Cosmological particle creation in Weyl geometry

TL;DR

This paper explores cosmological solutions in Weyl geometry, demonstrating how matter particles can be created from vacuum through quadratic curvature terms and Weyl vector interactions, with implications for dark matter.

Contribution

It introduces a conformally invariant quadratic curvature gravity model in Weyl geometry and analyzes matter creation, including potential dark matter candidates, from vacuum.

Findings

Perfect fluid particles can be created from vacuum in this model.

Vacuum can persist against non-dust matter creation but not against dust particles.

Created dust particles may serve as dark matter candidates.

Abstract

We investigated the possibility of the homogeneous and isotropic cosmological solution in Weyl geometry, which differs from the Riemannian geometry by adding the so called Weyl vector. The Weyl gravity is obtained by constructing the gravitational Lagrangian both to be quadratic in curvatures and conformal invariant. It is found that such solution may exist provided there exists the direct interaction between the Weyl vector and the matter fields. Assuming the matter Lagrangian is that of the perfect fluid, we found how such an interaction can be implemented. Due to the existence of quadratic curvature terms and the direct interaction the perfect fluid particles may be created straight from the vacuum, and we found the expression for the rate of their production which appeared to be conformal invariant. In the case of creating the universe ``from nothing'' in the vacuum state, we investigated the problem, whether this vacuum may persist or not. It is shown that the vacuum may persist with respect to producing the non-dust matter (with positive pressure), but cannot resist to producing the dust particles. These particles, being non-interactive, may be considered as the candidates for dark matter.