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Cosmological Solutions in Bimetric Gravity and their Observational Tests

Mikael von Strauss, Angnis Schmidt-May, Jonas Enander, Edvard Mortsell, S. F. Hassan

TL;DR

The paper develops the cosmological dynamics of ghost-free bimetric gravity with two interacting spin-2 fields, deriving the general evolution equations under a homogeneous and isotropic ansatz and showing that generically the expansion history approaches a de Sitter or AdS attractor while recovering a GR-like phase at early times. It analyzes two analytically tractable subcases (β3=0 and β1=β3=0 minimal model), and demonstrates that at the background level a GR-like expansion with an effective cosmological constant is often recovered, with the minimal model indistinguishable from ΛCDM for the background. The authors parameterize the solutions in terms of a few variables (notably α, M, and M_*) and fit to Type Ia supernova, CMB, and BAO data, finding that observations favor regions near the minimal model, or small departures therefrom, with a mass scale around the Hubble rate. The work highlights the viability of bimetric gravity as an alternative to dark energy for explaining cosmic acceleration and motivates further study of perturbations and local/gravitational tests to distinguish it from standard cosmology.

Abstract

We obtain the general cosmological evolution equations for a classically consistent theory of bimetric gravity. Their analytic solutions are demonstrated to generically allow for a cosmic evolution starting out from a matter dominated FLRW universe while relaxing towards a de Sitter (anti-de Sitter) phase at late cosmic time. In particular, we examine a subclass of models which contain solutions that are able to reproduce the expansion history of the cosmic concordance model inspite of the nonlinear couplings of the two metrics. This is demonstrated explicitly by fitting these models to observational data from Type Ia supernovae, Cosmic Microwave Background and Baryon Acoustic Oscillations.

Cosmological Solutions in Bimetric Gravity and their Observational Tests

TL;DR

The paper develops the cosmological dynamics of ghost-free bimetric gravity with two interacting spin-2 fields, deriving the general evolution equations under a homogeneous and isotropic ansatz and showing that generically the expansion history approaches a de Sitter or AdS attractor while recovering a GR-like phase at early times. It analyzes two analytically tractable subcases (β3=0 and β1=β3=0 minimal model), and demonstrates that at the background level a GR-like expansion with an effective cosmological constant is often recovered, with the minimal model indistinguishable from ΛCDM for the background. The authors parameterize the solutions in terms of a few variables (notably α, M, and M_*) and fit to Type Ia supernova, CMB, and BAO data, finding that observations favor regions near the minimal model, or small departures therefrom, with a mass scale around the Hubble rate. The work highlights the viability of bimetric gravity as an alternative to dark energy for explaining cosmic acceleration and motivates further study of perturbations and local/gravitational tests to distinguish it from standard cosmology.

Abstract

We obtain the general cosmological evolution equations for a classically consistent theory of bimetric gravity. Their analytic solutions are demonstrated to generically allow for a cosmic evolution starting out from a matter dominated FLRW universe while relaxing towards a de Sitter (anti-de Sitter) phase at late cosmic time. In particular, we examine a subclass of models which contain solutions that are able to reproduce the expansion history of the cosmic concordance model inspite of the nonlinear couplings of the two metrics. This is demonstrated explicitly by fitting these models to observational data from Type Ia supernovae, Cosmic Microwave Background and Baryon Acoustic Oscillations.

Paper Structure

This paper contains 24 sections, 84 equations, 3 figures.

Table of Contents

  1. Introduction and summary
  2. The bimetric gravity equations in the cosmological ansatz
  3. Review of bimetric gravity action and equations of motion
  4. Equations in the cosmological ansatz
  5. Viable cosmological solutions
  6. General features of solutions
  7. Models with $\beta_3=0$
  8. Models with $\beta_1=\beta_3=0$
  9. Parameterization of the solution
  10. Parameterization used for model fitting
  11. Model specific considerations
  12. Data
  13. Type Ia supernova data
  14. Cosmic Microwave Background and Baryon Acoustic Oscillations
  15. Results of observational tests
  16. ...and 9 more sections

Figures (3)

  • Figure 1: Cosmological constraints for $\alpha = 3/2$ using supernova distances (SN) and the ratio of the observed scales of the baryon acoustic oscillations as imprinted in the cosmic microwave background and the large scale galaxy distribution (CMB/BAO). In the left panel, a value of $M_*=1$ is assumed, in the right panel, $M_*=3$.
  • Figure 2: Cosmological constraints in the $[M,M_*]$-plane assuming $\alpha = 3/2$ and $\Omega_{m}=1$.
  • Figure 3: Left panel: Cosmological constraints in the $[\alpha,M]$-plane assuming $\Omega_{m}=1$ and $M_*=3$. Right panel: Constraints in the $[\alpha,M]$-plane for $\Omega_{m}=1$ after marginalizing over $M_*$ with a flat prior in the interval $[0,10]$.