A New Action for Cosmology

Abstract

We present a new action which reproduces the cosmological sector of general relativity in both the Friedmann-Lemaître-Robertson-Walker (FLRW) and Bianchi models. This action makes no reference to the scale factor, and is of a frictional type first examined by Herglotz. We demonstrate that the extremization of this action reproduces the usual dynamics of physical observables, and the symplectification of this action is the Einstein-Hilbert action for cosmological models. We end by discussing some of the increased explanatory power produced by considering the reduced physical ontology resulting from eliminating scale.

The Herglotz principle and vakonomic dynamics

“…Furthermore variational integrators based on the Herglotz principle have been developed [19,2]. Contact dynamics and the Herglotz principle have applications on the description of many physical systems, such as mechanical systems with friction, thermodynamic systems and some cosmological models [5,16,17,18].…”