Cosmology in a locally scale invariant gravity

TL;DR

This paper proposes a Weyl-invariant scalar-tensor cosmological model featuring a bouncing universe, where cosmic evolution is driven by a complex scalar field, potentially explaining dark sector phenomena without singularities.

Contribution

It introduces a novel Weyl-invariant scalar-tensor theory with a conserved charge, modeling a non-singular bouncing universe and addressing dark sector dynamics.

Findings

The model predicts a stable, non-singular bounce in the early universe.

Cosmological redshift arises from the evolution of the Rydberg constant.

The theory naturally avoids horizon and flatness problems.

Abstract

A `bouncing' cosmological model is proposed in the context of a Weyl-invariant scalar-tensor (WIST) theory of gravity. In addition to being Weyl-invariant the theory is U(1)-symmetric and has a conserved global charge. The entire cosmic background evolution is accounted for by a complex scalar field that evolves in the static `comoving' frame. Its (dimensional) modulus $\chi$ regulates the dynamics of masses and the apparent space expansion. Cosmological redshift is essentially due to the cosmic evolution of the Rydberg constant in the comoving frame. The temporal evolution of $\chi$ is analogous to that of a point particle in the presence of a central potential $V(\chi)$. The scalar field sources the spacetime curvature; as such it can account for the (cosmological) Dark Sector. An interplay between the energy density of radiation and that of the kinetic energy associated with the phase $\alpha$ of the scalar field (which are of opposite signs) results in a classical non-singular stable and nearly-symmetric bouncing dynamics deep in the radiation-dominated era. This encompasses the observed redshifting era which preceded by a `bounce' that follows a blushifting era. The model is essentially free of the horizon or flatness problems. Big Bang nucleosynthesis sets a lower 1-10 MeV bound on the typical energy scale at the `bounce'.