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How does an incomplete sky coverage affect the Hubble Constant variance?

Carlos A. P. Bengaly, Uendert Andrade, Jailson S. Alcaniz

TL;DR

This study investigates the Hubble constant tension between local SN-based measurements and CMB inferences by analyzing directional variations of $H_0$ across the sky using low-$z$ Pantheon SN data. By employing hemispherical comparisons on a HEALPix grid and a cosmographic expansion for $D_L(y)$, the authors quantify the cosmic variance induced by incomplete sky sampling via three Monte Carlo realizations, including isotropic and Pantheon-like sky distributions. They find that cosmic variance can reduce the tension from about $4.4\sigma$ down to roughly $2.7$–$3.4\sigma$, depending on sky coverage, with non-uniform sampling elevating the variance. Importantly, projections to larger future SN samples show a substantial reduction in $\Delta h$ and suggest that cosmic variance alone may be unable to fully explain the tension, highlighting the potential need for new physics or unidentified systematics; forthcoming wide-area surveys and standard-siren measurements will be crucial to resolve whether the discrepancy signals beyond-$\Lambda$CDM physics or remains a sampling artifact.

Abstract

We address the $\simeq 4.4σ$ tension between local and the CMB measurements of the Hubble Constant using simulated Type Ia Supernova (SN) data-sets. We probe its directional dependence by means of a hemispherical comparison through the entire celestial sphere as an estimator of the $H_0$ cosmic variance. We perform Monte Carlo simulations assuming isotropic and non-uniform distributions of data points, the latter coinciding with the real data. This allows us to incorporate observational features, such as the sample incompleteness, in our estimation. We obtain that this tension can be alleviated to $3.4σ$ for isotropic realizations, and $2.7σ$ for non-uniform ones. We also find that the $H_0$ variance is largely reduced if the data-sets are augmented to 4 and 10 times the current size. Future surveys will be able to tell whether the Hubble Constant tension happens due to unaccounted cosmic variance, or whether it is an actual indication of physics beyond the standard cosmological model.

How does an incomplete sky coverage affect the Hubble Constant variance?

TL;DR

This study investigates the Hubble constant tension between local SN-based measurements and CMB inferences by analyzing directional variations of across the sky using low- Pantheon SN data. By employing hemispherical comparisons on a HEALPix grid and a cosmographic expansion for , the authors quantify the cosmic variance induced by incomplete sky sampling via three Monte Carlo realizations, including isotropic and Pantheon-like sky distributions. They find that cosmic variance can reduce the tension from about down to roughly –, depending on sky coverage, with non-uniform sampling elevating the variance. Importantly, projections to larger future SN samples show a substantial reduction in and suggest that cosmic variance alone may be unable to fully explain the tension, highlighting the potential need for new physics or unidentified systematics; forthcoming wide-area surveys and standard-siren measurements will be crucial to resolve whether the discrepancy signals beyond-CDM physics or remains a sampling artifact.

Abstract

We address the tension between local and the CMB measurements of the Hubble Constant using simulated Type Ia Supernova (SN) data-sets. We probe its directional dependence by means of a hemispherical comparison through the entire celestial sphere as an estimator of the cosmic variance. We perform Monte Carlo simulations assuming isotropic and non-uniform distributions of data points, the latter coinciding with the real data. This allows us to incorporate observational features, such as the sample incompleteness, in our estimation. We obtain that this tension can be alleviated to for isotropic realizations, and for non-uniform ones. We also find that the variance is largely reduced if the data-sets are augmented to 4 and 10 times the current size. Future surveys will be able to tell whether the Hubble Constant tension happens due to unaccounted cosmic variance, or whether it is an actual indication of physics beyond the standard cosmological model.

Paper Structure

This paper contains 4 sections, 9 equations, 3 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Data Analysis
  3. Results
  4. Conclusions

Figures (3)

  • Figure 1: Left panel: The sky distribution of SN at $0.023 < z < 0.150$ following the MC-iso1 prescription. Central panel: Same as the left panel, but for the MC-iso2 instead. Right panel: A realization assuming the original SN celestial distribution, corresponding to the MC-pantheon case.
  • Figure 2: The $\Delta h$ of all MC realizations compared to the value obtained from the real data (pink vertical line), as well as the $\Delta h^{\rm tension}$ at $1$ and $2\sigma$ C.L. displayed in light gray and blue shades, respectively.
  • Figure 3: Left panel: The $\Delta h$ of 200 MC-iso1 realizations assuming the original number of data points, as well as for those assuming samples 4 and 10 times larger. Right panel: Same as before, but for MC-iso2 instead. The light gray and blue shades are the same as Fig. \ref{['fig:deltah_pantheon']}, but $\Delta h$ was clipped at $0.05$ to ease visualization.