar-tensor correspondence.

Abstract

We apply the bottom-up reconstruction technique in the context of bouncing cosmology in F(R) gravity, where the starting point is a suitable ansatz of observable quantity (like spectral index or tensor to scalar ratio) rather than a priori form of Hubble parameter. In inflationary scenario, the slow roll conditions are assumed to hold true, and thus the observational indices have general expressions in terms of the slow-roll parameters, as for example the tensor to scalar ratio in F(R) inflation can be expressed as $r = 48\epsilon_F^2$ with $\epsilon_F = -\frac{1}{H_F^2}\frac{dH_F}{dt_F}$ and $H_F$, $t_F$ are the Hubble parameter, cosmic time respectively. However, in the bouncing cosmology (say in F(R) gravity theory), the slow-roll conditions are not satisfied, in general, and thus the observable quantities do not have any general expressions that will hold true irrespective of the form of F(R). Thus, in order to apply the bottom-up reconstruction procedure in F(R) bouncing model, we use the conformal correspondence between F(R) and scalar-tensor model where the conformal factor in the present context is chosen in a way such that it leads to an inflationary scenario in the scalar-tensor frame. Due to the reason that the scalar and tensor perturbations remain invariant under conformal transformation, the observable viability of the scalar-tensor inflationary model confirms the viability of the conformally connected F(R) bouncing model. Motivated by these arguments, here we construct a viable non-singular bounce in F(R) gravity directly from the observable indices of the corresponding scalar-tensor inflationary model.