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The Price of Shifting the Hubble Constant

Jarah Evslin, Anjan A Sen, Ruchika

TL;DR

This work argues that an anisotropic BAO measurement fixes the product $H_0 r_d$, implying that a higher local $H_0$ necessitates a smaller acoustic scale $r_d$ and thus modifications to early‑time cosmology. By fitting BAO data with strong lensing time‑delay distances and megamaser distances across several dark‑energy models via a profile likelihood, the authors find $r_d$ values around 136–137 Mpc, with Planck’s ΛCDM baseline (~147 Mpc) remaining in tension, especially when the local $H_0$ ladder is included. The results show that $r_d$ is robust to the assumed late‑time dark energy dynamics, and dynamical dark energy does not alleviate the tension with Planck. The analysis highlights that resolving the $H_0$ discrepancy would require genuine changes to early‑time cosmology, while simple dark radiation or early dark energy models face constraints from CMB observables such as the damping scale and high‑$ ext{l}$ polarization. The paper emphasizes the pivotal role of BAO in constraining pre‑recombination physics and outlines future avenues with improved lensing and maser measurements to sharpen these inferences.

Abstract

An anisotropic measurement of the baryon acoustic oscillation (BAO) feature fixes the product of the Hubble constant and the acoustic scale $H_0 r_d$. Therefore, regardless of the dark energy dynamics, to accommodate a higher value of $H_0$ one needs a lower $r_d$ and so necessarily a modification of early time cosmology. One must either reduce the age of the Universe at the drag epoch or else the speed of sound in the primordial plasma. The first can be achieved, for example, with dark radiation or very early dark energy, automatically preserving the angular size of the acoustic scale in the Cosmic Microwave Background (CMB) with no modifications to post-recombination dark energy. However it is known that the simplest such modifications fall afoul of CMB constraints at higher multipoles. As an example, we combine anisotropic BAO with geometric measurements from strong lensing time delays from H0LiCOW and megamasers from the Megamaser Cosmology Project to measure $r_d$, with and without the local distance ladder measurement of $H_0$. We find that the best fit value of $r_d$ is indeed quite insensitive to the dark energy model, and is also hardly affected by the inclusion of the local distance ladder data.

The Price of Shifting the Hubble Constant

TL;DR

This work argues that an anisotropic BAO measurement fixes the product , implying that a higher local necessitates a smaller acoustic scale and thus modifications to early‑time cosmology. By fitting BAO data with strong lensing time‑delay distances and megamaser distances across several dark‑energy models via a profile likelihood, the authors find values around 136–137 Mpc, with Planck’s ΛCDM baseline (~147 Mpc) remaining in tension, especially when the local ladder is included. The results show that is robust to the assumed late‑time dark energy dynamics, and dynamical dark energy does not alleviate the tension with Planck. The analysis highlights that resolving the discrepancy would require genuine changes to early‑time cosmology, while simple dark radiation or early dark energy models face constraints from CMB observables such as the damping scale and high‑ polarization. The paper emphasizes the pivotal role of BAO in constraining pre‑recombination physics and outlines future avenues with improved lensing and maser measurements to sharpen these inferences.

Abstract

An anisotropic measurement of the baryon acoustic oscillation (BAO) feature fixes the product of the Hubble constant and the acoustic scale . Therefore, regardless of the dark energy dynamics, to accommodate a higher value of one needs a lower and so necessarily a modification of early time cosmology. One must either reduce the age of the Universe at the drag epoch or else the speed of sound in the primordial plasma. The first can be achieved, for example, with dark radiation or very early dark energy, automatically preserving the angular size of the acoustic scale in the Cosmic Microwave Background (CMB) with no modifications to post-recombination dark energy. However it is known that the simplest such modifications fall afoul of CMB constraints at higher multipoles. As an example, we combine anisotropic BAO with geometric measurements from strong lensing time delays from H0LiCOW and megamasers from the Megamaser Cosmology Project to measure , with and without the local distance ladder measurement of . We find that the best fit value of is indeed quite insensitive to the dark energy model, and is also hardly affected by the inclusion of the local distance ladder data.

Paper Structure

This paper contains 14 sections, 11 equations, 10 figures, 7 tables.

Table of Contents

  1. Introduction
  2. Motivation
  3. Methodology
  4. Data
  5. BAO Data
  6. Other Data
  7. Results
  8. Models
  9. Analysis
  10. Results
  11. Marginalized likelihoods
  12. Discussion
  13. Consistency with CMB Data
  14. Concluding Remarks

Figures (10)

  • Figure 1: BAO only results. Top: In the $\Lambda$CDM model, the only relevant parameters are $\Omega_m$ and $c/(H_0r_d)$. The standard error ellipses are plotted, corresponding to $\Delta\chi^2_{\rm{BAO}}=2.3,\ 6.0$ and $11.8$. The Planck benchmark value, with its corresponding error bars derived in the case of a $\Lambda$CDM model, is included for comparison. Bottom: $\Delta\chi^2$ is plotted for various values of $c/(H_0 r_d)$ with all nuisance parameters optimized. The red, green, blue and black curves correspond to the $H\Lambda$CDM-Planck, $\Lambda$CDM, wCDM and CPL models respectively.
  • Figure 2: BAO and strong lensing time delay results. Top: In the $\Lambda$CDM model, the only relevant parameters are $\Omega_m$, $r_d$ and $H_0$. The standard error ellipses are plotted with $\Omega_m$ optimized, $H_0$ in units of km/s/Mpc and $r_d$ in units of Mpc. Bottom: $\Delta\chi^2$ is plotted for various values of $H_0$ with all nuisance parameters optimized. The red, green, blue, black and brown curves correspond to the $\Lambda$CDM-Planck, H$\Lambda$CDM-Planck, $\Lambda$CDM, wCDM and CPL models respectively.
  • Figure 3: As in the bottom panel of Fig. \ref{['baolfig']}, but also including megamaser data.
  • Figure 4: The profiled values of the nuisance parameters in the fit of BAO, lensing and maser data. The red, green, blue, black and brown curves correspond to the $\Lambda$CDM-Planck, H$\Lambda$CDM-Planck, $\Lambda$CDM, wCDM and CPL models respectively.
  • Figure 5: The standard error ellipses corresponding to the profile likelihood for $H_0$ and $r_d$, with all nuisance parameters optimized. BAO, strong lensing and megamaser data are used. Top-left: H$\Lambda$CDM-Planck, Top-right: $\Lambda$CDM, Bottom-left: wCDM and Bottom-right: CPL model.
  • ...and 5 more figures