Is the Hubble tension a hint of AdS phase around recombination?

Abstract

Anti-de Sitter (AdS) vacua, being theoretically important, might have an unexpected impact on the observable universe. We find that in early dark energy (EDE) scenarios the existence of AdS vacua around recombination can effectively lift the CMB-inferred $H_0$ value. As an example, we study a phenomenological EDE model with an AdS phase starting at the redshift $z\sim2000$ and ending shortly after recombination (hereafter the universe will settle down in a $Λ>0$ phase until now), and obtain a best-fit $H_0=72.74$ km/s/Mpc without degrading the CMB fit compared with the standard $Λ$CDM model.

Figures (5)

• Figure 1: A sketch of the potential with an AdS phase. Initially the field is frozen at $\phi_i$. It starts rolling down the potential at the redshift $z\sim3500$ when $H$ drops below its effective mass $m_\phi$, and enters an AdS phase at $z\sim2000$. The field straightly rolls over the AdS region and does not oscillate. It climbs up to the $\Lambda>0$ region shortly after recombination, hereafter the universe is effectively described by the standard $\Lambda$CDM model.
• Figure 2: Energy fraction $f_{EDE}$ of EDE with respect to redshift $z$, plotted using the best-fit models. The scalar field energy density quickly redshifts away after the field starts rolling, so the recombination redshift $z_{rec}$ is nearly the same in both EDE models and the standard $\Lambda$CDM. Scalar field energy in the $\phi^4+AdS$ model redshifts much faster due to the AdS phase (shaded region, from $z=2063$ to $z=802$ in the best-fit model).
• Figure 3: The 1-sigma contour plot of $H_0$ versus $\omega_{scf}$ and $\ln(1+z_c)$. The models compared are oscillating $\phi^4$ (red), $\alpha_{ads}=0$ (blue) and $\alpha_{ads}=3.79\times10^{-4}$ (green). The colored bands represent the 1-sigma $H_0$ in $\Lambda$CDM (gray) and SH0ES measurement (orange).
• Figure 4: Difference between various models fitted to full datasets and a reference $\Lambda$CDM model obtained using only the Planck2018 data. The upper panel is for the TT spectrum and the lower one for the EE spectrum.
• Figure 5: Marginalized posterior distributions of $\{H_0,n_s,\omega_{scf},\ln(1+z_c)\}$. $H_0$ is correlated with $n_s$ and $\omega_{scf}$, as explained in the text.