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

Understand

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.