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

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.

accepted for publication as a Rapid Communication in Physical Review D

References in corpus (1)

• Dark Energy and the Accelerating Universe

Cited by in corpus (4)

• To conserve, or not to conserve: A review of nonconservative theories of gravity
• Noether theorem for action-dependent Lagrangian functions: conservation laws for non-conservative systems
• On the existence of static spherically-symmetric objects in action-dependent Lagrangian theories
• Wormhole geometries induced by action-dependent Lagrangian theories