Bounding $f(R)$ gravity by particle production rate

TL;DR

This paper constrains $f(R)$ gravity models by analyzing quantum vacuum states and particle production rates, linking cosmological observations with quantum field theory to refine model parameters.

Contribution

It introduces a method to constrain $f(R)$ models using Bogolubov transformations and particle production rates in both metric and Palatini formalisms.

Findings

Constraints on $f(R)$ parameters consistent with high redshift data.

Particle production rates linked to the Hubble parameter and $f(R)$ models.

Method applicable to both metric and Palatini formalisms.

Abstract

Several models of $f(R)$ gravity have been proposed in order to address the dark side problem in cosmology. However, these models should be constrained also at ultraviolet scales in order to achieve some correct fundamental interpretation. Here we analyze this possibility comparing quantum vacuum states in given $f(R)$ cosmological backgrounds. Specifically, we compare the Bogolubov transformations associated to different vacuum states for some $f(R)$ models. The procedure consists in fixing the $f(R)$ free parameters by requiring that the Bogolubov coefficients can be correspondingly minimized to be in agreement with both high redshift observations and quantum field theory predictions. In such a way, the particle production is related to the value of the Hubble parameter and then to the given $f(R)$ model. The approach is developed in both metric and Palatini formalism.