Why Noether symmetry of F(R) theory yields three-half power law?

TL;DR

This paper demonstrates that Noether symmetry in F(R) gravity leads to a unique three-half power law of R, which simplifies the cosmological model and provides insights into early universe evolution, though less so for late stages.

Contribution

It shows that the three-half power law of R arises from Noether symmetry in F(R) gravity and explores its implications for cosmological solutions and the Palatini approach.

Findings

The three-half power law of R is derived from Noether symmetry.

This power law yields a unique solution useful for early universe modeling.

The Palatini variational technique offers additional insights into the solutions.

Abstract

Noether symmetry of F(R) theory of gravity in vacuum or in matter dominated era yields three-half power law of R. We show that this particular curvature invariant term is very special in the context of isotropic and homogeneous cosmological model as it makes the first fundamental form cyclic. As a result, it allows a unique power law solution, typical for this particular fourth order theory of gravity, both in the vacuum and in the matter dominated era. This power law solution has been found to be quite good to explain the early stage but not so special and useful to explain the late stage of cosmological evolution. The usefulness of Palatini variational technique in this regard has also been discussed.