$f(R)$ gravity with broken Weyl gauge symmetry, cosmological backreaction, and its effects on CMB anisotropy (2209.02277v3)

Abstract: We propose a new class of $f(R)$ theory where its Weyl gauge symmetry is broken in the primordial era of the universe. This symmetry forces one to adopt a new scalar field, namely a Weyl field and a gauge vector boson. Furthermore, an equivalent form of the Einstein-Hilbert Lagrangian with a non-minimally coupled scalar field corresponding to the function $f(R)$ is found. Due to the geometrical feature of the Weyl field, it turns out that the symmetry breaking induces a non-minimal coupling, which cannot be expected in the standard $f(R)$ theories. We explain how this affects the evolution of the universe at cosmological scales. It is shown that there may be a value shift in the Planck constant and the cosmological constant. This can be regarded as a genuine exemplification of the cosmological backreaction. Furthermore, one also finds new features in the evolution of perturbational variables and cosmic microwave background anisotropy. Moreover, we prove that when a specific $f(R)$ model invokes inflation, the amplitude of the primordial gravitational waves affects the evolution of scalar perturbation due to the new non-minimal coupling. As a case study, we explain how this can be embodied in the Starobinsky inflation. Finally, we discuss some impacts that this physics can bear and the possibility of giving a new restriction of the estimation of cosmological variables such as the gravitational wave amplitude with experiments.