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.

arXiv commentaccepted for publication as a Rapid Communication in Physical Review D

References in corpus (2)

• Dark Energy and the Accelerating Universe
• The fundamental constants and their variation: observational status and theoretical motivations

Cited by in corpus (24)

• Stellar structure models in modified theories of gravity: lessons and challenges
• Imperfect fluid description of modified gravities
• To conserve, or not to conserve: A review of nonconservative theories of gravity
• Contact variational integrators
• Invariant measures for contact Hamiltonian systems: symplectic sandwiches with contact bread
• An Action Principle for Action-dependent Lagrangians: toward an Action Principle to non-conservative systems
• Cosmology from a new non-conservative gravity
• Noether theorem for action-dependent Lagrangian functions: conservation laws for non-conservative systems
• Numerical integration in celestial mechanics: a case for contact geometry
• Hamilton-Jacobi theory and integrability for autonomous and non-autonomous contact systems
• Tidal Love numbers of neutron stars in Rastall gravity
• Nonconservative traceless type gravity
• Generalized nonconservative gravitational field equations from Herglotz action principle
• On the existence of static spherically-symmetric objects in action-dependent Lagrangian theories
• Wormhole geometries induced by action-dependent Lagrangian theories
• A variational derivation of the field equations of an action-dependent Einstein-Hilbert Lagrangian
• Nonsmooth Herglotz variational principle
• Dark energy with zero pressure: Accelerated expansion and large scale structure in action-dependent Lagrangian theories
• Braneworld gravity within non-conservative gravitational theory
• Practical Introduction to Action-Dependent Field Theories
• Some effects of non-conservative gravity on cosmic string configurations
• Fermat's Principle in General Relativity via Herglotz Variational Formalism
• When action is not least for systems with action-dependent Lagrangians
• Complex Lagrangian dynamics