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

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

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R.A. Battye

J.A. Pearson


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.


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.

Journal Article Type Article
Publication Date Oct 1, 2013
Deposit Date Dec 11, 2013
Publicly Available Date Aug 5, 2014
Journal Physical Review D
Print ISSN 1550-7998
Electronic ISSN 1550-2368
Publisher American Physical Society
Peer Reviewed Peer Reviewed
Volume 88
Issue 8
Article Number 084004


Published Journal Article (337 Kb)

Copyright Statement
Reprinted with permission from the American Physical Society: Phys. Rev. D 88, 084004 © (2013) by the American Physical Society. Readers may view, browse, and/or download material for temporary copying purposes only, provided these uses are for noncommercial personal purposes. Except as provided by law, this material may not be further reproduced, distributed, transmitted, modified, adapted, performed, displayed, published, or sold in whole or part, without prior written permission from the American Physical Society.

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