Higher-order corrections to the effective gravitational action from Noether symmetry approach

Higher-order corrections of the Einstein-Hilbert action of general relativi ty can be recovered by imposing the existence of a Noether symmetry to a cl ass of theories of gravity where the Ricci scalar R and its d'Alembertian s quare R are present. In several cases, it is possible to get exact cosmolog ical solutions or, at least, to simplify the dynamics by recovering constan ts of motion. The main result is that a Noether vector seems to rule the pr esence of higher-order corrections of gravity.