Noether analysis of Scalar-Tensor Cosmology

Understand

A scalar--tensor theory of gravity, containing an arbitrary coupling function $F(\phi)$ and a general potential $V(\phi)$, is considered in the context of a spatially flat FLRW model.

• The use of reparametrization invariance enables a particular lapse parametrization in which the mini--superspace metric completely specifies the dynamics of the system.
• A requirement of existence of the maximal possible number of autonomous integrals of motion is imposed.
• This leads to a flat mini--superspace metric realized by a particular relation between the coupling function and the potential.