# From an Action Principle for Action-dependent Lagrangians toward non-conservative Gravity: accelerating Universe without dark energy

## TL;DR

This paper introduces a new action principle for non-conservative gravity, leading to modified Einstein equations that can explain cosmic acceleration without dark energy, and predicts unique gravitational wave behaviors.

## Contribution

It generalizes the Herglotz variational principle to multiple variables, deriving a novel non-conservative gravity theory with cosmological implications.

## Key findings

- Accelerating universe explained without dark energy.
- Predicted damped or amplified gravitational waves.
- Modified Einstein equations with a cosmological four-vector.

## Abstract

In the present work, we propose an Action Principle for Action-dependent Lagrangians by generalizing the Herglotz variational problem for several independent variables. This Action Principle enables us to formulate Lagrangian densities for non-conservative fields. In special, from a Lagrangian depending linearly on the Action, we obtain a generalized Einstein's field equations for a non-conservative gravity and analyze some consequences of their solutions to cosmology and gravitational waves. We show that the non-conservative part of the field equations depends on a constant cosmological four-vector. Depending on this four-vector, the theory displays damped/amplified gravitational waves and an accelerating Universe without dark energy.