Noether symmetry approach in pure gravity with variable G and Lambda

TL;DR

This paper uses Noether symmetry to find exact solutions in cosmology with variable G and Lambda, revealing new relations and power-law inflation in pure gravity models.

Contribution

It introduces a novel application of Noether symmetry to derive exact solutions with dynamic G and Lambda, generalizing previous cosmological models.

Findings

Derived new functional relations between Lambda and G.

Found exact solutions exhibiting power-law inflation.

Generalized symmetry principles in cosmology.

Abstract

We find exact cosmological solutions when the Newton parameter and the cosmological term are dynamically evolving in a renormalization-group improved Hamiltonian approach. In our derivation we use the Noether symmetry approach, leading to an interesting variable transformation which yields exact and general integration of the cosmological equations. The functional dependence of Lambda on G is determined by the method itself, therefore generalizing previous results on symmetry principles in cosmology. We find new functional relations between Lambda and G, jointly with power-law inflation for pure gravity.