Sounds Discordant: Classical Distance Ladder & $Λ$CDM -based Determinations of the Cosmological Sound Horizon

TL;DR

This paper compares empirical determinations of the cosmological sound horizon $r_{ m s}$, obtained via the classical distance ladder (CDL) and BAO/SNe/Cepheid data, with model-based inferences from ΛCDM plus CMB observations. Using CDL (BAO, SNe Ia, and Cepheid calibrations) and a spline-parameterized expansion history, the authors find $r_{ m s}$ around $137.7$–$138.0$ Mpc, which is in tension with ΛCDM+CMB inferences by about $2$–$3\sigma$. Extensions such as varying the effective number of light species $N_{ m eff}$ or primordial helium $Y_{ m P}$ do not fully resolve the discrepancy, and the authors argue that any viable cosmological solution to align the CDL and CMB results would likely require significant changes in the pre-recombination epoch. They forecast that future CMB surveys (e.g., SPT-3G) could dramatically improve constraints on $r_{ m s}$ and test early-universe modifications, offering a path to resolving the tension or constraining new physics prior to recombination.

Abstract

Type Ia Supernovae, calibrated by classical distance ladder methods, can be used, in conjunction with galaxy survey two-point correlation functions, to empirically determine the size of the sound horizon $r_{\rm s}$. Assumption of the $Λ$CDM model, together with data to constrain its parameters, can also be used to determine the size of the sound horizon. Using a variety of cosmic microwave background (CMB) datasets to constrain $Λ$CDM parameters, we find the model-based sound horizon to be larger than the empirically-determined one with a statistical significance of between 2 and 3$σ$, depending on the dataset. If reconciliation requires a change to the cosmological model, we argue that change is likely to be important in the two decades of scale factor evolution prior to recombination. Future CMB observations will therefore likely be able to test any such adjustments; e.g., a third generation CMB survey like SPT-3G can achieve a three-fold improvement in the constraints on $r_{\rm s}$ in the $Λ$CDM model extended to allow additional light degrees of freedom.

Figures (3)

• Figure 1: Comoving angular-diameter distance measurements, $D_A(z)$, together with best-fit models. BAO results have been converted from $D_A(z)/r_{\rm s}$ to $D_A(z)$ by assumption of $r_{\rm s} = 138.09$ Mpc. Supernovae distance moduli have been converted to $D_A(z)$ assuming $M=-19.26$. In the residuals panel, $\Delta D_A(z) = D_A(z)-D_{A,\Lambda{\rm CDM}}(z)$ where $D_{A,\Lambda{\rm CDM}}(z)$ is the comoving angular-diameter distance for the best-fit $\Lambda$CDM cosmology. The gray band shows the 68% confidence interval for the spline model.
• Figure 2: Expansion rate measurements together with best-fit models. BAO data have been converted to $H(z)$ by assumption of $r_{\rm s} = 138.09$ Mpc. The gray band shows the 68% confidence interval for the spline model.
• Figure 3: Sound horizon determinations from existing data (solid symbols) and forecasts (open symbols). The numbers down the middle give the difference with the Cepheids+SNe+BAO Spline model result for $r_{\rm s}$ in units of the standard deviation, with the standard deviation computed via quadrature sum. We see that the classical distance ladder constraints (top panel) on $r_{\rm s}$ come out systematically lower than the $\Lambda$CDM-based constraints (biggest panel). The three model extensions considered in the three remaining panels do not significantly weaken the discrepancy. Code and data for this figure is available here: https://github.com/marius311/sounds_discordant_plot/blob/2c4735a17229ec14f3e54e2a594803d2a1bb34ca/summaryplot.ipynb