Probing Anisotropic Cosmic Birefringence with Foreground-Marginalised SPT B-mode Likelihoods

TL;DR

The paper develops foreground-marginalised, CMB-only BB likelihoods from SPT-3G D1 BB and SPTpol BB data using the CMB-lite compression framework to enable efficient cosmological inference of anisotropic cosmic birefringence. It models the BB spectrum as a sum of tensor, lensing, and birefringence templates with amplitudes $r$, $A_{ m LT}$, and $A_{ m CB}$, and performs MCMC with optional lensing priors. The analysis yields the strongest BB-based constraints to date on anisotropic birefringence, reporting $A_{ m CB} < 1.2\times 10^{-4}$ without and $A_{ m CB} < 0.53\times 10^{-4}$ with a lensing prior, with no evidence of anisotropic rotation. The compressed likelihoods are publicly released to enable rapid, reproducible analyses and will benefit future CMB polarization surveys from experiments like SPT, BICEP/Keck, the Simons Observatory, and LiteBIRD.

Abstract

In this work, we construct foreground-marginalised versions of the SPT-3G D1 and SPTpol cosmic microwave background (CMB) B-mode polarisation likelihoods. The compression is performed using the CMB-lite framework and we use the resulting data sets to constrain anisotropic cosmic birefringence, parametrised by the amplitude of a scale-invariant anisotropic birefringence spectrum, $A_{\rm CB}$. Using the new SPT-3G data we report a $95\%$ upper limit on $A_{\rm CB}$ of $ 1.2\times 10^{-4}$, which tightens to $0.53\times 10^{-4}$ when imposing a prior on the amplitude of gravitational lensing based on CMB lensing reconstruction analyses. These are the tightest constraints on anisotropic birefringence from BB power spectrum measurements to-date, demonstrating the constraining power of the South Pole Telescope. The likelihoods used in this work are made publicly available at https://github.com/lbalkenhol/candl_data

Figures (6)

• Figure 1: Histogram of MCMC samples of the common CMB power in the five SPT-3G D1 $B\!B$ band powers (black). The distribution is visibly non-Gaussian in the first two bins, which contain fewer modes. We fit offset log-normal distributions to the histograms (orange dashed lines), which serve as the basis for the compressed CMB-only likelihood.
• Figure 2: CMB-only band powers derived from SPT-3G D1 $B\!B$ data (orange, zebrowski25) and SPTpol $B\!B$ data (blue, sayre20). In contrast to the SPTpol data, the distribution of SPT-3G band powers on large scales is appreciably non-Gaussian; we indicate the median along with 16$\%$ and 84$\%$ intervals in this case. The black lines indicate the predicted power from the lensing of $E$ modes (solid line, $A_{\rm LT}=1$), primordial gravitational waves (dotted line, $r=0.1$), and anisotropic birefringence (dashed line, $A_{\rm CB}=10^{-4}{}$).
• Figure 3: One-dimensional marginalised posterior distributions for the amplitude parameters $r$ and $A_{\rm LT}{}$ multiplying templates for gravitational waves and lensed $E$ modes, respectively, derived using multi-frequency and lite likelihoods. For both cases, the compressed lite likelihoods recover the constraints of the reference multi-frequency likelihoods within MC precision. Left: SPT-3G D1 $B\!B$ multi-frequency analysis (blue solid line) compared to the lite likelihood (orange dashed line). Right: SPTpol $B\!B$ multi-frequency likelihood using the radio-galaxy foreground model (blue solid line) used to build the lite likelihood (orange dashed line). For reference we indicate the constraints using the multi-frequency likelihood with the original foreground model (green dotted line).
• Figure 4: One-dimensional marginalised $A_{\rm CB}{}$ posterior distributions derived using the SPT-3G D1 $B\!B$ lite likelihood without (solid orange) and with (dotted green) the $A_{\rm LT}{}$ APS prior qu25. We also show the SPTpol constraint with the same prior (dashed blue), which is consistent with results in the literature namikawa24lonappan25. The SPT-3G data place a tight $95\,\%$ upper limit on anisotropic birefringence of $A_{\rm CB}{} < 1.2\,\times 10^{-4}{}$ without and $A_{\rm CB}{} < 0.53\,\times 10^{-4} {}$ with the $A_{\rm LT}{}$ APS prior.
• Figure 5: Posteriors in the $A_{\rm CB}{}$-$A_{\rm LT}{}$ plane derived from SPT-3G data (no $A_{\rm LT}$ prior: orange filled, $A_{\rm LT}$ APS prior: red line) and SPTpol data (no $A_{\rm LT}$ prior: blue filled, $A_{\rm LT}$ APS prior: grey line). Without an external prior on $A_{\rm LT}$ the two data sets constrain bands in the $A_{\rm CB}{}$-$A_{\rm LT}{}$ plane. The SPTpol data can support larger values in both parameters than the SPT-3G data, such that the SPTpol (SPT-3G) band intersects the $A_{\rm CB}{}=0$ axis mostly above (below) $A_{\rm LT}{}=1$. The tight $A_{\rm LT}{}$ prior provided by the lensing reconstruction slices through the two bands such that in the case of SPT-3G we have a tight upper limit, whereas for SPTpol data we have a posterior that is mildly detached from $A_{\rm CB}{}=0$.