Cosmological stability bound in massive gravity and bigravity

By Matteo Fasiello, A. Tolley. 2013

147 citations recorded by the source corpus.

We give a simple derivation of a cosmological bound on the graviton mass for spatially flat FRW solutions in massive gravity with an FRW reference metric and for bigravity theories. This bound comes from the requirement that the kinetic term of the helicity zero mode of the graviton is positive definite. The bound is dependent only on the parameters in the massive gravity potential and the Hubble expansion rate for the two metrics.We derive the decoupling limit of bigravity and FRW massive gravity, and use this to give an independent derivation of the cosmological bound. We recover our previous results that the tension between satisfying the Friedmann equation and the cosmological bound is sufficient to rule out all observationally relevant FRW solutions for massive gravity with an FRW reference metric. In contrast, in bigravity this tension is resolved due to different nature of the Vainshtein mechanism. We find that in bigravity theories there exists an FRW solution with late-time self-acceleration for which the kinetic terms for the helicity-2, helicity-1 and helicity-0 are generically nonzero and positive making this a compelling candidate for a model of cosmic acceleration.We confirm that the generalized bound is saturated for the candidate partially massless (bi)gravity theories but the existence of helicity-1/helicity-0 interactions implies the absence of the conjectured partially massless symmetry for both massive gravity and bigravity.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/afec5fe5d851f4afd9841adb135331ef93a4aa9f

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Citations in the corpus

On couplings to matter in massive (bi-)gravity (2014, background): “In bi-gravity, there is a choice associated with how to introduce these fields [83].”
Bimetric gravity is cosmologically viable (2015, background): “The same scale also appears in the decoupling-limit analysis of bimetric theory [37], where m is now the parameter in front of the potential in the action (1).”
Cosmology and Fundamental Physics with the Euclid Satellite (2012, background): “FRW metric leads to a generalized Higuchi bound and one encounters similar problems (Fasiello and Tolley 2013).”
Does the Hubble constant tension call for new physics? (2018, background): “massive spin-2 eld in a de Sitter background will be ghost like if 0 <m2 <2H2. The corresponding bound to avoid the Higuchi ghost in general isotropic and homogeneous backgrounds was derived in [60]. As shown in [61], solutions fullling the Higuchi bound, exhibits a phantom behaviour of the ee”
Dark Energy in Light of Multi-Messenger Gravitational-Wave Astronomy (2018, background): “, 2013) and satisfying the Higuchi stability bound (Fasiello and Tolley, 2013).”
A systematic approach to generalisations of General Relativity and their cosmological implications (2018, background): “Another interesting property of the Galileon which is worth exploring is the existence of dual descriptions [119, 120, 121].”
Massive Gravity (2014, methodology): “One may show [224] that it is straightforward to find solutions of both Friedmann equations which are consistent with the Higuchi bound over the entire history of the universe.”
Beyond the Cosmological Standard Model (2014, unknown): “As was shown in [593, 620], by performing simultaneously a field-dependent coordinate transformation and a field redefinition y 7−→ x + 1 Λ ∂ρ (6.”