Implications of Cosmic Birefringence for Multi-Field ALP Dark Matter

TL;DR

This work tackles the tension between isotropic cosmic birefringence signals and the washout effect in ultralight ALP dark matter by introducing a two-field ALP framework with independent masses $m_1,m_2$ and a common photon coupling $g_{\phi\gamma}$. It derives analytic bounds on the coupling for the two-field case and performs numerical evaluations of the CMB polarization rotation, using a realistic last-scattering epoch and a 1% ALP DM fraction. The key finding is that when the two ALP masses are comparable, the washout constraint is relaxed by about a factor of $\sqrt{2}$, enlarging the viable parameter space to accommodate the observed birefringence; large mass differences revert to the single-field result and reimpose the washout limit. The study also discusses prospects for extending to $N$ fields and assesses compatibility with Planck/WMAP and ACT measurements, highlighting the role of local DM density in reducing required field numbers. Overall, the results suggest multi-field ALP dark matter as a plausible origin of cosmic birefringence and motivate further exploration of parity-violating cosmologies with more complex ALP sectors.

Abstract

Cosmic birefringence, characterized by the observed rotation of the polarization plane of the cosmic microwave background (CMB) radiation, serves as a critical probe for testing theories beyond the standard cosmological scenario. As a major component of the universe, dark matter plays a pivotal role in cosmic evolution, particularly in the formation of large-scale structures. However, its fundamental nature remains elusive. Axion-like particles (ALPs), as promising dark matter candidates, possess unique advantages in naturally explaining such phenomena. Previous studies on the implications of cosmic birefringence for these ultralight ALP fields have focused on single-field models with conventional potentials. These models face exclusion due to the washout effect - a suppression of the CMB polarization power spectrum induced by oscillatory dynamics of the scalar field within the mass range of less than $10^{-23}$ eV. To address this limitation, we develop a more general theoretical framework incorporating two ALP fields, providing analytical approximations and numerical calculations. Our findings reveal that the superposition of two ALP fields with distinct masses can relax the constraints imposed by the washout effect and reconcile with observations.

Figures (4)

• Figure 1: The constraints on the coupling constant from cosmic birefringence and Washout effect. The green area represents the coupling constant required to produce cosmic birefringence, where the solid green line, dashed line, and sparse dashed line correspond from bottom to top to different rotation angles( $\overline{\beta}=0.215^\circ,\sigma=0.074^\circ$ ). At the same time, the allowable parameter space should be below the blue solid line, so as not to be excluded by the Washout effect and it is easy to see that the washout effect's limitation on the coupling constant is ruled out by ACT observations within 1 $\sigma$ error range. In this plot, we assume that the local fraction of dark matter abundance is equal to the cosmological fraction of dark matter density: $\kappa_\phi = f_\phi$.
• Figure 2: Constraints on the coupling constant from cosmic birefringence and the washout effect. Here $f_1=f_2=0.5 f_{\phi}$ with both ALP fields contributing equally to the total dark matter density. The panels correspond to $m_1=10^{-24}\,\mathrm{eV}$ and $m_1=10^{-23}\,\mathrm{eV}$ from left to right, respectively. The horizontal axis represents $m_2$. The green region indicates the coupling strength required to reproduce the observed cosmic birefringence, where the solid, dashed, and sparsely dashed lines correspond (from bottom to top) to different rotation angles ($\overline{\beta}=0.215^\circ$,$\sigma=0.074^\circ$). The solid blue line denotes the limit imposed by the washout effect. When the two masses are comparable, the two-field model yields a parameter space consistent with observations within $1\sigma$.
• Figure 3: Constraints with $m_1 = 10^{-23}$ eV but with different $f_1$ and $f_2$. In left panel, $f_1=0.1f_{\phi}, \ f_2=0.9f_{\phi}$ . A viable parameter region consistent with observations within 1$\sigma$ still exists, but shifts toward larger masses. For extreme case (right panel) with $f_1=0.001f_{\phi}, \ f_2=0.999f_\phi$, across the entire mass range of interest, the two-field model is excluded by the washout effect within 1$\sigma$, effectively corresponding to the single-field prediction.
• Figure 4: Constraints from the combined Planck HFI + LFI + WMAP data. The left panel shows the two-field model with $f_1=f_2=0.5 f_{\phi}$ and $m_1=10^{-24}\,\mathrm{eV}$ , while the right panel displays the corresponding single-field case.While the two-field model does not fully account for the observed static cosmic birefringence within the $2 \sigma$ constraints from Planck HFI + LFI + WMAP, it nevertheless provides a better fit than the single-field model.