The isotropy of Hubble expansion in the early and late Universe

TL;DR

The paper addresses whether the Hubble expansion is isotropic across both early and late cosmic epochs. It combines three independent distance probes—Type Ia supernovae, fundamental plane galaxies, and CMB temperature fluctuations—to construct full-sky maps of expansion-rate residuals and tests isotropy with an inverse-variance weighted multi-tracer framework based on power-spectrum statistics. The main findings are that the SN and CMB maps are consistent with isotropy, yielding 99% upper limits of 0.39% for low-redshift probes, 0.95% for high-redshift probes, and 0.37% when combined at a 60-degree smoothing scale, while a localized FP anomaly likely stems from DESI systematics and shows no cross-correlation with the other tracers. These results strengthen ΛCDM isotropy claims and demonstrate the utility of cross-epoch, multi-tracer analyses for constraining directional variations in cosmic expansion, with future DESI data expected to further clarify the FP feature.

Abstract

We test the isotropy of Hubble expansion by combining several probes for the first time, constructing full-sky maps of expansion rate variation using Type Ia supernovae, fundamental plane galaxies, and CMB temperature fluctuations. We find no hint of anisotropy or correlation between early- and late-Universe expansion across all systematic models. The 99% confidence upper limits on expansion rate anisotropy are 0.39% for low-redshift supernovae, 0.95% for high-redshift CMB, and 0.37% when combined at a 60-degree smoothing scale. A significant anomaly in the fundamental plane residual map may reflect systematics in the current DESI dataset, as evidenced by the absence of cross-correlation with other tracers and its correlation with spatial density variations.

Figures (4)

• Figure 1: The $h$ and uncertainty $\sigma$ maps for supernovae (left), fundamental plane galaxies (middle) and CMB (right). All maps are calibrated to the Planck cosmology using fiducial analysis settings. Color bars mark the 5th, 50th and 95th percentiles. $f_\text{sky} = 0.41, 0.12, 0.52$.
• Figure 2: Pixel value histograms of $\delta_\mathrm{SN}$, $\delta_\mathrm{FP}$, and $\delta_\mathrm{CMB}$. Solid lines show fiducial configurations; dashed lines show systematic variants. The inset shows $\delta_\mathrm{CMB}$ histograms with error bars indicating 1$\sigma$ cosmological uncertainty. The distributions are zero-centered and approximately Gaussian. $\delta_\mathrm{SN}$ has the smallest scatter and $\delta_\mathrm{CMB}$ the largest.
• Figure 3: Weighted $C_\ell$ (Eq. \ref{['eqn:cl']}) of the Hubble residual maps $\delta_{\rm SN}$, $\delta_{\rm FP}$, and $\delta_{\rm CMB}$. The weighted auto-$C_\ell$ is scaled by $f_\text{sky}$ so that the area under the curve approximates the variance of the full-sky $\delta$ field. Solid lines represent the data, while shaded regions represent the 1$\sigma$ intervals of isotropic noise realizations. For the fiducial model (black), $\delta_\mathrm{SN}$ and $\delta_\mathrm{CMB}$ are consistent with isotropy, whereas the FP auto-$C_\ell$ is not, with a significant peak around $\ell = 6$. The SN and FP systematic variants (blue) do not remove peculiar velocities and hence exhibit anisotropic contamination from the large-scale structures.
• Figure 4: Upper limits on Hubble constant anisotropy as a function of smoothing scale. Solid lines show the mean noise level from isotropic realizations, while dashed lines indicate 99% confidence upper limits for the SNe, CMB, and the combined maps