Reconstruction of f(R) models with Scale-invariant Power Spectrum

TL;DR

This paper reconstructs $f(R)$ gravity models that naturally produce a scale-invariant power spectrum, linking them to scalar field theories without extra fields, and provides numerical analysis of these models.

Contribution

It offers a method to reconstruct $f(R)$ models corresponding to scale-invariant spectra, avoiding additional scalar fields and establishing a direct Einstein frame correspondence.

Findings

Reconstructed $f(R)$ models consistent with scale-invariant spectra.

Numerical plots of $f(R)$ functional form and $R(t)$ evolution.

Established one-to-one correspondence between $f(R)$ and Einstein frame models.

Abstract

Following our previous work in [JCAP 1206, 041 (2012)], in this paper, we continue our study of reconstructing $f(R)$ modified gravity models that can be connected to a single scalar field in general relativity via conformal transformation, which lead to scale-invariant power spectrum in the early universe. With $f(R)$ modified gravity, one does not need to introduce extra scalar, the nature of which are to be explained. Different from general nonminimal coupling theory, the behavior of the $f(R)$ theory has been fixed by its counterpart in Einstein frame, and thus have one to one correspondence. Numerical plots of the functional form of $f(R)$ as well as the evolution of $R$ in terms of cosmic time $t$ are also presented.