Higher-order corrections to the effective gravitational action from Noether symmetry approach (Q1585787)

The authors consider effective gravitational actions of the form Einstein-Hilbert action plus higher-order corrections. They restrict the class of theories by postulating the existence of a Noether symmetry of the Lagrangian and insert Friedmann-Robertson-Walker metrics into the equations. The field equations then can be treated as a dynamical system with only finitely many degrees of freedom. Symmetry classes, constants of motion, and some exact solutions are presented.