New exact and analytic solutions in Weyl Integrable cosmology from Noether symmetry analysis

TL;DR

This paper derives new exact and analytic solutions in Weyl Integrable cosmology by applying Noether symmetry analysis, revealing conserved quantities and solving the Hamilton-Jacobi equation for a scalar field interacting with an ideal gas.

Contribution

The study introduces a novel application of Noether symmetry to find exact solutions in Weyl Integrable cosmology with a scalar field and ideal gas, including explicit expressions for the Hubble function.

Findings

New family of solutions in Weyl Integrable cosmology.

Conserved quantities derived from Noether symmetries.

Explicit forms of the Hubble function obtained.

Abstract

We consider a cosmological model in a Friedmann--Lema\^{\i}tre--Robertson--Walker background space with an ideal gas defined in Weyl Integrable gravity. In the Einstein-Weyl theory a scalar field is introduced in a geometric way. Furthermore, the scalar field and the ideal gas interact in the gravitational Action Integral. Furthermore, we introduce a potential term for the scalar field potential and we show that the field equations admit a minisuperspace description. Noether's theorem is applied for the constraint of the potential function and the corresponding conservation laws are constructed. Finally, we solve the Hamilton-Jacobi equation for the cosmological model and we derive a family of new solutions in Weyl Integrable cosmology. Some closed-form expressions for the Hubble function are presented.