Hubble tension in an anisotropic Universe

TL;DR

This work tests whether a late-time anisotropy modeled by a Bianchi type-I extension of ΛCDM can address the $H_0$ tension. By deriving the anisotropic distance modulus and performing Bayesian parameter inference with multiple samplers under uniform and Gaussian priors, the authors probe the viability and data-dependence of $H_0^{\text{anis}}$, $\Omega_m^{\text{anis}}$, and the anisotropy amplitude $\epsilon_r$. Across BAO, CC, and Pantheon+SH0ES data, they find that $\epsilon_r$ is generally small and that the inferred $H_0^{\text{anis}}$ depends strongly on dataset choice and prior assumptions, with no robust, universal alleviation of the tension. The study demonstrates methodological robustness and highlights the need for more comprehensive anisotropic models and additional cosmological probes to draw firmer conclusions about the role of anisotropy in the expansion history.

Abstract

We explore the Hubble tension within an anisotropic cosmological framework by revisiting the Bianchi type-I model introduced in Le Delliou et al. 2020. Motivated by ongoing debates surrounding back-reaction effects and observed anomalies in the cosmic microwave background (CMB), we investigate whether a departure from isotropy in the late Universe could reconcile the observed discrepancies in Hubble constant measurements. Using a Bayesian inference framework, we constrain the model parameters employing multiple nested sampling algorithms: bilby, PyMultiNest, and nessai. We perform the analysis under both uniform and Gaussian priors, allowing us to systematically assess the sensitivity of the inferred cosmological parameters to different prior assumptions. This dual-prior strategy balances agnostic parameter exploration with constraints informed by theory and observation. Our findings demonstrate the reliability of our inference pipeline across different samplers and emphasize the crucial role of prior selection in non-standard cosmological model testing. The results suggest that anisotropic models remain viable contenders in addressing current cosmological tensions: even though the present model does not show alleviation of the Hubble tension, the data points towards anisotropies. Future work may extend this methodology to more complex anisotropic scenarios and incorporate additional cosmological probes such as CMB polarization and gravitational wave standard sirens.

Figures (8)

• Figure 1: (a) Analytical component of the integral from Eq.\ref{['eq:dist_modulus_a0R']}, as a function of $t_{0}$ for different ratios, $a/a_{0}$ (see legend). Solid lines correspond to $H_{0}=67.27~\text{km}\text{s}^{-1}\text{Mpc}^{-1}$ and $\Omega_{m} = 0.21$, while dashed lines represent $\Omega_{m} = 0.25$. The remaining parameters, such as $n$, $\epsilon_{r}$ are arbitrary. All results are presented up to the divergence threshold. (b) Graph showing the numerical solution to Eq. \ref{['eq:zOfAsA0']}. The choice of $\epsilon_{r}$ has a negligible impact on the evolution of $a/a(0)$: the curves corresponding to different $\epsilon_{r}$ values completely overlap.
• Figure 2: Hubble diagram. $H_{0}$ of observational CC and BAO data vs. $z$. (a). The 3 dots represent the galaxy distribution measurements at $z=0.38; 0.51; 0.61$, see Sect.\ref{['sec:DataUsed']} for mode details; (b) Hubble parameter observation measured with BAO method; (c) CC observations measured with DA method; (d) combined sample CC and BAO datasets fitted with bilby with uniform prior PDFs for $\epsilon_{r}$ and $n$.
• Figure 3: Marginalized Bayesian posterior distributions, $H_{0}-\Omega_{m}$(bottom), $H_{0}-\epsilon_{r}$ (center), $H_{0}-n$ (top), corresponding to the grayscales on Fig.\ref{['fig:result_fit_dist_CC']}, of the model parameters for three sampler methods used in this paper, namely bilby, nessai, and PyMultiNest. From left to right using the CC observations measured with DA method; BAO dataset; combined sample CC and BAO datasets.
• Figure 4: The anisotropic BAO parameter, $D_{A}(z)/r_{d}$, vs. $z$ (top) and $r_{s}(z_{d})/D_{V}(z)$ vs. $z$ (bottom). The data points are taken from the compilation of BAO measurements from diverse releases, see Table \ref{['tab:zi_dzi_onlyBAO']}. The red dotted line shows the $D_{A}(z)/r_{d}$ as function of redshift from the result parameters obtained from the Bayesian sampling to 3 galaxy distributions, see Fig.\ref{['fig:result_fit_dist_CC']}(a). The red dashed line shows the $D_{A}(z)/r_{d}$ as function of redshift from the result parameters obtained from the Bayesian sampling to $H_{0}$ parameter observation measured with BAO method, see Fig.\ref{['fig:result_fit_dist_CC']}(b); The red dot-dashed line shows the $D_{A}(z)/r_{d}$ as function of redshift from the result parameters obtained from the Bayesian sampling to CC data measured with DA method, see Fig.\ref{['fig:result_fit_dist_CC']}(c); The blue solid line shows the $D_{A}(z)/r_{d}$ as function of redshift from the result parameters obtained from the Bayesian sampling to BAO distance measurements data with the help of the bilby method; The blue short-dashed shows the same, using the nessai method; The blue long-dashed shows the same, using the PyMultiNest method. The thin gray lines illustrates the Bayesian posterior sampling.
• Figure 5: Two-dimensional marginalized posterior distributions for the anisotropic Hubble constant ($H_0^{\rm{anis}}$) and the matter density parameter ($\Omega_m^{\rm{anis}}$), derived from Bayesian analysis under different data, as shown on Fig. \ref{['fig:result_fit_dist_BAO']}. The four panels correspond to: (top-left) BAO data in the $z - D_{A}(z)/r_{d}$ plane with uniform priors; (top-right) the same BAO data with Gaussian priors; (bottom-left) BAO data in the $z - r_s(z_d)/D_V(z)$ plane with uniform priors; (bottom-right) BAO+DA dataset with Gaussian priors. Each plot shows combined results from three samplers (bilby, PyMultiNest, and nessai), illustrating the influence of prior selection and data combination on the joint constraints of the cosmological parameters. The contours represent 68% and 95% confidence intervals.