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

We consider a cosmological model in a Friedmann-Lemaitre-Robertson-Walker background space with an ideal gas defined in Weyl Integrable gravity. In the Weyl-Einstein 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 analytic solutions in Weyl Integrable cosmology. Some closed-form expressions for the Hubble function are presented.

Automated summary

This article investigates a cosmological model in a Friedmann-Lemaitre-Robertson-Walker background space, characterized by an ideal gas in Weyl Integrable gravity. A scalar field is introduced in a geometric way in the Weyl-Einstein gravity. The scalar field and the ideal gas interact in the gravitational Action Integral. Additionally, a potential term for the scalar field potential is introduced, and it is shown that the field equations can be described in a minisuperspace. The constraint of the potential function is analyzed using Noether's theorem, and corresponding conservation laws are established. Furthermore, a family of new analytic solutions in Weyl Integrable cosmology is derived by solving the Hamilton-Jacobi equation for the cosmological model, and closed-form expressions for the Hubble function are presented.