Is cosmic birefringence due to dark energy or dark matter? Simulation-based inference

TL;DR

This paper applies simulation-based inference with neural likelihood and posterior estimation to analyze cosmic birefringence, aiming to distinguish between dark energy and dark matter origins using CMB polarization data.

Contribution

It introduces a neural SBI framework to constrain parameters of cosmic birefringence, revealing non-Gaussian likelihoods and sensitivity to the scalar field mass scale.

Findings

Posterior on scalar field mass shows two regimes separated at 10^{-32} eV.

Instrumental miscalibration and lensing limit the exclusion of dark energy models.

Likelihood of EB correlation at low multipoles is highly non-Gaussian.

Abstract

Simulation-based inference (SBI) is a powerful inference technique for cases where the exact functional form of the likelihood is not known. A prime example is the likelihood of cross-correlation power spectra of the cosmic microwave background (CMB) fields at low multipoles, $\ell\lesssim 10$. In this paper, we investigate a parity-violating cross-correlation between $E$- and $B$- mode polarization fields using SBI. The $EB$ correlation at low $\ell$ is essential to distinguish between possible axion dark energy and dark matter interpretations of `cosmic birefringence', a rotation of the plane of linear polarization of the CMB, recently reported from WMAP, Planck, and Atacama Cosmology Telescope data. We use neural likelihood estimation to infer the likelihood of the $EB$ correlation at low $\ell$ and show that it is highly non-Gaussian. We then employ neural posterior estimation to constrain the scalar field mass ($m_\phi$), the cosmic birefringence amplitude ($g\phi_\mathrm{in}/2$), and the instrumental miscalibration angle ($\alpha$), from simulated datasets. We find that the posterior on $m_{\phi}$ shows two regimes, with a transition marked by $10^{-32}$ eV, highlighting a strong sensitivity to the scale dependence of cosmic birefringence. To quantify this behavior, we compute the probability $p(m_{\phi} < 10^{-32}$ eV) for various fiducial values of $m_{\phi}$. We find that $\alpha$ and the contribution of lensed $B$ modes ultimately limit our ability to exclude the dark energy scenario fully.