Noether symmetry approach to scalar-field-dominated cosmology with dynamically evolving G and Lambda

TL;DR

This paper applies the Noether symmetry approach to a cosmological model with a scalar field, where both G and Lambda vary dynamically, revealing constraints on their functional forms but resulting in complex equations.

Contribution

It demonstrates that Noether symmetry can determine the functional dependence of Lambda on G and the scalar potential in a dynamical G and Lambda cosmology.

Findings

Noether symmetry constrains Lambda as a function of G

It fixes the scalar potential V(Phi)

Results in complex, higher-dimensional equations

Abstract

This paper studies the cosmological equations for a scalar field Phi in the framework of a quantum gravity modified Einstein--Hilbert Lagrangian where G and Lambda are dynamical variables. It is possible to show that there exists a Noether symmetry for the point Lagrangian describing this scheme in a FRW universe. Our main result is that the Noether Symmetry Approach fixes both Lambda = Lambda(G) and the potential V = V(Phi) of the scalar field. The method does not lead, however, to easily solvable equations, by virtue of the higher dimensionality of the reduced configuration space involved, the additional variable being the running Newton coupling.