Cosmology in a locally scale invariant gravity

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'.