Are new pre-recombination physics or calibrator systematics behind the short sound horizon inferred from late-time distance indicators?

Late-time distance measurements calibrated independently of the cosmic microwave background (CMB) — Cepheid and tip-of-the-red-giant-branch distance ladders and strong-gravitational-lensing time delays — infer $H_0\approx 70$ –73 km s $^{-1}$ Mpc $^{-1}$ together with a sound horizon $r_{\rm d}\approx 137\pm 4$ Mpc, jointly discrepant with the Planck $\Lambda$ CDM values ( $H_0\approx 67.4$ km s $^{-1}$ Mpc $^{-1}$ , $r_{\rm d}\approx 147$ Mpc) at between 2.3 and 5.1 $\sigma$ depending on the calibrator. The problem posed by Arendse et al. (2020) is to determine the origin of this joint discrepancy: new pre-recombination physics (additional relativistic energy density or an early-dark-energy component) or residual, collectively important systematics in the late-time calibrators and their modeling; whether a physically well-motivated early-Universe model can reconcile Planck with all robust late-time calibrations without displacing tension onto other observables; and two named diagnostics — whether the weak per-lens trend of inferred $r_{\rm d}$ with lens redshift is physical or a fluctuation, and the impact of assuming the general-relativistic relation between lensing and dynamical potentials on time-delay absolute distances.

Background

The sound horizon $r_{\rm d}$ is the comoving distance a pressure wave in the photon–baryon plasma travels between the Big Bang and the epoch of baryon decoupling; in the standard cosmological model ( $\Lambda$ CDM with standard recombination) it is fixed to $\approx 147$ Mpc by CMB data. Baryon acoustic oscillations (BAO), the frozen remnant of this scale in the galaxy distribution, calibrate relative distances through the 'inverse distance ladder': combining BAO with type Ia supernovae determines $H_0 r_{\rm d}$ accurately, so an absolute distance anchor — Cepheid variables on a period–luminosity (Leavitt) relation, the tip of the red giant branch (TRGB) in old stellar populations, or strong-lensing time delays — converts it into simultaneous constraints on $H_0$ and $r_{\rm d}$ that are independent of the CMB and of any assumed cosmological model. In time-delay cosmography, the arrival-time differences between multiple images of a lensed quasar or supernova, combined with a model of the lens mass and the lens-galaxy stellar velocity dispersion, yield an absolute angular-diameter distance to the lens; the dominant residual systematic is the mass-sheet degeneracy, a transformation of the lens mass profile that leaves imaging and time-delay observables unchanged and is degenerate with $H_0$ . Knox and Millea (2020) showed that the tension is fundamentally an $H_0$ – $r_{\rm d}$ anticorrelation: modifications of the expansion history after recombination can raise $H_0$ but leave the CMB-inferred $r_{\rm d}$ (and the inverse-distance-ladder $r_{\rm d}$ ) unchanged, so only physics before recombination — for example extra relativistic energy density, parametrized by the effective number of neutrino species $N_{\rm eff}$ , or early dark energy (EDE), a dark-energy component that contributes a few percent of the total density around redshift $z\sim 10^4$ and then dilutes away — can shorten the sound horizon. Arendse et al. (2020) combined BAO and supernovae calibrated by Cepheids (the SH0ES team, Supernovae H0 for the Equation of State), the TRGB (the Chicago–Carnegie Hubble Program, CCHP), and six time-delay lenses from H0LiCOW (H0 Lenses in COSMOGRAIL's Wellspring), obtaining $r_{\rm d}=(137\pm 3_{\rm stat}\pm 2_{\rm sys})$ Mpc and a joint $H_0$ – $r_{\rm d}$ tension with Planck of 2.3–5.1 $\sigma$ ; they confirmed that post-recombination extensions ( $w$ CDM, the standard model with a free constant dark-energy equation-of-state parameter $w$ , and the phantom-like phenomenologically emergent dark energy, PEDE) fail because they shift only $H_0$ , while pre-recombination extensions (free $N_{\rm eff}=3.24\pm 0.16$ , EDE) are permitted by the data unless the Cepheid calibration is included. They also noted two specific uncontrolled ingredients of the lensing arm: the inferred $r_{\rm d}$ from individual lenses shows a weak trend with lens redshift (about 1.6 $\sigma$ , not statistically significant), which could be a statistical fluke, a lens-model systematic, or an environmental effect; and the conversion of time-delay plus stellar-kinematics observables into absolute distances assumes the general-relativistic (GR) relation that the lensing potential is exactly twice the dynamical potential, a dependence that is subdominant at current 10–20% distance uncertainties but not quantified at the precision needed to settle the discrepancy. Subsequent work has sharpened every ingredient without resolving the diagnosis: SH0ES finds $H_0=73.04\pm 1.04$ km s $^{-1}$ Mpc $^{-1}$ (5 $\sigma$ from Planck) and photometry from the James Webb Space Telescope (JWST) rejects Cepheid crowding as the explanation at 8 $\sigma$ ; the CCHP finds $H_0=70.39\pm 1.22\pm 1.33\pm 0.70$ from JWST TRGB, an intermediate value, so calibrator-level differences persist; the Time-Delay COSMOgraphy collaboration (TDCOSMO)'s hierarchical analysis shows the time-delay $H_0$ shifts from $74.5^{+5.6}_{-6.1}$ to $67.4^{+4.1}_{-3.2}$ when the mass-sheet degeneracy is controlled only by stellar kinematics and external lens samples, and the first JWST spatially resolved stellar kinematics of a lens galaxy have only recently been obtained; EDE models remain without a consistent joint fit, with analyses of the Atacama Cosmology Telescope data release 6 (ACT DR6) and the Dark Energy Spectroscopic Instrument data release 2 (DESI DR2) showing no preference for EDE over $\Lambda$ CDM, while the DESI BAO shift in the $\Omega_{\rm m}$ – $r_{\rm s}H_0$ plane partially strengthens it, and independent arguments that early-time new physics alone cannot resolve all tensions simultaneously.

Problem Statement

Determine the physical origin of the joint late-time–CMB discrepancy in the pair $(H_0, r_{\rm d})$ : is the preference of CMB-independent late-time data (BAO and supernovae anchored by Cepheids, TRGB, and time-delay strong lenses) for a higher $H_0$ and a shorter sound horizon ( $r_{\rm d}\approx 137\pm 4$ Mpc versus $\approx 147$ Mpc from Planck $\Lambda$ CDM, a 2.3–5.1σ joint tension) caused by new pre-recombination physics or by residual systematics in the late-time calibrators and their modeling? A complete answer must attribute the joint discrepancy by establishing one of the two branches at a precision that removes it rather than merely reducing it — bringing the joint residual $(H_0, r_{\rm d})$ tension with the Planck values below $2\sigma$ : either (a) identify and quantitatively demonstrate, on independent evidence rather than through a correction fitted to restore agreement, the specific systematics (in Cepheid calibration, TRGB calibration, or lens mass profiles and stellar kinematics in time-delay cosmography) whose correction brings the three late-time calibrators (Cepheid-calibrated supernovae, TRGB-calibrated supernovae, and the time-delay lenses) into mutual agreement and into consistency with the CMB-inferred $r_{\rm d}$ ; or (b) exhibit a physically well-motivated pre-recombination model (e.g. additional relativistic energy density or early dark energy) that simultaneously matches Planck CMB data and all three of those calibrations in both $H_0$ and $r_{\rm d}$ , without creating statistically significant tensions in other observables. Refuting one branch alone — for instance, showing that no viable pre-recombination model exists, or that no candidate systematic reconciles the calibrators — narrows the attribution but is not by itself a complete answer, which requires establishing branch (a) or (b). Two lensing-arm diagnostics bear on the same attribution objective — in particular on branch (a) — and resolving them would constitute progress toward it, but the source raises them as diagnostics and outlook items rather than as completion requirements independent of branches (a)/(b): (i) whether the weak per-lens trend of inferred $r_{\rm d}$ with lens redshift (≈1.6σ in the source sample) is a statistical fluctuation, a lens-model systematic, or a physical/environmental effect; the source notes that checking the robustness of the trend requires cosmography-grade models of more lenses and that lens mass-model systematics can be assessed once high-S/N spatially resolved stellar kinematics are available; and (ii) the source-noted dependence of time-delay absolute distances on the GR assumption that the lensing potential equals twice the dynamical potential, which the source describes as subdominant at the current 10–20% distance uncertainties.

References

N. Arendse, R. J. Wojtak, A. Agnello, G. C.-F. Chen, C. D. Fassnacht, D. Sluse, S. Hilbert, M. Millon, V. Bonvin, K. C. Wong, F. Courbin, S. H. Suyu, S. Birrer, T. Treu, L. V. E. Koopmans, 'Cosmic dissonance: are new physics or systematics behind a short sound horizon?', Astronomy & Astrophysics 639, A57 (2020). DOI: 10.1051/0004-6361/201936720, https://doi.org/10.1051/0004-6361/201936720 (arXiv:1909.07986)
L. Knox, M. Millea, 'Hubble constant hunter's guide', Physical Review D 101, 043533 (2020). DOI: 10.1103/PhysRevD.101.043533, https://doi.org/10.1103/PhysRevD.101.043533 (arXiv:1908.03663)
K. C. Wong, S. H. Suyu, G. C.-F. Chen, C. E. Rusu, M. Millon, D. Sluse, V. Bonvin, C. D. Fassnacht, S. Taubenberger, M. W. Auger, S. Birrer, J. H. H. Chan, F. Courbin, S. Hilbert, O. Tihhonova, T. Treu, A. Agnello, X. Ding, I. Jee, E. Komatsu, A. J. Shajib, A. Sonnenfeld, R. D. Blandford, L. V. E. Koopmans, P. J. Marshall, G. Meylan, 'H0LiCOW – XIII. A 2.4 per cent measurement of H0 from lensed quasars: 5.3σ tension between early- and late-Universe probes', Monthly Notices of the Royal Astronomical Society 498, 1420 (2020). DOI: 10.1093/mnras/stz3094, https://doi.org/10.1093/mnras/stz3094 (arXiv:1907.04869)
S. Birrer, A. J. Shajib, A. Galan, M. Millon, T. Treu, A. Agnello, M. Auger, G. C.-F. Chen, L. Christensen, T. Collett, F. Courbin, C. D. Fassnacht, L. V. E. Koopmans, P. J. Marshall, J.-W. Park, C. E. Rusu, D. Sluse, C. Spiniello, S. H. Suyu, S. Wagner-Carena, K. C. Wong, M. Barnabè, A. S. Bolton, O. Czoske, X. Ding, J. A. Frieman, L. Van de Vyvere, 'TDCOSMO – IV. Hierarchical time-delay cosmography – joint inference of the Hubble constant and galaxy density profiles', Astronomy & Astrophysics 643, A165 (2020). DOI: 10.1051/0004-6361/202038861, https://doi.org/10.1051/0004-6361/202038861 (arXiv:2007.02941)
T. Treu, S. H. Suyu, P. J. Marshall, 'Strong lensing time-delay cosmography in the 2020s', The Astronomy and Astrophysics Review 30, 8 (2022). DOI: 10.1007/s00159-022-00145-y, https://doi.org/10.1007/s00159-022-00145-y (arXiv:2210.15794)
A. J. Shajib, T. Treu, S. H. Suyu, D. Law, A. Yıldırım, M. Cappellari, A. Galan, S. Knabel, H. Wang, S. Birrer, F. Courbin, C. D. Fassnacht, J. A. Frieman, A. Melo, T. Morishita, P. Mozumdar, D. Sluse, M. Stiavelli, 'TDCOSMO – XXIV. First spatially resolved kinematics of the lens galaxy obtained using JWST-NIRSpec to improve time-delay cosmography', Astronomy & Astrophysics 707, A314 (2026). DOI: 10.1051/0004-6361/202556126, https://doi.org/10.1051/0004-6361/202556126 (arXiv:2506.21665)
M. Pascale, B. L. Frye, J. D. R. Pierel, W. Chen, P. L. Kelly, S. H. Cohen, R. A. Windhorst, A. G. Riess, P. S. Kamieneski, J. M. Diego, A. K. Meena, S. Cha, M. Oguri, A. Zitrin, M. J. Jee, N. Foo, R. Leimbach, A. M. Koekemoer, C. J. Conselice, L. Dai, A. Goobar, M. R. Siebert, L. Strolger, S. P. Willner, 'SN H0pe: The First Measurement of H0 from a Multiply Imaged Type Ia Supernova, Discovered by JWST', The Astrophysical Journal 979, 13 (2025). DOI: 10.3847/1538-4357/ad9928, https://doi.org/10.3847/1538-4357/ad9928 (arXiv:2403.18902)
A. G. Riess, W. Yuan, L. M. Macri, D. Scolnic, D. Brout, S. Casertano, D. O. Jones, Y. Murakami, G. S. Anand, L. Breuval, T. G. Brink, V. A. Filippenko, S. Hoffmann, S. W. Jha, W. D'arcy Kenworthy, J. Mackenty, B. E. Stahl, W. Zheng, 'A Comprehensive Measurement of the Local Value of the Hubble Constant with 1 km s−1 Mpc−1 Uncertainty from the Hubble Space Telescope and the SH0ES Team', The Astrophysical Journal Letters 934, L7 (2022). DOI: 10.3847/2041-8213/ac5c5b, https://doi.org/10.3847/2041-8213/ac5c5b (arXiv:2112.04510)
A. G. Riess, G. S. Anand, W. Yuan, S. Casertano, A. Dolphin, L. M. Macri, L. Breuval, D. Scolnic, M. Perrin, I. R. Anderson, 'JWST Observations Reject Unrecognized Crowding of Cepheid Photometry as an Explanation for the Hubble Tension at 8σ Confidence', The Astrophysical Journal Letters 962, L17 (2024). DOI: 10.3847/2041-8213/ad1ddd, https://doi.org/10.3847/2041-8213/ad1ddd (arXiv:2401.04773)
W. L. Freedman, B. F. Madore, T. J. Hoyt, I. S. Jang, A. J. Lee, K. A. Owens, 'Status Report on the Chicago-Carnegie Hubble Program (CCHP): Measurement of the Hubble Constant Using the Hubble and James Webb Space Telescopes', The Astrophysical Journal 985, 203 (2025). DOI: 10.3847/1538-4357/adce78, https://doi.org/10.3847/1538-4357/adce78 (arXiv:2408.06153)
V. Poulin, T. L. Smith, T. Karwal, M. Kamionkowski, 'Early Dark Energy Can Resolve The Hubble Tension', Physical Review Letters 122, 221301 (2019). DOI: 10.1103/PhysRevLett.122.221301, https://doi.org/10.1103/PhysRevLett.122.221301 (arXiv:1811.04083)
J. S. Cruz, F. Niedermann, M. S. Sloth, 'A grounded perspective on new early dark energy using ACT, SPT, and BICEP/Keck', Journal of Cosmology and Astroparticle Physics 2023(02), 041 (2023). DOI: 10.1088/1475-7516/2023/02/041, https://doi.org/10.1088/1475-7516/2023/02/041 (arXiv:2209.02708)
V. Poulin, T. L. Smith, R. Calderón, T. Simon, 'Impact of ACT DR6 and DESI DR2 for early dark energy and the Hubble tension', Physical Review D 113, 063519 (2026). DOI: 10.1103/bx25-1g5d, https://doi.org/10.1103/bx25-1g5d (arXiv:2505.08051)
J.-Q. Jiang, 'Status of early dark energy after DESI: The role of $\Omega_m$ and $r_s H_0$ ', Physics of the Dark Universe 48, 101902 (2025). DOI: 10.1016/j.dark.2025.101902, https://doi.org/10.1016/j.dark.2025.101902 (arXiv:2502.15541)
S. Vagnozzi, 'Seven Hints That Early-Time New Physics Alone Is Not Sufficient to Solve the Hubble Tension', Universe 9, 393 (2023). DOI: 10.3390/universe9090393, https://doi.org/10.3390/universe9090393 (arXiv:2308.16628)
E. Di Valentino, O. Mena, S. Pan, L. Visinelli, W. Yang, A. Melchiorri, D. F. Mota, A. G. Riess, J. Silk, 'In the realm of the Hubble tension—a review of solutions', Classical and Quantum Gravity 38, 153001 (2021). DOI: 10.1088/1361-6382/ac086d, https://doi.org/10.1088/1361-6382/ac086d (arXiv:2103.01183)
L. Pogosian, G.-B. Zhao, K. Jedamzik, 'Recombination-independent determination of the sound horizon and the Hubble constant from BAO', The Astrophysical Journal Letters 904, L17 (2020). DOI: 10.3847/2041-8213/abc6a8, https://doi.org/10.3847/2041-8213/abc6a8 (arXiv:2009.08455)
J.-Q. Jiang, Y.-S. Piao, 'Can the sound horizon-free measurement of $H_0$ constrain early new physics?', Physical Review D 111, 103505 (2025). DOI: 10.1103/PhysRevD.111.103505, https://doi.org/10.1103/PhysRevD.111.103505 (arXiv:2501.16883)
E. Di Valentino, J. Levi Said, A. Riess, A. Pollo, V. Poulin, A. Gómez-Valent, A. Weltman, et al., 'The CosmoVerse White Paper: Addressing observational tensions in cosmology with systematics and fundamental physics', Physics of the Dark Universe 49, 101965 (2025). DOI: 10.1016/j.dark.2025.101965, https://doi.org/10.1016/j.dark.2025.101965 (arXiv:2504.01669)