PREPRINT
056C832F-39B3-435F-9139-FBCA02A5A9F5

# $f\left(R\right)$ gravity with a broken Weyl gauge symmetry, CMB anisotropy and Integrated-Sachs-Wolfe effect

Jiwon Park, Tae Hoon Lee
arXiv:2209.02277

Submitted on 6 September 2022

## Abstract

We propose a new class of $f\left(R\right)$ theory where its Weyl gauge symmetry is broken in the primordial era of the universe. We prove that, even though the theory is transformed into the Einstein-Hilbert action with a non-minimally coupled scalar field at the non-perturbative level, there exists an additional non-minimal coupling at the perturbational level. As an important example, we study its effect on Staronbinsky inflation. We show that the amplitude of the primordial gravitational waves also affects scalar perturbation due to the presence of the non-minimal coupling, although its effect on cosmic microwave background(CMB) anisotropy is negligible in practice. Consequently, CMB observables may have distinct values depending only on the mass of the perturbed Weyl field. Moreover, we discuss the possibility of resolving Hubble tension with this example, including an analysis of the integrated-Sachs-Wolfe effect.

## Preprint

Comment: 11 pages, 7 figures

Subjects: General Relativity and Quantum Cosmology; Astrophysics - Cosmology and Nongalactic Astrophysics