On the cosmological solutions in Weyl geometry

TL;DR

This paper explores homogeneous and isotropic cosmological solutions within Weyl geometry, deriving conditions for conformal invariance and discovering new vacuum and radiation-dominated solutions that differ from General Relativity, with implications for dark matter and energy.

Contribution

It introduces new vacuum and radiation-dominated cosmological solutions in Weyl geometry, expanding understanding beyond General Relativity and exploring conformal invariance conditions.

Findings

Found new vacuum solutions absent in General Relativity.

Discovered solutions for radiation-dominated universe with cosmological term.

Discussed potential links to dark matter and dark energy.

Abstract

We investigated the possibility of construction the homogeneous and isotropic cosmological solutions in Weyl geometry. We derived the self-consistency condition which ensures the conformal invariance of the complete set of equations of motion. There is the special gauge in choosing the conformal factor when the Weyl vector equals zero. In this gauge we found new vacuum cosmological solutions absent in General Relativity. Also, we found new solution in Weyl geometry for the radiation dominated universe with the cosmological term, corresponding to the constant curvature scalar in our special gauge. Possible relation of our results to the understanding both dark matter and dark energy is discussed.