Bimetric gravity improves the fit to DESI BAO and eases the Hubble tension

TL;DR

This study tests dynamical dark energy as a solution to the Hubble tension by comparing a phenomenological $w_0 w_a$CDM model with a fundamental bimetric gravity framework using DESI DR2 BAO, Planck 2018 + ACT CMB data, and multiple SN Ia compilations. The CPL approach provides a modest fit improvement over ΛCDM but aggravates the $H_0$ discrepancy, while bimetric gravity offers a small gain in fit quality and raises $H_0$ to about $69.0 m \,km\,s^{-1}\,Mpc^{-1}$, reducing the tension to roughly $3.7\sigma$. Including locally calibrated SNe Ia strengthens the case for bimetric gravity to around $2\sigma$ over ΛCDM, comparable to the CPL model when the local calibration is accounted for. Overall, the results favor a theoretically well-motivated dynamical dark energy scenario (bimetric gravity) with distinct predictions (e.g., gravitational-wave signatures) that are testable with future observations, though the evidence remains non-definitive.

Abstract

We investigate whether the latest combination of DESI DR2 baryon acoustic oscillation (BAO) measurements, cosmic microwave background (CMB) data (Planck 2018 + ACT), and Type Ia supernovae (SNe Ia) compilations (Pantheon+, Union3, and DES Y5) favor a dynamical dark energy component, and explore if such a scenario can simultaneously help resolve the Hubble tension. We contrast two frameworks: the widely used phenomenological $w_0 w_a$CDM model, and bimetric gravity, a fundamental modification of general relativity that naturally gives rise to phantom dark energy. The $w_0 w_a$CDM model is moderately preferred over $Λ$CDM, at the $2$-$4 \, σ$ level, when fitting DESI DR2 + CMB + SNe Ia, but it exacerbates the Hubble tension. By comparison, bimetric gravity provides a modest improvement in fit quality, at the $1 \, σ$ level, but, by inferring $H_0 = 69.0 \pm 0.4 \, \mathrm{km/s/Mpc}$, it partially eases the Hubble tension, from a $5 \,σ$ discrepancy to a $3.7 \, σ$ tension. Including locally calibrated SNe Ia brings the overall preference for the bimetric model over $Λ$CDM to the $2 \, σ$ level, comparable to that of the $w_0 w_a$CDM model when including the local SN Ia calibration.

Figures (5)

• Figure 1: Redshift evolution of the dark energy density for three different values of the bimetric mass parameter $m_\mathrm{FP}$. For reference, $H_0 \sim 10^{-33} \, \mathrm{eV}$. While the detailed evolution of $\Omega_\mathrm{DE}$ can vary considerably depending on the theory parameters, it always follows the same qualitative pattern: beginning as a (possibly negative) cosmological constant in the early universe, here around $-4$, then transitioning to a greater late-time value $\Omega_\Lambda$. A larger $m_\mathrm{FP}$ corresponds to an earlier transition. For comparison, the evolution of a $w_0 w_a$CDM model with $w_0 = -0.8$ and $w_a = -0.9$ is also shown, highlighting differences in behavior between the bimetric and $w_0 w_a$CDM models.
• Figure 2: Results for a general bimetric model. Marginalized posterior constraints on $H_0$ and $\theta$ from BAO (DESI DR2), CMB (Planck 2018 + ACT), and three different SNe Ia compilations. Contours show the $68 \, \%$ and $95 \, \%$ credence regions. In the limit $\theta \to 0$, the standard $\Lambda$CDM model is recovered. In contrast to the $w_0 w_a$CDM model, the results show strong consistency across the three SNe Ia compilations. The inferred Hubble constant is significantly higher than for the $w_0 w_a$CDM and $\Lambda$CDM models, thereby reducing the Hubble tension from the $5 \, \sigma$ level to $3.7 \, \sigma$.
• Figure 3: Results for a general bimetric model. Marginalized posterior constraints on $\theta$ and $m_\mathrm{FP}$ from BAO (DESI DR2), CMB (Planck 2019 + ACT), and three different SNe Ia compilations. Contours show the $68 \, \%$ and $95 \, \%$ credence regions. While the mixing angle $\theta$ is constrained, the mass scale $m_\mathrm{FP}$ only exhibits a lower bound $m_\mathrm{FP} > 3.0 \times 10^{-32} \, \mathrm{eV}$ at $68 \, \%$ credence. For reference, $H_0 \sim 10^{-33} \, \mathrm{eV}$.
• Figure 4: Comparing data to models shown in residual form relative to a fiducial $\Lambda$CDM model, following the style of Fig. 13 of Ref. DESI:2025zgx. The fiducial $\Lambda$CDM model is the CMB prediction for the distance ratios. The BAO (DESI DR2) data points are shown with error bars. Here, $D_M$ denotes the angular diameter distance, $D_H$ the Hubble distance, and $r_d$ the sound horizon at the baryon drag epoch. The best-fit $w_0 w_a$CDM and bimetric models are shown as dashed lines. The primary improvement in the quality of fit of the $w_0 w_a$CDM model compared with the bimetric model arises from the low-redshift Hubble distance ratios at $z_\mathrm{eff} = 0.51$ and $z_\mathrm{eff} = 0.71$ (right panel). Conversely since the Hubble distance is inversely proportional to the Hubble parameter, $D_H(z) = c / H(z)$, the bimetric model predicts a higher value for $H_0$ compared with the $w_0 w_a$CDM model, thus reducing the Hubble tension.
• Figure 5: Redshift evolution of the dark energy equation of state for the best-fit bimetric and $w_0 w_a$CDM models from the combined BAO (DESI DR2), CMB (Planck 2018 + ACT), and SNe Ia (DES Y5) data. For the $w_0 w_a$CDM model, $w_\mathrm{DE}$ is $<-1$ and approximately constant at early times, crosses the phantom divide at $z \simeq 0.4$, and approaches $-0.8$ today. For the bimetric model $w_\mathrm{DE}$, starts at $-1$ in the early universe, then rises monotonically after recombination, with $\Omega_\mathrm{DE}$ increasing from a negative value, crossing zero at $z \simeq 5$, where the equation of state formally diverges, and remaining below $-1$ thereafter, steadily approaching $-1$. The divergence in $w_\mathrm{DE}$ simply reflects the change of sign in the energy density and does not indicate a physical pathology. This is a behavior that the CPL parameterization cannot capture.