Probing axionlike particles via cosmic microwave background polarization

Axionlike particles (ALPs) rotate the linear polarization of photons through the ALP-photon coupling and convert the cosmic microwave background (CMB) $E$ mode to the $B$ mode. We derive the relation between the ALP dynamics and the rotation angle by assuming that the ALP $\varphi$ has a quadratic potential, $V=m^2{\varphi }^2/2$. We compute the current and future sensitivities of CMB observations to the ALP-photon coupling $g$, which can reach $g=4\times {10}^{-21}{\mathrm{GeV}}^{-1}$ for ${10}^{-32}\mathrm{eV}\lesssim m\lesssim {10}^{-28}\mathrm{eV}$ and extensively exceed the other searches for any mass $m\lesssim {10}^{-25}\mathrm{eV}$. We find that the fluctuation of the ALP field at the observer, which has been neglected in previous studies, can induce significant isotropic rotation of the CMB polarization. The measurements of isotropic and anisotropic rotation allow us to put bounds on relevant quantities, such as the ALP mass $m$ and the ALP density parameter ${\mathrm{\Omega }}_{\varphi }$. In particular, if LiteBIRD detects anisotropic rotation, we obtain the lower bound on the tensor-to-scalar ratio as $r>5\times {10}^{-9}$.

Figure 1

Panel (a) shows the current best sensitivities to the ALP-photon coupling $g$ against the ALP mass $m$ from $\mathrm{\Delta }\overline{\varphi }$ (purple), $\delta {\varphi }_{\mathrm{LSS}}$ (red), and $\delta {\varphi }_{\text{obs}}$ (blue). The purple line assumes the maximum ${\mathrm{\Omega }}_{\varphi }$ in Eq. (18), and the others assume $r=0.06$, while the sensitivities are lower for smaller ${\mathrm{\Omega }}_{\varphi }$ or $r$ as shown in Eqs. (19)–(22). The purple dots show the current EoS parameter $w$ satisfying $w+1={10}^{-3},{10}^{-2}$, and 0.06 from left to right. We extrapolated the sensitivity from $\delta {\varphi }_{\text{obs}}$ with a light blue line proportional to $m$ for $m>{10}^2{H}_0$ due to high computational costs. The shaded regions have been excluded by OSQAR [58] (orange), CAST [59] (light blue), SN1987A [60] (light green), and Chandra [61] (pink). Panel (b) shows future sensitivities to the ALP-photon coupling $g$ of LiteBIRD, SO, and CMB-S4 (dotted lines), and current sensitivities (solid lines) with $r={10}^{-3}$. The horizontal dotted lines show the projected sensitivities of ALPSII [62] (orange), IAXO [17, 63] (light blue), and Athena [64] (pink).