Massive gravity, the elasticity of space-time, and perturbations in the dark sector

Battye, R.A.; Pearson, J.A.

Abstract

We consider a class of phenomenological modified gravity models where the terms added to the standard Einstein-Hilbert Lagrangian are just a function of the metric only. For linearized perturbations around an isotropic space-time, this class of models is entirely specified by a rank-4 tensor that encodes possibly time-dependent masses for the gravitons. This tensor has the same symmetries as an elasticity tensor, suggesting an interpretation of massive gravity as an effective rigidity of space-time. If we choose a form for this tensor that is compatible with the symmetries of Friedmann-Robertson-Walker and enforce full reparametrization invariance, then the only theory possible is a cosmological constant. However, in the case where the theory is only time translation invariant, the ghost-free massive gravity theory is equivalent to the elastic dark energy scenario with the extra Lorentz violating vector giving rise to 2 transverse and 1 longitudinal degrees of freedom, whereas when one demands spatial translation invariance one is left with a theory where the entropy perturbation is not gauge invariant.

Citation

Battye, R., & Pearson, J. (2013). Massive gravity, the elasticity of space-time, and perturbations in the dark sector. Physical Review D, 88(8), Article 084004. https://doi.org/10.1103/physrevd.88.084004

• Journal Article Type: Article
• Publication Date: Oct 1, 2013
• Deposit Date: Dec 11, 2013
• Publicly Available Date: Aug 5, 2014
• Journal: Physical Review D - Particles, Fields, Gravitation, and Cosmology
• Print ISSN: 1550-7998
• Electronic ISSN: 1550-2368
• Publisher: American Physical Society
• Peer Reviewed: Peer Reviewed
• Volume: 88
• Issue: 8
• Article Number: 084004
• DOI: https://doi.org/10.1103/physrevd.88.084004
• Public URL: https://durham-repository.worktribe.com/output/1465940