Generalized nonconservative gravitational field equations from Herglotz action principle

TL;DR

This paper introduces a fully covariant nonconservative gravitational theory based on the Herglotz variational principle, which can explain cosmic acceleration without dark energy and exhibits dissipative gravitational wave behavior.

Contribution

It develops a new covariant gravitational theory using the Herglotz principle, improving previous models by removing coordinate restrictions and providing a covariant framework.

Findings

The theory reduces to a function acting as a cosmological constant.

It explains accelerated expansion without dark energy.

The linearized theory shows dissipative gravitational waves.

Abstract

We present an alternative nonconservative gravitational theory based on the Herglotz variational principle in a fully covariant form. The present model may be seen as an improvement of the theory proposed in Ref. [Lazo et al, Phys. Rev. D 95, 101501 (2017)], whose resulting theory is meaningful just in particular coordinate systems. In the present work, we report a new theory that is free from such a restriction. It is also obtained using the Herglotz variational principle and by taking advantage of the restricted equivalence between Lagrangian functions in the scope of such action principle. The more restricted class of equivalent Lagrangian functions, in comparison with the Hamilton variational principle, is the key point to find a Lagrangian that furnishes a new alternative gravitational theory that is fully covariant. Once the equations that govern the dynamics of the gravitational field are obtained, a few simple cosmological models are investigated. It is found that the Herglotz gravitational field reduces to a single function that, under certain conditions, plays the role of the cosmological constant in general relativity, turning unnecessary the use of dark energy to explain the accelerated expansion of the universe. The linearized version of the theory is also investigated and it is verified that the theory shows a dissipative character in regard to gravitational waves. From observational data, in both scenarios, the Herglotz vector field is estimated.