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Constraining Fifth Forces using the Local Distance Ladder: Implications for the Hubble Tension

Marcus Högås, Edvard Mörtsell, Harry Desmond, Adam Riess

TL;DR

This work tests whether a screened fifth force could bias the local distance ladder and thus alleviate the Hubble tension. Using a full Bayesian recalibration of the SH0ES Cepheid–SN Ia ladder, augmented by three environmental proxy fields ($\\Phi$, $a$, $K$) and multiple $R_{ m max}$ scales, the authors quantify how a fifth force would shift Cepheid luminosities and TRGB distances within a unified framework, optionally including TRGB data. Across three proxy-fields and five cutoff scales, the posterior consistently favors no fifth-force effect ($\\Delta G/G_{ m N}=0$) and finds $H_0 = 73.1 \pm 1.0$ km s$^{-1}$ Mpc$^{-1}$, leaving the Planck–AIL tension intact. Model comparison via BIC/AIC strongly disfavors screened fifth-force extensions, with only marginal, model-dependent exceptions that disappear when TRGB data are included. The results thus place robust astrophysical constraints on environmental screening and argue against screened fifth forces as a solution to the Hubble tension.

Abstract

We revisit the local distance ladder measurement of the Hubble constant in models where gravity is modified by a fifth force, an additional long-range interaction. In many such theories the force is screened; suppressed in dense environments but potentially active in galaxies used for distance calibration. We model this environmental dependence using three quantities that characterize each galaxy's large-scale gravitational environment: the external gravitational potential $Φ$, acceleration $a$, and curvature $K$. Our baseline analysis recalibrates the SH0ES-team's Cepheid-supernova distance ladder, incorporating the fifth force via its impact on the Cepheid period-luminosity relation. Across models, a fifth force is strongly constrained, with posteriors concentrated around a null result. The inferred Hubble constant is $H_0 = 73.1 \pm 1.0 \, \mathrm{km/s/Mpc}$, retaining the Hubble tension at $>5 \, σ$. As an additional test, we incorporate four independent Tip of the Red Giant Branch (TRGB) distance datasets into a joint Cepheid-TRGB-supernova calibration. These combined analyses further constrain the magnitude of fifth-force effects. Taken together, our results show that, across the class of screened fifth-force models we analyze, the calibration of the local distance ladder remains essentially unchanged, leaving the Hubble tension intact.

Constraining Fifth Forces using the Local Distance Ladder: Implications for the Hubble Tension

TL;DR

This work tests whether a screened fifth force could bias the local distance ladder and thus alleviate the Hubble tension. Using a full Bayesian recalibration of the SH0ES Cepheid–SN Ia ladder, augmented by three environmental proxy fields (, , ) and multiple scales, the authors quantify how a fifth force would shift Cepheid luminosities and TRGB distances within a unified framework, optionally including TRGB data. Across three proxy-fields and five cutoff scales, the posterior consistently favors no fifth-force effect () and finds km s Mpc, leaving the Planck–AIL tension intact. Model comparison via BIC/AIC strongly disfavors screened fifth-force extensions, with only marginal, model-dependent exceptions that disappear when TRGB data are included. The results thus place robust astrophysical constraints on environmental screening and argue against screened fifth forces as a solution to the Hubble tension.

Abstract

We revisit the local distance ladder measurement of the Hubble constant in models where gravity is modified by a fifth force, an additional long-range interaction. In many such theories the force is screened; suppressed in dense environments but potentially active in galaxies used for distance calibration. We model this environmental dependence using three quantities that characterize each galaxy's large-scale gravitational environment: the external gravitational potential , acceleration , and curvature . Our baseline analysis recalibrates the SH0ES-team's Cepheid-supernova distance ladder, incorporating the fifth force via its impact on the Cepheid period-luminosity relation. Across models, a fifth force is strongly constrained, with posteriors concentrated around a null result. The inferred Hubble constant is , retaining the Hubble tension at . As an additional test, we incorporate four independent Tip of the Red Giant Branch (TRGB) distance datasets into a joint Cepheid-TRGB-supernova calibration. These combined analyses further constrain the magnitude of fifth-force effects. Taken together, our results show that, across the class of screened fifth-force models we analyze, the calibration of the local distance ladder remains essentially unchanged, leaving the Hubble tension intact.

Paper Structure

This paper contains 17 sections, 32 equations, 4 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Theory
  3. Data
  4. Influence of a fifth force
  5. The fifth-force model
  6. Statistical methodology
  7. Results
  8. Baseline SH0ES calibration with a fifth force
  9. Impact of proxy-field uncertainties
  10. Minimum allowed $H_0$
  11. Including the Planck prior
  12. Discussion
  13. Conclusions
  14. Standard linear model
  15. Marginalization
  16. ...and 2 more sections

Figures (4)

  • Figure 1: Proxy-field values for the galaxies used in the SH0ES distance ladder: the anchor galaxies, whose geometric distances calibrate the Cepheid period--luminosity relation, and SN Ia host galaxies. Some of the galaxies also have TRGB-based distance estimates, and are marked in bold orange. The MW is shown in red, N4258 in green, and LMC/SMC in purple whereas the SN Ia host galaxies appear as blue points. The three panels illustrate the three alternative proxy-field descriptions of the fifth-force strength for a common cutoff radius $R_\mathrm{max} = 0.4 \, \mathrm{Mpc}$. Top: gravitational potential $\Phi$. Middle: acceleration $a$. Bottom: curvature $K$.
  • Figure 2: Posterior distributions of the fifth-force parameters for the $\Phi$-screening model with $R_\mathrm{max} = 5.1 \, \mathrm{Mpc}$, as an example. Shown are the $68 \, \%$ and $95 \, \%$ confidence contours for the recalibrated SH0ES dataset, and the same when the first two rungs of the distance ladder are replaced by the TRGB distances of L24, yielding weaker constraints. For the SH0ES calibration, the posterior is concentrated near regions consistent with $\Delta G / G_\mathrm{N} = 0$, showing no significant evidence for a fifth-force deviation. The left (right) vertical line indicates the $p_0$-value below (above) which all galaxies are screened (unscreened).
  • Figure 3: Collection of $\Delta\mathrm{BIC}$ values across all fifth-force models. Each entry corresponds to one combination of screening proxy ($\Phi$, $a$, $K$) and smoothing scale $R_{\max}$. Negative $\Delta\mathrm{BIC}$ values indicate preference for the standard SH0ES calibration without a fifth force. The histogram shows that all fifth-force models lie deep in the region disfavored by the BIC, confirming the absence of statistical support for a fifth-force extension of the distance ladder.
  • Figure 4: Unified posterior distributions for the Hubble constant $H_0$ obtained by combining results from all 15 screened-gravity models (three proxy fields, five cutoff radii). The result is $H_0 = 73.1 \pm 1.0 \, \mathrm{km/s/Mpc}$. For comparison, the Planck estimate is also shown, $H_0 = 67.4 \pm 0.5 \, \mathrm{km/s/Mpc}$, as well as the standard SH0ES calibration without a fifth force, $H_0 = 73.0 \pm 1.0 \, \mathrm{km/s/Mpc}$. The Hubble tension remains at $> 5 \, \sigma$ also in the presence of a fifth force.