Stable and unstable cosmological models in bimetric massive gravity
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Nonlinear, ghost-free massive gravity has two tensor fields; when both are dynamical, the mass of the graviton can lead to cosmic acceleration that agrees with background data, even in the absence of a cosmological constant. Here the question of the stability of linear perturbations in this bimetric theory is examined. Instabilities are presented for several classes of models, and simple criteria for the cosmological stability of massive bigravity are derived. In this way, we identify a particular self-accelerating bigravity model, infinite-branch bigravity (IBB), which exhibits both viable background evolution and stable linear perturbations. We discuss the modified gravity parameters for IBB, which do not reduce to the standard $\mathrm{\ensuremath{\Lambda}}\mathrm{CDM}$ result at early times, and compute the combined likelihood from measured growth data and type Ia supernovae. IBB predicts a present matter density ${\mathrm{\ensuremath{\Omega}}}_{m0}=0.18$ and an equation of state $w(z)=\ensuremath{-}0.79+0.21z/(1+z)$. The growth rate of structure is well approximated at late times by $f(z)\ensuremath{\approx}{\mathrm{\ensuremath{\Omega}}}_{m}^{0.47}[1+0.21z/(1+z)]$. The implications of the linear instability for other bigravity models are discussed: the instability does not necessarily rule these models out, but rather presents interesting questions about how to extract observables from them when linear perturbation theory does not hold.
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Adding a second dynamical metric in bimetric massive gravity provides stable self-accelerating cosmological solutions with no need for a dark energy component.
“In addition to realizing a massive gravity theory, adding a second dynamical metric has been shown to provide stable self-accelerating cosmological solutions with no need for a dark energy component, see e.g. Hassan and Rosen (2011, 2012a, b), Koennig et al. (2014a, b) and Akrami et al. (2015).”
From Testing general relativity in cosmology (2019) · cites this paper as Koennig et al. 2014a, b
Bimetric massive gravity theories have a branch of models that admit a limit in which the Planck mass associated to the second metric is small and any scalar instabilities can be pushed to very early times where they are not observable.
“These theories have a branch of models that admit a limit in which the Planck mass associated to the second metric is small and any scalar instabilities can be pushed to very early times where they are not observable (Koennig et al. 2014a; Lagos and Ferreira 2014; Cusin et al. 2015a, b, 2016; Akrami et al. 2015; Schmidt-May and von Strauss 2016).”
From Testing general relativity in cosmology (2019) · cites this paper as Koennig et al. 2014a
For the infinite branch, Koennig et al. found only models with non-vanishing and are self-accelerating, viable and stable for all cosmic evolution.
“For the infinite branch, they found only models with non-vanishing and are self-accelerating, viable and stable for all cosmic evolution and they focused their analysis on those models.”
From Testing general relativity in cosmology (2019) · cites this paper as Koennig et al. 2014a
In bimetric massive gravity, the background dynamics depend entirely on the Hubble parameter of the metric and the ratio of the two scale factors.
“As can be seen from Eqs. (202) and (203), and stressed in Koennig et al. (2014a, b), the background dynamics depend entirely on the Hubble parameter of the metric and the ratio of the two scale factors.”
From Testing general relativity in cosmology (2019) · cites this paper as Koennig et al. 2014a, b
Koennig et al. found there are no self-accelerating models with a viable background evolution and stable perturbations on the finite branch.
“They found there are no self-accelerating models (i.e., ) with a viable background evolution and stable perturbations on the finite branch.”
From Testing general relativity in cosmology (2019) · cites this paper as Koennig et al. 2014a
Koennig et al. found that the only single parameter models without instabilities at early times are models with or .
“Koennig et al. (2014a) performed a stability analysis finding that the only single parameter models without instabilities at early times are models with or .”
From Testing general relativity in cosmology (2019) · cites this paper as Koennig et al. 2014a
The only bimetric massive gravity models with a stable cosmological evolution are those with non-vanishing parameters.
“They found that the only models with a stable cosmological evolution are the ones with non vanishing , and parameters.”
From Testing general relativity in cosmology (2019) · cites this paper as Koennig et al. 2014a
The IBB model fits the growth and supernova data with an effective dark energy equation of state and a growth rate of structure that is well approximated at late times by a specific form.
“They found that the IBB model fits the data with and an effective dark energy equation of state . They also found that growth rate of structure in IBB is well-approximated at late times by .”
From Testing general relativity in cosmology (2019) · cites this paper as Koennig et al. 2014a
Koennig et al. identified a self-accelerating branch of bimetric massive gravity that is consistent with the expansion history and stable to linear perturbations, called the infinite-branch of bimetric gravity (IBB).
“Koennig et al. (2014a) considered perturbations of bimetric massive gravity and identified a self-accelerating branch that is consistent with the expansion history and stable to linear perturbations. They call this the infinite-branch of bimetric gravity (IBB) based on the behavior of the ratio of the scale factor in the two metrics.”
From Testing general relativity in cosmology (2019) · cites this paper as Koennig et al. 2014a
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References 74 · Cited by 128
- Authors
- Koennig, F., Akrami, Y., Amendola, L., Motta, M., & Solomon, A. R.
- Affiliations
- University of Oslo (NO)
- Heidelberg University (DE)
- University of Geneva (CH)
- University of Cambridge (GB)
- Venue
- Physical Review D
- Publisher
- American Physical Society (APS)
- Published
- 2014-12-03
- Volume
- 90
- Issue
- 12
- ISSN
- 0556-2821 (ISSN-L)
- 1550-7998
- 1550-2368
- OpenAlex
- W2058970436
- Cited by
- 128
- References
- 74
- Citations by year
- 2026: 1 · 2025: 2 · 2023: 7 · 2021: 9 · 2020: 7 · 2019: 5 · 2018: 29 · 2017: 10 · 2016: 23 · 2015: 30 · 2014: 5
- FWCI
- 12.22
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields (publishedVersion)
- arXiv (Cornell University) (publishedVersion)
- arXiv (Cornell University)
- Funders
- Deutsche Forschungsgemeinschaft
- European Research Council (StG2010-257080)
- Swiss National Science Foundation
- University of Cambridge
- David Gledhill Research Studentship
- Sidney Sussex College
- Isaac Newton Fund and Studentships
- Topics
- Physical Sciences › Physics and Astronomy › Astronomy and Astrophysics › Cosmology and Gravitation Theories
- Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Noncommutative and Quantum Gravity Theories
- Physical Sciences › Physics and Astronomy › Nuclear and High Energy Physics › Black Holes and Theoretical Physics
- Keywords
- bigravity, cosmological stability, linear perturbations, cosmic acceleration, modified gravity, structure growth, dark energy equation of state, Type Ia supernovae, matter density, linear instability
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