Local and Non-Local Conservation Laws for Constrained Lagrangians and Applications to Cosmology

Abstract

We study the existence of conservation laws in constrained systems described by quadratic Lagrangians; the type of which is encountered in mini-superspace cosmology. As is well known, variational symmetries lead to conserved quantities that can be used in the classical and quantum integration of a system. Additionally - and due to the parametrization invariance of such Lagrangians - conditional symmetries defined on phase space can lead to non-local integrals of motion. The latter may be of importance in various cosmological configurations. As an example we present the case of scalar field cosmology with an arbitrary potential.