A New Action for Cosmology

TL;DR

This paper introduces a novel action principle for cosmology that reproduces general relativity's dynamics without referencing the scale factor, offering new insights into the physical ontology of cosmological models.

Contribution

It presents a scale-independent action for cosmology, extending Herglotz's frictional action, and shows its equivalence to Einstein-Hilbert action in cosmological settings.

Findings

Reproduces standard cosmological dynamics without scale factor

Establishes equivalence to Einstein-Hilbert action for cosmology

Suggests new perspectives on physical ontology in cosmology

Abstract

We present a new action which reproduces the cosmological sector of general relativity in both the Friedmann-Lemaitre-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.