Cosmic dissonance: new physics or systematics behind a short sound horizon?

TL;DR

The paper investigates the tension between late-time, CMB-independent measurements and CMB-inferred cosmology by jointly constraining the sound horizon $r_{ m d}$ and the Hubble constant $H_0$ using Cepheid-based, TRGB, and time-delay lens calibrations alongside SN and BAO data. It employs cosmology-independent polynomial parametrizations to derive $H_0$ and $r_{ m d}$ at low redshift, then compares these against Planck Planck2018 results within $\Lambda$CDM and several pre- and post-recombination extensions. The analysis finds $r_{ m d}=(137\pm3^{stat.}\pm2^{syst.})$ Mpc and a tension in $(H_0, r_{ m d})$ of up to $\sim 5\sigma$, with late-time extensions unable to fully reconcile the discrepancy and pre-recombination extensions offering partial relief depending on calibrations. The work underscores that any resolution must address both the Hubble constant and the sound horizon, and highlights the need for more lenses and independent distance anchors to disentangle new physics from systematics. Overall, the results point to possible new early-Universe physics or unidentified systematics in distance calibrations as the source of the mismatch.

Abstract

Persistent tension between low-redshift observations and the Cosmic Microwave Background radiation (CMB), in terms of two fundamental distance scales set by the sound horizon $r_d$ and the Hubble constant $H_0$, suggests new physics beyond the Standard Model or residual systematics. We examine recently updated distance calibrations from Cepheids, gravitational lensing time-delay observations, and the Tip of the Red Giant Branch. Calibrating the Baryon Acoustic Oscillations (BAO) and Type Ia supernovae with combinations of the distance indicators, we obtain a joint and self-consistent measurement of $H_0$ and $r_d$ at low redshift, independent of cosmological models and CMB inference. In an attempt to alleviate the tension between late-time and CMB-based measurements, we consider four extensions of the standard $Λ$CDM model. The sound horizon from our different measurements is $r_d=(137\pm3^{stat.}\pm2^{syst.})$~Mpc. Depending on the adopted distance indicators, the $combined$ tension in $H_0$ and $r_d$ ranges between 2.3 and 5.1 $σ$. We find that modifications of $Λ$CDM that change the physics after recombination fail to solve the problem, for the reason that they only resolve the tension in $H_0$, while the tension in $r_d$ remains unchanged. Pre-recombination extensions (with early dark energy or the effective number of neutrinos $\rm{N}_{\rm{eff}}=3.24 \pm 0.16$) are allowed by the data, unless the calibration from Cepheids is included. Results from time-delay lenses are consistent with those from distance-ladder calibrations and point to a discrepancy between absolute distance scales measured from the CMB (assuming the standard cosmological model) and late-time observations. New proposals to resolve this tension should be examined with respect to reconciling not only the Hubble constant but also the sound horizon derived from the CMB and other cosmological probes.

Figures (8)

• Figure 1: Constraints on the sound horizon $r_{\rm d}$, the Hubble constant $H_0$ and $\Omega_k$ from late-time observations including BAO (BOSS), type Ia supernovae (Pantheon), gravitational lensing (H0LiCOW) and the cosmic distance ladder calibrated with Cepheids (SH0ES). The panels show results for three cosmology-independent models listed in Table \ref{['table:models']} and a $\Lambda$CDM cosmological model. The red lines indicate the best fit values obtained from Planck for a flat $\Lambda$CDM cosmological model. The contours indicate 1-, 2- and 5$\sigma$ confidence regions of the posterior probability (the latter obtained by Gaussian extrapolation). All panels demonstrate a 5$\sigma$ tension between $r_{\rm d}$ and $H_0$ measured from the CMB and the late-time observations.
• Figure 2: Comparison between the sound horizon $r_{\rm d}$ and the Hubble constant $H_0$ measured from Planck observations of the CMB (assuming a flat $\Lambda$CDM) and late-time observations (using flat model 3) obtained by calibrating SN and BAO measurements with three different absolute distance calibrations from: gravitational lensing (H0LiCOW), the cosmic distance ladder with Cepheids (SH0ES) or the TRGB (CCHP). For the late-time data, the contours show 1-, 2- and 5$\sigma$ confidence regions of the posterior probability (the latter obtained by Gaussian extrapolation). The Planck constraints (1- and 2$\sigma$ confidence regions) are obtained for the standard effective number of neutrinos (black solid line) and a model with a free effective number of neutrinos (black dashed lines, color points).
• Figure 3: The effect of four different extensions of the flat $\Lambda$CDM model on the sound horizon and the Hubble constant measured from the Planck data. The models considered here are $\Lambda$CDM + free $\textrm{N}_{\textrm{eff}}$, early dark energy, wCDM and PEDE. The CMB-based constraints are compared to the measurements from late-time observations (SN + BAO + H0LiCOW + SH0ES/CCHP) shown with the gray shaded contours. The late-time measurements are obtained with model 3 (see Table \ref{['table:models']}) and show the $2\sigma$ credibility regions.
• Figure 4: Tension between the sound horizon and the Hubble constant measured from late-time observations and the CMB for the following cosmological models: $\Lambda$CDM, $\Lambda$CDM + $\textrm{N}_{\textrm{eff}}$, early DE, wCDM, PEDE-CDM (flatness assumed in all cases). Late-time observations include BAO, type Ia supernovae and three different absolute distance calibrations from gravitational lensing (H0LiCOW), the cosmic distance ladder with Cepheids (SH0ES) or the TRGB (CCHP).
• Figure 5: The sound horizon $r_{\rm d}$ measured from combining BAO and SNe data with H0LiCOW lensing observations of each lens separately. Here the distance calibration is set solely by the lensing observations of each individual lens. The measured sound horizon is shown as a function of lens redshift for fits with a flat model 3 (solid error bars) and a flat PEDE-CDM model (dashed error bars). For both models, the measurements show a slight trend of $r_{\rm d}$ increasing with lens redshift. The inference from models 1 and 2 is fully consistent with the model 3 results. The gray dashed line with shaded region shows Planck's value of $r_{\rm d}$ and its (sub-percent) uncertainty obtained for the standard flat $\Lambda$CDM model.