Probing cosmic isotropy: Hubble constant and matter density large-angle variations with the Pantheon+SH0ES data

TL;DR

This work tests the cosmological principle by searching for large-angle anisotropies in the Hubble constant $H_0$ and matter density $Ω_m$ within flat-$\Lambda$CDM, using the Pantheon+SH0ES SN sample. It implements a hemispherical directional analysis, estimating $H_0^J$ and $Ω_m^J$ in each hemisphere ($N_{caps}=48$) via MCMC while propagating the full covariance $C$, and then compares the resulting angular power spectra to 1000 isotropic realizations to assess significance. The authors find a dominant dipole in both parameter maps but no significant large-scale anisotropy for $z_{min}=0.015$ (≈60 Mpc); a strong low-redshift $H_0$ dipole appears due to peculiar velocities when including nearby SNe. Overall, the results support isotropy of cosmic expansion and matter distribution at cosmological scales in agreement with flat-$\Lambda$CDM, with local velocity fields accounting for near-field anisotropies.

Abstract

In this study we investigate potential large-angle anisotropies in the angular distribution of the cosmological parameters $H_0$ (the Hubble constant) and $Ω_m$ (the matter density) in the flat-$Λ$CDM framework, using the Pantheon+SH0ES supernovae catalog. For this we perform a directional analysis by dividing the celestial sphere into a set of directions, and estimate the best-fit cosmological parameters across the sky using a MCMC approach. Our results show a dominant dipolar pattern for both parameters in study, suggesting a preferred axis in the universe expansion and in the distribution of matter. However, we also found that for $z \gtrsim 0.015$, this dipolar behavior is not statistically significant, confirming the expectation -- in the $Λ$CDM scenario -- of an isotropic expansion and a uniform angular distribution of matter (both results at $1\,σ$ confidence level). Nevertheless, for nearby supernovae, at distances $\lesssim 60$ Mpc or $z \lesssim 0.015$, the peculiar velocities introduce a highly significant dipole in the angular distribution of $H_0$. Furthermore, we perform various robustness tests that support our findings, and consistency tests of our methodology.

Figures (16)

• Figure 1: Histogram of the redshift distribution of the Pantheon+SH0ES supernovae catalog, in the CMB redshift frame.
• Figure 2: Mollweide projection in galactic coordinates of the Pantheon+SH0ES supernovae events, represented as colored dots, on the celestial sphere. The colors of the SNe events represent the redshift of the galaxy host. The solid red line represents the celestial equator.
• Figure 3: The $H_0$-map (upper map) and the $\Omega_m$-map (lower map), shown in Galactic coordinates, resulting from our directional analysis of the redshift bin with $z_{\text{min}} = 0.015$, considering 48 hemispheres. Grid lines mark Galactic longitudes and latitudes in $30^{\circ}$ intervals.
• Figure 4: The standard deviation maps: $\sigma_{H_0}$-map and $\sigma_{\Omega_m}$-map in Galactic coordinates. These analyses resulted from the study of the bin redshift with $z_{\text{min}} = 0.015$, and considering 48 hemispheres.
• Figure 5: Statistics of the information contained in the maps displayed in Figure \ref{['fig:h0_map_0p015']}. In the first row, we display the distributions of the pixel values for the $H_0$-map and $\sigma_{H_0}$-map, obtaining the medians $73.99$ and $3.48$, and standard deviations $0.24$ and $0.13$ for the $H_0$- and $\sigma_{H_0}$-maps, respectively. In the second row, we show the distributions of the pixel values for the $\Omega_m$-map and $\sigma_{\Omega_m}$-map, obtaining the medians $0.354$ and $0.025$, and standard deviations $0.025$ and $0.003$ for the $\Omega_m$- and $\sigma_{\Omega_m}$-maps, respectively. Instead, in the third row we present the statistics of the $M_B$-map and $\sigma_{M_B}$-map, with median values $M_B=-19.22$ with standard deviation $0.007$ and $\sigma_{M_B} = 0.10$ and standard deviation $0.004$; one notices that the dispersion of values of this parameter is, indeed, very small.