$\mathrm{BICEP}/Keck\text{ }$ XII: Constraints on axionlike polarization oscillations in the cosmic microwave background

$BICEP / K e c k$ XII: Constraints on axionlike polarization oscillations in the cosmic microwave background

P. A. R. Ade et al. (BICEP/Keck Collaboration)

Phys. Rev. D 103, 042002 – Published 12 February 2021

Abstract

We present a search for axionlike polarization oscillations in the cosmic microwave background (CMB) with observations from the Keck Array. A local axion field induces an all-sky, temporally sinusoidal rotation of CMB polarization. A CMB polarimeter can thus function as a direct-detection experiment for axionlike dark matter. We develop techniques to extract an oscillation signal. Many elements of the method are generic to CMB polarimetry experiments and can be adapted for other datasets. As a first demonstration, we process data from the 2012 observing season to set upper limits on the axion-photon coupling constant in the mass range $10^{- 21} - 10^{- 18} eV$ , which corresponds to oscillation periods on the order of hours to months. We find no statistically significant deviations from the background model. For periods larger than 24 hr (mass $m < 4.8 \times 10^{- 20} eV$ ), the median 95% confidence upper limit is equivalent to a rotation amplitude of 0.68°, which constrains the axion-photon coupling constant to $g_{ϕ γ} < (1.1 \times 10^{- 11} {GeV}^{- 1}) m / (10^{- 21} eV)$ , if axionlike particles constitute all of the dark matter. The constraints can be improved substantially with data already collected by the BICEP series of experiments. Current and future CMB polarimetry experiments are expected to achieve sufficient sensitivity to rule out unexplored regions of the axion parameter space.

Received 17 November 2020
Accepted 7 January 2021

DOI:https://doi.org/10.1103/PhysRevD.103.042002

Physics Subject Headings (PhySH)

Axions Cosmic microwave background Dark matter

Gravitation, Cosmology & AstrophysicsParticles & Fields

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BICEP/ $K e c k$ XIV: Improved constraints on axionlike polarization oscillations in the cosmic microwave background

P. A. R. Ade et al. (BICEP/Keck Collaboration)

Phys. Rev. D 105, 022006 (2022)

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Vol. 103, Iss. 4 — 15 February 2021

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Figure 1
Flow diagram of the axion oscillation analysis pipeline. The three main components are indicated on the left, and more detail is presented in the rest of the figure. The mapmaking step is similar to that of a standard CMB analysis, though the reobservation must now include a component that represents polarization oscillations (Secs. 3b, 3d, and 3g). The coadds are estimates of the time-averaged Stokes parameters $⟨ Q (\hat{n}) ⟩$ and $⟨ U (\hat{n}) ⟩$ . The global rotation angle $f (t) / 2$ is obtained through the correlation method of Sec. 3e with some of the computational speedups of Sec. 3g. The likelihood and Bayesian analysis are described in Sec. 4. The ensemble of simulations is used to construct a model distribution, which we can resample to form large numbers of Gaussian pseudosimulations (Sec. 4a1). The model distribution also implies a likelihood function (Sec. 4b) that is used to set Bayesian upper limits (Sec. 4c). At the same time, we estimate test statistics to check consistency with the background model (Sec. 4d) and to test for spurious systematic signals (Sec. 5). Based on the results of the systematics checks, which we call “jackknife tests,” we unblind the real nonjackknife data (Sec. 6b).
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Figure 2
An illustration of the correlation method introduced in Sec. 3e for a simulation of a single detector and a single observation. Top: the pair difference ${\bar{D}}_{i} (\hat{n}, τ)$ (blue) from a constant-elevation scan is plotted against right ascension (RA). The pair difference is dominated by atmospheric loading and fluctuates strongly. In this simulation, a global rotation of 3° has been imposed. The oscillating component ${\bar{D}}_{i}^{(osc)} (\hat{n}, τ)$ (red) is hidden underneath the atmospheric fluctuations. The rotated map ${\bar{r}}_{i} (\hat{n}, τ)$ (orange) is used as a template to pick out global polarization rotations. Bottom: the correlation $ρ (τ)$ [Eq. (21) summed over detector $i$ only] between the template and the full pair difference (blue) has a large variance but a mean of zero. The correlation with the oscillating component (red) is biased positive.
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Figure 3
A simulated time series $\hat{f} (τ)$ [blue] with an input rotation amplitude $A / 2 = 3 °$ , chosen to be relatively large in order to illustrate the effect more clearly. The background ${\hat{f}}^{(bkg)} (τ)$ [cyan, defined explicitly in Eq. (52)] dominates over the oscillating component ${\hat{f}}^{(osc)} (τ)$ [red, Eq. (51)]. The template maps $\bar{Q} (\hat{n})$ and $\bar{U} (\hat{n})$ are constructed from standard BICEP simulations of only the 2012 observing season of the Keck Array, so the underlying true oscillation $f (t)$ (orange) is not recovered at full strength but is instead suppressed by $\sim 30 %$ as described in Sec. 3f.
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Figure 4
The test statistic $Δ q_{m}$ for consistency with the background model [Eq. (67)] for real data from the 2012 observing season of the Keck Array. We plot $Δ q_{m}^{1 / 4}$ on the vertical axis in order to compress the distribution for visual purposes, and we plot frequency $m / (2 π)$ in units of inverse days ( $d^{- 1}$ ) on the horizontal axis. The maximum and minimum values are indicated in the legend with their corresponding oscillation periods. The levels for global $2.5 σ$ fluctuations in both directions are indicated by horizontal red lines—i.e., there is a 1.2% probability in the background model that at least one value of $Δ q_{m}$ will lie outside the region bounded by the red lines.
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Figure 5
Bayesian 95% confidence upper limits on rotation amplitude $A / 2$ (Sec. 4c). We also provide the median expectation (black dashes) from background-only simulations as well as $1 σ$ (green) and $2 σ$ (yellow) regions. These expectations represent local rather than global percentiles. With nearly $10^{4}$ frequencies under consideration, we expect several values outside of the $2 σ$ region. The question of background consistency is addressed by Fig. 4 and the test statistic $Δ \hat{q}$ [Eq. (68)]. The median limit for oscillation periods larger than 24 hr (frequency less than $1 d^{- 1}$ ) is 0.68°. For shorter periods (larger frequencies), the limits are degraded due to binning observations in $\sim 1 hr$ scansets (Sec. 3c). Additionally, we plot a smoothed approximation to our upper limits [Eq. (78)] in cyan.
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Figure 6
Excluded regions in the mass-coupling parameter space for axionlike dark matter (cf. Fig. 3 in Ref. [15]). All constraints push the allowed regions to larger masses and smaller coupling constants—i.e., toward the bottom right of the figure. If the dark matter is assumed to consist entirely of axionlike particles—i.e., if $κ = 1$ , then our constraints (blue) are immediately implied by Eq. (4) and the results of Fig. 5. A smoothed approximation is shown in cyan [Eq. (80)]. The orange dot-dashed and dotted lines show the constraints that would be achieved if the rotation amplitude were constrained to 0.1° and 0.01°, respectively. The green solid line shows the constraint set by Fedderke et al. [15] by searching for the washout effect (Sec. 1) in publicly available Planck power spectra. The dashed green line shows the cosmic variance limit for the washout effect. The dashed gray horizontal line shows the limit from searching for a gamma-ray excess from SN1987A [22]. The solid gray horizontal line is the limit set by the CAST experiment [21]. The dotted gray vertical line is a constraint on the minimum axion mass from observations of small-scale structure in the Lyman- $α$ forest [26], though we note that several similar bounds have also been set by other considerations of small-scale structure [27, 28].
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Physical Review D

covering particles, fields, gravitation, and cosmology

$BICEP / K e c k$ XII: Constraints on axionlike polarization oscillations in the cosmic microwave background

P. A. R. Ade et al. (BICEP/Keck Collaboration)

Phys. Rev. D 103, 042002 – Published 12 February 2021

Abstract

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BICEP/ $K e c k$ XIV: Improved constraints on axionlike polarization oscillations in the cosmic microwave background

P. A. R. Ade et al. (BICEP/Keck Collaboration)

Phys. Rev. D 105, 022006 (2022)

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Physical Review D

covering particles, fields, gravitation, and cosmology

BICEP/Keck XII: Constraints on axionlike polarization oscillations in the cosmic microwave background

P. A. R. Ade et al. (BICEP/Keck Collaboration)

Phys. Rev. D 103, 042002 – Published 12 February 2021

Abstract

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BICEP/Keck XIV: Improved constraints on axionlike polarization oscillations in the cosmic microwave background

P. A. R. Ade et al. (BICEP/Keck Collaboration)

Phys. Rev. D 105, 022006 (2022)

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$BICEP / K e c k$ XII: Constraints on axionlike polarization oscillations in the cosmic microwave background

BICEP/ $K e c k$ XIV: Improved constraints on axionlike polarization oscillations in the cosmic microwave background