A Vacuum Phase Transition Solves $H_0$ Tension

TL;DR

The paper addresses the persistent $H_0$ tension between Planck CMB in ΛCDM and local measurements by testing the Parker vacuum metamorphosis (VM), a physically motivated phase-transition model of gravity with a single scale $M$ and no cosmological constant. Using Planck TT, Planck, and the R16 $H_0$ prior in Bayesian analyses, VM can reconcile $H_0$ with local values and provide a better fit than ΛCDM (e.g., a $ar\chi^2_{\rm eff}$ improvement of up to about $-7.5$ for a 9-parameter extension), while also impacting $\Omega_m$, $\sigma_8$, and $S_8$ in favorable ways for some datasets. The authors explore both a fixed-$M$ VM and an elaborated VM with a varying $M$, as well as a scale-dependent lensing amplitude $A_{\rm lens}$, finding that scale dependence does not resolve the tension and that Planck–lensing data remain in mild tension. Overall, VM presents a compelling, theoretically grounded extension to ΛCDM that can alleviate the $H_0$ problem and related tensions, warranting further tests with upcoming CMB and large-scale-structure data.

Abstract

Taking the Planck cosmic microwave background data and the more direct Hubble constant measurement data as unaffected by systematic offsets, the values of the Hubble constant $H_0$ interpreted within the $Λ$CDM cosmological constant and cold dark matter cosmological model are in $\sim 3.3 σ$ tension. We show that the Parker vacuum metamorphosis model, physically motivated by quantum gravitational effects and with the same number of parameters as $Λ$CDM, can remove the $H_0$ tension, and can give an improved fit to data (up to $Δχ^2=-7.5$). It also ameliorates tensions with weak lensing data and the high redshift Lyman alpha forest data. We separately consider a scale dependent scaling of the gravitational lensing amplitude, such as provided by modified gravity, neutrino mass, or cold dark energy, motivated by the somewhat different cosmological parameter estimates for low and high CMB multipoles. We find that no such scale dependence is preferred.

Figures (5)

• Figure 1: The effective dark energy equation of state evolution is plotted vs redshift for several values of the mass parameter $M$, for $\Omega_m=0.3$. The bold blue curve shows the original case (our preferred model) where there is no cosmological constant, while the medium black curves show the elaborated case with an added cosmological constant, and the dotted red curve shows one with a negative cosmological constant (causing $w$ to first shoot up to large positive values before it plummets to highly negative values).
• Figure 2: The distance-redshift relation for the vacuum metamorphosis model without a cosmological constant -- the fastest evolving one -- is well fit by a standard $w_0$--$w_a$ model. Here the comoving distance, which enters the CMB distance to last scattering, and weak lensing, BAO, and supernova observations, is plotted vs redshift.
• Figure 3: Triangular plot showing the posteriors of the cosmological parameters for $\Lambda\mathrm{CDM}$ and the original VM model, along with their 2D joint confidence contour at 68% CL and 95% CL. This is for baseline CMB data only, in the $6$ parameter space.
• Figure 4: Constraints on the $M$-$H_0$ space of the elaborated VM model from the Planck and Planck+R16 datasets in the $6+1$ parameters analysis.
• Figure 5: Triangular plot showing the posteriors of $A_{\rm lens,0}$ and $B$ for the datasets considered, as well as their 2D joint confidence contour at 68% CL.