Probing the Cosmological Principle with CMB lensing and cosmic shear

TL;DR

This work addresses testing the Cosmological Principle by probing potential late-time isotropy violations through the cross-correlation between CMB lensing convergence $\kappa$ and galaxy $B$-mode shear within an axisymmetric Bianchi I framework. The authors formulate the κ–$B$ cross-signal using a Bipolar Spherical Harmonics (BipoSH) approach, derive its theoretical construction with Limber-approximation kernels, and evaluate signal-to-noise for a Euclid-like survey in combination with Planck2018 and SO-LAT data. They find that most information resides on large angular scales ($\ell \lesssim 200$), with percent-level sensitivity to anisotropy and a modest ~20% improvement from tomography; incorporating galaxy $E$-$B$ cross-correlations could further tighten constraints. Overall, the study demonstrates that lensing-based observables offer a complementary and promising avenue to test isotropy on the largest scales, motivating future analyses that combine multiple probes and fully account for cross-covariances.

Abstract

The standard cosmological model assumes the Cosmological Principle. However, recent observations hint at possible violations of isotropy on large scales, possibly through late-time anisotropic expansion. Here we investigate the potential of cross-correlations between CMB lensing convergence $κ$ and galaxy cosmic shear $B$-modes as a novel probe of such late-time anisotropies. Our signal-to-noise forecasts reveal that information from the $κ$-$B$ cross-correlation is primarily contained on large angular scales ($\ell \lesssim 200$). We find that this cross-correlation for a Euclid-like galaxy survey is sensitive to anisotropy at the percent level. Making use of tomography yields a modest improvement of $\sim 20\%$ in detection power. Incorporating the galaxy $E$-$B$ cross-correlations would further enhance these constraints.

Figures (12)

• Figure 2.1: Evolution of density parameters $\Omega_m$, $\Omega_{de}$ and $\Omega_{\sigma}$ (scaled by a factor of 100) up to $z=2.5$ for various values of $\Omega_{\sigma0}$.
• Figure 3.1: Evolution of $\alpha_\perp$, $\beta_\perp$, and $\sigma_{\perp}/H_0$ up to $z=2.5$ for a final shear strength of $\Omega_{\sigma0} = 10^{-4}$ (i.e. $\sigma_{\perp0}/H_0 = 10^{-2}$).
• Figure 3.2: Integrand of $\mathcal{P}_{\ell M}^{\kappa i}$, given by \ref{['eqn:P_lM_defn_Limber']}, scaled by the $\ell$-dependent prefactors from \ref{['eqn:EB_BipoSH_Coeff_Dominant']}, as a function of redshift up to $z = 2.5$ for a final shear strength of $\Omega_{\sigma 0} = 10^{-4}$ (i.e., $\sigma_{\perp0} / H_0 = 10^{-2}$). Curves are shown for four representative redshift bins, as well as for the full (non-tomographic) redshift distribution, over the range $10 \leq \ell \leq 250$. Note that changing variables in \ref{['eqn:P_lM_defn_Limber']} from $\chi$ to $z$ introduces a factor of $H^{-1}=(1+z)^{-1}\mathcal{H}^{-1}$ into each integrand.
• Figure 3.3: Amplitude of the BipoSH coefficient $^{\kappa B^i}\!\mathcal{A}^{2,0}_{\ell, \ell + 1}$ over the range $10 \leq \ell \leq 750$, shown for the same redshift bins and distributions as in \ref{['fig:A2M_lp1_Integrand']}. Different colours indicate 10 values of the shear strength in the range $\Omega_{\sigma 0} \leq 10^{-2}$ (i.e., $\sigma_{\perp0} / {H}_0 \leq 10^{-1}$). The turnover scale $\bar{\ell}$ for each redshift bin is indicated with a vertical dashed line.
• Figure 3.4: Linear convergence power spectrum computed using CLASS (solid black) alongside the Planck2018 minimum-variance power spectrum (solid blue). The minimum-variance reconstruction noise/bias spectra for Planck2018 (dotted blue) and Simons (dotted red) are also shown.