Higher-Order Corrections to the Effective Gravitational Action from Noether Symmetry Approach

TL;DR

This paper explores how Noether symmetry can identify higher-order corrections in gravitational theories involving Ricci scalar and its derivatives, leading to exact solutions and simplified dynamics.

Contribution

It demonstrates that Noether symmetry can be used to recover and analyze higher-order gravitational corrections and their impact on cosmological solutions.

Findings

Noether symmetry constrains higher-order gravity models.

Exact cosmological solutions are obtainable via symmetry methods.

Constants of motion simplify the analysis of complex gravitational theories.

Abstract

Higher-order corrections of Einstein-Hilbert action of general relativity can be recovered by imposing the existence of a Noether symmetry to a class of theories of gravity where Ricci scalar R and its d'Alembertian $\Box R$ are present. In several cases, it is possible to get exact cosmological solutions or, at least, to simplify dynamics by recovering constants of motion. The main result is that a Noether vector seems to rule the presence of higher-order corrections of gravitaty.