Removing external priors and hidden model dependence from sound-horizon-agnostic inference of $H_0$ and $\Sigma m_\nu$ with LSST/Euclid and next-generation CMB lensing

The sound-horizon-agnostic program measures the Hubble constant $H_0$ and the neutrino mass sum $\Sigma m_\nu$ without computing the baryon-acoustic-oscillation sound horizon $r_d$, treating $r_d$ as a free parameter and breaking the resulting degeneracy with CMB and galaxy lensing. Its current implementation (García Escudero, Mirpoorian & Pogosian 2026) reaches percent-level $H_0$ only with an external prior on the primordial amplitude $A_s$ that is itself derived under standard recombination, and yields neutrino-mass bounds far weaker than conventional derived-$r_d$ analyses. The open problem, stated explicitly in that work, is whether the program can be made fully self-contained: whether LSST/Euclid tomographic clustering and weak lensing combined with low-noise CMB lensing can break the $A_s$–$\Omega_m h^2$–$\Sigma m_\nu$ degeneracy without external priors, whether $r_d$-agnostic $\Sigma m_\nu$ bounds can approach conventional precision without reintroducing recombination modeling, what a principled prior treatment for $\Sigma m_\nu$ is, and whether the $\theta_{\star}$ anchor's $r_{\star}\approx r_d/1.02$ relation is robust across all plausible recombination-modifying scenarios.

Background

The Hubble tension — the roughly $5\sigma$ discrepancy between the local distance-ladder measurement $H_0\approx 73$ km/s/Mpc from the SH0ES collaboration (Supernovae $H_0$ for the Equation of State) and the value $H_0\approx 67$ km/s/Mpc inferred from the Planck cosmic microwave background (CMB) under the standard cosmological model — is the central anomaly of precision cosmology. Most proposed resolutions inject new pre-recombination physics that shrinks the sound horizon $r_d$, the comoving distance sound waves traveled in the early-universe photon–baryon plasma before baryons gravitationally decoupled (the drag epoch). Because $r_d$ is a prediction of a recombination model, any $H_0$ inference that uses a computed $r_d$ is contaminated by exactly the model it is meant to test. Baryon acoustic oscillations (BAO), the fossil imprint of those sound waves in galaxy clustering, measure combinations such as $D_M(z)/r_d$ (transverse) and $D_H(z)/r_d$ (radial); treating $r_d$ as a free nuisance parameter leaves uncalibrated distance ratios that constrain $r_d H_0$ and the matter density $\Omega_m$ but not $H_0$ alone. Pogosian, Zhao & Jedamzik (2020) showed that these uncalibrated BAO ratios can be combined with probes of the physical matter density $\Omega_m h^2$ — CMB lensing (the gravitational deflection of CMB photons by intervening large-scale structure, measured by the Planck satellite, the Atacama Cosmology Telescope (ACT) and the third-generation South Pole Telescope camera, SPT-3G) and galaxy weak lensing and clustering (the 3×2pt correlations of galaxy positions and shapes, e.g. from the Dark Energy Survey, DES) — to break the degeneracy and determine $H_0$ with no recombination modeling and no supernova calibration. One can add the CMB acoustic scale angle $\theta_{\star}$ (the angular size of the sound horizon at photon decoupling, measured by Planck to sub-percent precision) as an effective high-redshift transverse BAO point; this requires only the ratio between the sound horizon at decoupling and at drag, $r_{\star}\approx r_d/1.02$, which Pogosian, Zhao & Jedamzik (2024) verified is nearly invariant across known early-Universe extensions that modify $r_d$ (extra relativistic species, massive neutrinos, primordial magnetic fields, early dark energy). Massive neutrinos add a further complication: they suppress the growth of small-scale structure and dilute matter clustering, so lensing data can bound the mass sum $\Sigma m_\nu$ (neutrino oscillation experiments require $\Sigma m_\nu\geq 0.06$ eV), but their effect is strongly degenerate with the matter density and the primordial scalar fluctuation amplitude $A_s$. García Escudero, Mirpoorian & Pogosian (2026) implemented this program using DESI (Dark Energy Spectroscopic Instrument) DR2 BAO, current CMB lensing, DES Year-3 3×2pt data and the Pantheon+ sample of Type Ia supernovae, obtaining $H_0 = 70.0 \pm 1.7$ km/s/Mpc with $\Sigma m_\nu$ fixed, tightening to $70.03 \pm 0.97$ km/s/Mpc when an informative prior on $A_s$ is added. The residual external input is the problem: the $A_s$ prior comes from CMB analyses that assume standard recombination, so it is precisely the kind of hidden model dependence the method was designed to avoid. Its role is to break the $\Omega_m h^2$–$A_s$ degeneracy, since present lensing data measure the late-time matter amplitude rather than the primordial one; the authors' forecasts with Simons-Observatory-like CMB lensing (a next-generation ground-based CMB survey), a next-generation 3×2pt dataset, completed DESI BAO and future supernovae still need the $A_s$ prior to reach $\sigma(H_0)\simeq 0.67$ km/s/Mpc. Allowing $\Sigma m_\nu$ to vary degrades the constraints further and exposes a strong sensitivity to the prior adopted for $\Sigma m_\nu$ (a uniform prior biases results toward larger masses and higher $H_0$; a logarithmic prior reduces the bias), while the resulting $r_d$-agnostic $\Sigma m_\nu$ bounds are substantially weaker than the derived-$r_d$ bound $\Sigma m_\nu < 0.022$ eV (68% CL) from the same data.

Problem Statement

Determine whether the sound-horizon-agnostic inference program — in which $r_d$ is a free parameter, uncalibrated BAO constrain $r_d H_0$ and $\Omega_m$, and CMB/galaxy lensing constrain $\Omega_m h^2$ — can be made fully self-contained, i.e. free of external $\Lambda$CDM-derived priors and of unvalidated recombination-model assumptions, while retaining competitive precision. Concretely, as posed by García Escudero, Mirpoorian & Pogosian (2026): (1) quantify whether forthcoming tomographic galaxy clustering and weak-lensing surveys (the Vera Rubin Observatory's Legacy Survey of Space and Time, LSST, and Euclid) combined with low-noise, wide-area CMB lensing can break the $A_s$–$\Omega_m h^2$–$\Sigma m_\nu$ degeneracy sufficiently to deliver recombination-independent, percent-level (or better) $H_0$ without any external prior on the primordial amplitude $A_s$, identifying the survey precision, mode coverage and systematics regime in which this becomes possible; (2) establish whether and how $\Sigma m_\nu$ bounds in the $r_d$-free framework can approach the precision of the conventional derived-$r_d$ analysis of the same data combination (whose $\Sigma m_\nu$ bounds currently lie at the $0.02$–$0.06$ eV level), i.e. reach bounds of that order, without reintroducing sensitivity to recombination modeling; (3) establish a principled or fully data-driven prior treatment for $\Sigma m_\nu$ in recombination-agnostic analyses — one whose functional form is physically or information-theoretically motivated (e.g. a reference or hierarchical data-driven prior) and which leaves the inferred $\Sigma m_\nu$ and $H_0$ robust under reasonable reparameterizations — thereby resolving the demonstrated uniform-versus-logarithmic prior sensitivity of the inferred $H_0$; and (4) validate the use of the CMB acoustic scale $\theta_{\star}$ as a high-redshift anchor by testing the near-invariance of $r_{\star}\approx r_d/1.02$ — which Pogosian, Zhao & Jedamzik (2024) found to hold across the known early-Universe extensions (extra relativistic species, massive neutrinos, primordial magnetic fields, early dark energy) — across a bounded, parameterized family of recombination-history modifications that reaches beyond those known extensions and spans the modifications capable of altering $H_0$ at the few-km/s/Mpc level relevant to the Hubble tension, with a scenario counted as validated when the fractional variation it induces in $r_{\star}/r_d$ is small compared with the sub-percent precision of the $\theta_{\star}$ measurement, so that the anchor does not silently reintroduce model dependence. These four components jointly support one objective: eliminating all hidden early-Universe model dependence from the $r_d$-agnostic pipeline while quantifying its achievable precision on $H_0$ and $\Sigma m_\nu$. A complete answer requires all four; an answer that addresses only part of them resolves the corresponding sub-question(s) alone and leaves the overall objective open.

References

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