Constraints on axionlike polarization oscillations in the cosmic microwave background with POLARBEAR

Very light pseudoscalar fields, often referred to as axions, are compelling dark matter candidates and can potentially be detected through their coupling to the electromagnetic field. Recently a novel detection technique using the cosmic microwave background (CMB) was proposed, which relies on the fact that the axion field oscillates at a frequency equal to its mass in appropriate units, leading to a time-dependent birefringence. For appropriate oscillation periods this allows the axion field at the telescope to be detected via the induced sinusoidal oscillation of the CMB linear polarization. We search for this effect in two years of POLARBEAR data. We do not detect a signal, and place a median 95% upper limit of 0.65° on the sinusoid amplitude for oscillation frequencies between $0.02{\mathrm{days}}^{-1}$ and $0.45{\mathrm{days}}^{-1}$, which corresponds to axion masses between $9.6\times {10}^{-22}\mathrm{eV}$ and $2.2\times {10}^{-20}\mathrm{eV}$. Under the assumptions that (1) the axion constitutes all the dark matter and (2) the axion field amplitude is a Rayleigh-distributed stochastic variable, this translates to a limit on the axion-photon coupling $g_{\varphi \gamma }<2.4\times {10}^{-11}{\mathrm{GeV}}^{-1}\times (m_{\varphi }/{10}^{-21}\mathrm{eV})$.

Figure 1

Left: the 515 estimated per-observation rotation angles ${\widehat{\alpha }}_j$ used in this analysis. Right: a histogram of the angles normalized by their error, ${\widehat{\alpha }}_j/{\sigma }_j$. The angles are Gaussian distributed.

Figure 2

The estimated typical maximum likelihood amplitude signal of the HWP angle offsets. 500 simulations containing only random offset angles were generated and run through the likelihood. The median recovered amplitude is shown here. The HWP step cadence begins to generate larger systematic issues at periods $>50\text{days}$. Based on these results, the maximum period used in this analysis is 50 days.

Figure 3

The significance test for the presence of an axion signal. Top: the calculation of $\mathrm{\Delta }{\chi }^2$. For each frequency in the discrete frequency domain, the MLE phase and amplitude are found, and $\mathrm{\Delta }{\chi }^2(f)$ is calculated. $\mathrm{\Delta }{\chi }^2$ is the largest among these. Bottom: the significance of $\mathrm{\Delta }{\chi }^2$ as compared to a set of 500 simulations.

Figure 4

A 95% upper confidence limit on the presence of a sinusoidal signal at each frequency. The $1\sigma$ and $2\sigma$ regions contain approximately 68% and 95% of the upper bounds calculated from 500 simulations at each frequency. The median values for these regions are indicated with dashed lines. Many individual frequencies exceed the $2\sigma$ threshold, which is to be expected based on the large number of test frequencies, and does not necessarily indicate a detection.

Figure 5

Bounds on the axion-photon coupling as a function of axion mass. Shown in solid red is the 95% upper limit obtained in this work using a stochastic local axion field amplitude and assuming the axion constitutes all the dark matter (see Sec. 6). The lighter oscillating result is the exact bound, and the median result, $g_{\varphi \gamma }<(2.4\times {10}^{-11}{\mathrm{GeV}}^{-1})\times (m_{\varphi }/{10}^{-21}\mathrm{eV})$, is shown in darker red. The median deterministic bounds for POLARBEAR, BICEP, and SPT are the dashed lines: these are the published results in [19] and [20]. The green “washout” bound was calculated in F19 from the lack of CMB polarization suppression. Lower bounds on the axion mass come from Milky Way satellites [33] and the Lyman-$\alpha$ forest [31]. Upper bounds on the axion-photon coupling from CAST [35] are also shown.