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

TL;DR

This work tackles the challenge of distinguishing dark-energy versus dark-matter origins of cosmic birefringence by exploiting the parity-violating $EB$ power spectrum at low multipoles, where the likelihood is intractable and non-Gaussian. It adopts simulation-based inference (SBI) with neural likelihood and posterior estimation, using a fast power-spectrum emulator and a forward simulator to constrain $(m_{\phi}, g\phi_{\mathrm{in}}/2, \alpha)$ from simulated $\widehat{C}_\ell^{EB}$. The analysis reveals two distinct posterior regimes separated near $m_{\phi}\sim 10^{-32}$ eV, with degeneracies between $\alpha$ and $g\phi_{\mathrm{in}}/2$ that are conditioned by the $EB$ shape and the presence of lensing $B$ modes; delensing can significantly improve discriminatory power, though polarization-angle calibration remains a critical factor. The work demonstrates a viable SBI pathway for low-$\ell$ CMB birefringence analyses and outlines practical steps toward applying these methods to real data and future surveys like LiteBIRD.

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 ($m_φ$), the cosmic birefringence amplitude ($gφ_\mathrm{in}/2$), and the instrumental miscalibration angle ($α$), from simulated datasets. We find that the posterior on $m_φ$ 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 $p(m_φ < 10^{-32}$\,eV) for various fiducial values of $m_φ$. We find that $α$ and the contribution of lensed $B$ modes ultimately limit our ability to exclude the dark energy scenario fully.

Figures (11)

• Figure 1: Left: Evolution of $\phi$ (normalized at its initial value) as a function of redshift for different masses. The shaded areas represent the reionization ($z \sim 10$) and recombination ($z \sim 1100$) epochs. Right: The corresponding CMB $EB$ power spectra for the same masses. For all spectra, the cosmic birefringence amplitude is $g \phi_{\mathrm{in}}/2 = 0.35^\circ$.
• Figure 2: Statistical distributions of the $EB$ power spectrum estimator $\widehat{C}_{\ell}^{EB}$, given a fiducial spectrum $C_{\ell}^{EB}$, for $\ell = 2, 3, 4, 5$. The distributions obtained with NLE (black) are compared to those assuming a Gaussian distribution (red). The upper panels correspond to a dark energy case with fiducial mass of $m_{\phi} = 10^{-32}$ eV, and the lower panels to a dark matter case with $m_{\phi} = 10^{-29}$ eV, for which the reionization $EB$ signal is nearly zero. The vertical dashed lines indicate the fiducial values of $C_{\ell}^{EB}$.
• Figure 3: Left:$68\%$ and $95\%$ highest-posterior density contours of $p(m_{\phi},g\phi_{\mathrm{in}}/2|\widehat{C}_{\ell}^{EB})$ for two fiducial masses: $\log m_{\phi}=-29.45$ (blue) and $\log m_{\phi}=-32.30$ (orange). The black dotted line shows the required value of $g\phi_{\mathrm{in}}/2$ for the $EB$ power spectrum at high mutipoles to match the fiducial cosmic birefringence amplitude ($0.35^\circ$) at recombination. Right: The corresponding $EB$ power spectra (same realization). Solid lines represent the fiducial $C_{\ell}^{EB}$ and the points show the estimated $\widehat{C}_{\ell}^{EB}$. Note the change from logarithmic to a linear scale for $\ell (\ell+1) C_{\ell}^{EB}/2\pi<5.10^{-4}\ \mu K^2$ to accommodate negative fluctuations.
• Figure 4: Marginal posterior distributions of $m_{\phi}$, $g\phi_{\mathrm{in}}/2$, and $\alpha$. The black dashed lines represent the ground truth parameters: $\alpha = 0 \degree$ and $g\phi_{\mathrm{in}}/2=0.35\degree$. The blue and orange dashed lines show two fiducial masses: $\log m_{\phi}=-29.45$ and $\log m_{\phi}=-32.30$, respectively. The grey line represents the prior distribution used for each parameter.
• Figure 5: Posterior distributions on $m_{\phi}$, $g\phi_{\mathrm{in}}/2$, and $\alpha$ with different fiducial masses (indicated with the colorbar). Each posterior is conditioned on the same CMB and noise realization, for both upper and lower panels. The black dashed lines represent $g\phi_{\mathrm{in}}/2 = 0.35 \degree$ and $\alpha =0\degree$. The upper panels show the case in which simulations include lensing $B$ modes, while the lower panels do not include them. The upper and lower panels are normalized such that the area under each histogram is 1.