Inferences of $H_0$ in presence of a non-standard recombination

TL;DR

The paper investigates whether a non-standard recombination history can reconcile the $H_0$ tension between local distance-ladder measurements and early-universe inferences by introducing a phenomenological shift and width modification to recombination, thereby altering the sound horizon and the BAO scale $r_{\rm drag}$. By implementing a two-parameter recombination model in a modified CLASS and analyzing Planck data (with/without lensing and high-$\ell$ polarization), BAO, and a BBN prior via MCMC, they show that $H_0$ can be drawn closer to the local value when Planck data are used alone, though the tension is reduced rather than eliminated. The inclusion of Planck lensing and high-$\ell$ polarization tends to revert $H_0$ toward the standard $\Lambda$CDM value, leaving a residual tension at about $2$–$3\sigma$, while also significantly affecting $r_{\rm drag}$. The study demonstrates that non-standard recombination is a plausible reconciliation mechanism worth testing with future observations, such as CMB spectral distortions, though it remains speculative without a concrete physical model.

Abstract

Measurements of the Hubble parameter from the distance ladder are in tension with indirect measurements based on the cosmic microwave background (CMB) data and the inverse distance ladder measurements at 3-4 $σ$ level. We consider phenomenological modification to the timing and width of the recombination process and show that they can significantly affect this tension. This possibility is appealing, because such modification affects both the distance to the last scattering surface and the calibration of the baryon acoustic oscillations (BAO) ruler. Moreover, because only a very small fraction of the most energetic photons keep the early universe in the plasma state, it is possible that such modification could occur without affecting the energy density budget of the universe or being incompatible with the very tight limits on the departure from the black-body spectrum of CMB. In particular, we find that under this simplified model, with a conservative subset of Planck data alone, $H_0=73.44_{-6.77}^{+5.50}~{\rm km\ s}^{-1}\ {\rm Mpc}^{-1}$ and in combination with BAO data $H_0=68.86_{-1.35}^{+1.31}~{\rm km\ s}^{-1}\ {\rm Mpc}^{-1}$, decreasing the tension to $\sim 2σ$ level. However, when combined with Planck lensing reconstruction and high-$\ell$ polarization data, the tension climbs back to $\sim 2.7σ$, despite the uncertainty on non-ladder $H_0$ measurement more than doubling.

Figures (4)

• Figure 1: The free electron fraction for various values of recombination parameters $\delta z_{0.5}^{\rm rec}$ and $\Delta z^{\rm rec}$, where $\delta z_{0.5}^{\rm rec}$ shifts the recombination timing and $\Delta z^{\rm rec}$ changes the recombination width (see the main text for detailed description of our phenomenological model). In our convention, in terms of redshift, positive $\delta z_{0.5}^{\rm rec}$ corresponds to a later recombination timing, and positive $\Delta z^{\rm rec}$ corresponds to a narrower recombination width.
• Figure 2: Triangle plot of $\Omega_{\rm m}-H_0-r_{\rm drag}$ from Planck dataset alone. The red and blue contours display the parameter constraints for standard and modified recombination, respectively. The modified recombination significantly relaxes the $H_0$ constraint and the $r_{\rm drag}$ calibration of the BAO ruler.
• Figure 3: Triangle plot of $H_0-\delta z_{0.5}^{\rm rec}-\Delta z^{\rm rec}$ of modified recombination. The red, blue, and green contours display respectively the parameter constraints for Planck, Planck+BAO, and Planck+BBN. The dotted lines indicate $\delta z_{0.5}^{\rm rec}=0$ or $\Delta z^{\rm rec}=0$. Adding either BAO or BBN helps break the degeneracies, but the contours remain significantly enlarged compared to the standard recombination.
• Figure 4: Constraints on the Hubble parameter for various data combinations shown in each panel. The red circles and blue triangles with error bars display the constraints for the standard and modified recombination, respectively. The gray band display the 1 and $2\sigma$ constraint from Ref. Riess:2018byc. It is apparent that including the additional recombination parameters $\delta z_{0.5}^{\rm rec}$ and $\Delta z^{\rm rec}$ significantly enlarges the constraint on $H_0$, making the constraint from the early universe more consistent with the local distance ladder measurement.