# $F(R)$ gravity in the early Universe: Electroweak phase transition and chameleon mechanism

## TL;DR

This paper explores the quantum effects on the chameleon mechanism within $F(R)$ gravity during the electroweak phase transition, suggesting potential absence of the mechanism in early Universe scenarios and discussing related scalaron dynamics.

## Contribution

It introduces a new formulation of the chameleon mechanism considering quantum effects and analyzes its behavior during the electroweak phase transition in $F(R)$ gravity.

## Key findings

- Potential absence of the chameleon mechanism in early Universe
- Matter sector contribution matches classical approximation
- Scalaron oscillations and gravitational wave implications

## Abstract

It is widely believed that the screening mechanism is an essential feature for the modified gravity theory. Although this mechanism has been examined thoroughly in the past decade, their analyses are based on the classical configuration of the matter fields. In this paper, we demonstrate a new formulation of the chameleon mechanism in $F(R)$ gravity theory, to shed light on quantum-field theoretical effects on the chameleon mechanism as well as the related scalaron physics, induced by the matter sector. We show a potential absence of the chameleon mechanism in the cosmic history based on a scale-invariant-extended scenario beyond the standard model of particle physics, in which a realistic electroweak phase transition, possibly yielding the right amount of baryon asymmetry of Universe today, simultaneously breaks the scale invariance in the early Universe. Remarkably enough, the matter sector contribution to the trace of energy-momentum tensor turns out to be on the same order of magnitude as that computed in the classical perfect-fluid approximation, even though the theory involves the nontrivial electroweak-phase transition environment. We also briefly discuss the oscillation of the scalaron field and indirect generation of non-tensorial gravitational waves induced by the electroweak phase transition.