EE Power Spectra Research Articles

CLASS Data Pipeline and Maps for 40 GHz Observations through 2022

The Cosmology Large Angular Scale Surveyor (CLASS) is a telescope array that observes the cosmic microwave background over 75% of the sky from the Atacama Desert, Chile, at frequency bands centered near 40, 90, 150, and 220 GHz. This paper describes the CLASS data pipeline and maps for 40 GHz observations conducted from 2016 August to 2022 May. We demonstrate how well the CLASS survey strategy, with rapid (∼10 Hz) front-end modulation, recovers the large-scale Galactic polarization signal from the ground: the mapping transfer function recovers ∼67% (85%) of EE and BB (VV) power at ℓ = 20 and ∼35% (47%) at ℓ = 10. We present linear and circular polarization maps over 75% of the sky. Simulations based on the data imply the maps have a white noise level of and correlated noise component rising at low-ℓ as ℓ −2.4. The transfer-function-corrected low-ℓ component is comparable to the white noise at the angular knee frequencies of ℓ ≈ 18 (linear polarization) and ℓ ≈ 12 (circular polarization). Finally, we present simulations of the level at which expected sources of systematic error bias the measurements, finding subpercent bias for the Λ cold dark matter EE power spectra. Bias from E-to-B leakage due to the data reduction pipeline and polarization angle uncertainty approaches the expected level for an r = 0.01 BB power spectrum. Improvements to the instrument calibration and the data pipeline will decrease this bias.

Delensing of Cosmic Microwave Background Polarization with Machine Learning

Primordial B-mode detection is one of the main goals of next-generation cosmic microwave background (CMB) experiments. Primordial B-modes are a unique signature of primordial gravitational waves (PGWs). However, the gravitational interaction of CMB photons with large-scale structures will distort the primordial E modes, adding a lensing B-mode component to the primordial B-mode signal. Removing the lensing effect (“delensing”) from observed CMB polarization maps will be necessary to improve the constraint of PGWs and obtain a primordial E-mode signal. Here, we introduce a deep convolutional neural network model named multi-input multi-output U-net (MIMO-UNet) to perform CMB delensing. The networks are trained on simulated CMB maps with size 20° × 20°. We first use MIMO-UNet to reconstruct the unlensing CMB polarization (Q and U) maps from observed CMB maps. The recovered E-mode power spectrum exhibits excellent agreement with the primordial EE power spectrum. The recovery of the primordial B-mode power spectrum for noise levels of 0, 1, and 2 μK-arcmin is greater than 98% at the angular scale of ℓ < 150. We additionally reconstruct the lensing B map from observed CMB maps. The recovery of the lensing B-mode power spectrum is greater than roughly 99% at the scales of ℓ > 200. We delens the observed B-mode power spectrum by subtracting the reconstructed lensing B-mode spectrum. The recovery of tensor B-mode power spectrum for noise levels of 0, 1, and 2 μK-arcmin is greater than 98% at the angular scales of ℓ < 120. Even at ℓ = 160, the recovery of tensor B-mode power spectrum is still around 71%.

Recovering Cosmic Microwave Background Polarization Signals with Machine Learning

Primordial B-mode detection is one of the main goals of current and future cosmic microwave background (CMB) experiments. However, the weak B-mode signal is overshadowed by several Galactic polarized emissions, such as thermal dust emission and synchrotron radiation. Subtracting foreground components from CMB observations is one of the key challenges in searching for the primordial B-mode signal. Here, we construct a deep convolutional neural network (CNN) model, called CMBFSCNN (Cosmic Microwave Background Foreground Subtraction with CNN), which can cleanly remove various foreground components from simulated CMB observational maps at the sensitivity of the CMB-S4 experiment. Noisy CMB Q (or U) maps are recovered with a mean absolute difference of 0.018 ± 0.023 μK (or 0.021 ± 0.028 μK). To remove the residual instrumental noise from the foreground-cleaned map, inspired by the needlet internal linear combination method, we divide the whole data set into two “half-split maps,” which share the same sky signal, but have uncorrelated noise, and perform a cross-correlation technique to reduce the instrumental noise effects at the power spectrum level. We find that the CMB EE and BB power spectra can be precisely recovered with significantly reduced noise effects. Finally, we apply this pipeline to current Planck observations. As expected, various foregrounds are cleanly removed from the Planck observational maps, with the recovered EE and BB power spectra being in good agreement with the official Planck results.

Future Prospects on Constraining Neutrino Cosmology with the Ali CMB Polarization Telescope

We forecast the constraints on the parameters of neutrino physics with the constructions of Cosmic Microwave Background (CMB) temperature, E-mode polarization, and lensing spectra for the ground-based Ali Cosmic Microwave Background Polarization Telescope (AliCPT). To implement the forecast calculations, we perform numerical simulations which show that AliCPT would yield the result σ(N eff) = 0.56 and M ν < 1.10 eV (95% CL.) with TT, TE, EE, and CMB lensing power spectra for the first year of observation. Moreover, we investigate how the instrumental parameters, such as noise level, FWHM, and sky coverage can affect the constraints on these two parameters. Our forecasting results find that a larger aperture telescope with a larger sky survey strategy would significantly improve the current constraints for AliCPT.

Dust polarization spectral dependence from Planck HFI data

The search for the primordial B-modes of the cosmic microwave background (CMB) relies on the separation from the brighter foreground dust signal. In this context, the characterization of the spectral energy distribution (SED) of thermal dust in polarization has become a critical subject of study. We present a power-spectra analysis of Planck data, which improves upon previous studies by using the newly released SRoll2 maps that include corrections on residual data systematics and by extending the analysis to regions near the Galactic plane. Our analysis focuses on the lowest multipoles between ℓ = 4 and 32, as well as three sky areas with sky fractions of fsky = 80%, 90%, and 97%. The mean dust SED for polarization and the 353 GHz Q and U maps are used to compute residual maps at 100, 143, and 217 GHz, highlighting variations of the dust polarization SED on the sky and along the line of sight. Residuals are detected at the three frequencies for the three sky areas. We show that models based on total-intensity data end up underestimating (by a significant factor) the complexity of dust polarized CMB foreground. Our analysis emphasizes the need to include variations of the polarization angles of the dust polarized CMB foreground. The frequency dependence of the EE and BB power spectra of the residual maps yields further insight. We find that the moments expansion to the first order of the modified black-body (MBB) spectrum provides a good fit to the EE power-spectra. This result suggests that the residuals could follow mainly from variations of the dust MBB spectral parameters. However, this conclusion is challenged by cross-spectra showing that the residuals maps at the three frequencies are not fully correlated, as well as the fact that the BB power-spectra do not match the first order moment expansion of a MBB SED. This work sets new requirements for simulations of the dust-polarized foreground and component separation methods, showing that a significant refinement to the dust modeling is necessary to ensure an unbiased detection of the CMB primordial B-modes at the precision required by future CMB experiments. Further works would also be required to theoretically model the impact of polarization-angle variations on the EE and BB power spectra of residual maps.

Atacama Cosmology Telescope: Constraints on prerecombination early dark energy

The early dark energy (EDE) scenario aims to increase the value of the Hubble constant ($H_0$) inferred from cosmic microwave background (CMB) data over that found in $\Lambda$CDM, via the introduction of a new form of energy density in the early universe. The EDE component briefly accelerates cosmic expansion just prior to recombination, which reduces the physical size of the sound horizon imprinted in the CMB. Previous work has found that non-zero EDE is not preferred by Planck CMB power spectrum data alone, which yield a 95% confidence level (CL) upper limit $f_{\rm EDE} < 0.087$ on the maximal fractional contribution of the EDE field to the cosmic energy budget. In this paper, we fit the EDE model to CMB data from the Atacama Cosmology Telescope (ACT) Data Release 4. We find that a combination of ACT, large-scale Planck TT (similar to WMAP), Planck CMB lensing, and BAO data prefers the existence of EDE at $>99.7$% CL: $f_{\rm EDE} = 0.091^{+0.020}_{-0.036}$, with $H_0 = 70.9^{+1.0}_{-2.0}$ km/s/Mpc (both 68% CL). From a model-selection standpoint, we find that EDE is favored over $\Lambda$CDM by these data at roughly $3\sigma$ significance. In contrast, a joint analysis of the full Planck and ACT data yields no evidence for EDE, as previously found for Planck alone. We show that the preference for EDE in ACT alone is driven by its TE and EE power spectrum data. The tight constraint on EDE from Planck alone is driven by its high-$\ell$ TT power spectrum data. Understanding whether these differing constraints are physical in nature, due to systematics, or simply a rare statistical fluctuation is of high priority. The best-fit EDE models to ACT and Planck exhibit coherent differences across a wide range of multipoles in TE and EE, indicating that a powerful test of this scenario is anticipated with near-future data from ACT and other ground-based experiments.

Pseudoscalar sterile neutrino self-interactions in light of Planck, SPT and ACT data

We reassess the viability of a cosmological model including a fourth additional sterile neutrino species that self-interacts through a new pseudoscalar degree of freedom.We perform a series of extensive analyses fitting various combinations of cosmic microwave background (CMB) data from Planck, the Atacama Cosmology Telescope (ACT) and the South Pole Telescope (SPT), both alone and in combination with Baryon Acoustic Oscillation (BAO) and Supernova Ia (SnIa) observations.We show that the scenario under study, although capable to resolve the Hubble tension without worsening the so-called S_8 tension about the growth of cosmic structures, is severely constrained by high-multipole polarization data from both Planck and SPT.Intriguingly, when trading Planck TE-EE data for those from ACT, we find a ≳ 3σ preference for a non-zero sterile neutrino mass, ms = 3.6+1.1 0.6 eV (68% C.L.), compatible with the range suggested by longstanding short-baseline (SBL) anomalies in neutrino oscillation experiments. The pseudoscalar model provides indeed a better fit to ACT data compared to ΛCDM (Δχ2 ≃ -5, ΔAIC = -1.3), although in a combined analysis with Planck the ΛCDM model is still favoured, as the preference for a non-zero sterile neutrino mass is mostly driven by ACT favouring a higher value for the primordial spectral index ns with respect to Planck. We show that the mild tension between Planck and ACT is due to the different pattern in the TE and EE power spectra on multipoles between 350 ≲ ℓ ≲ 1000.We also check the impact of marginalizing over the gravitational lensing information in Planck data, showing that the model does not solve the CMB lensing anomaly.Future work including higher precision data from current and upcoming CMB ground-based experiments will be crucial to test these results.

Recovering the CMB Signal with Machine Learning

The cosmic microwave background (CMB), carrying the inhomogeneous information of the very early universe, is of great significance for understanding the origin and evolution of our universe. However, observational CMB maps contain serious foreground contaminations from several sources, such as Galactic synchrotron and thermal dust emissions. Here, we build a deep convolutional neural network (CNN) to recover the tiny CMB signal from various huge foreground contaminations. Focusing on CMB temperature fluctuations, we find that the CNN model can successfully recover the CMB temperature maps with high accuracy, and that the deviation of the recovered power spectrum C ℓ is smaller than the cosmic variance at ℓ > 10. We then apply this method to the current Planck observations, and find that the recovered CMB is quite consistent with that disclosed by the Planck Collaboration, which indicates that the CNN method can provide a promising approach to the component separation of CMB observations. Furthermore, we test the CNN method with simulated CMB polarization maps based on the CMB-S4 experiment. The result shows that both the EE and BB power spectra can be recovered with high accuracy. Therefore, this method will be helpful for the detection of primordial gravitational waves in current and future CMB experiments. The CNN is designed to analyze two-dimensional images, thus this method is not only able to process full-sky maps, but also partial-sky maps. Therefore, it can also be used for other similar experiments, such as radio surveys like the Square Kilometer Array.

Characterization of the polarized synchrotron emission from Planck and WMAP data

The purpose of this work is to characterize the diffuse Galactic polarized synchrotron, which is the dominant CMB foreground emission at low frequency. We present EE, BB, and EB power spectra estimated from polarization frequency maps at 23 and 30 GHz as observed respectively by the WMAP K-band and the Planck lowest frequency channel, for a set of six sky regions covering from 30% to 94% of the sky. We study the synchrotron polarization angular distribution and spectral energy distribution (SED) by means of the so-called pseudo-C ℓ formalism, provided by the NaMaster package, in the multipole interval 30 ≤ ℓ ≤ 300. Best results are obtained cross-correlating Planck and WMAP data. The EE and BB angular power spectra show a steep decay of the spectral amplitude as a function of multipole, approximated by a power law CEE,BB ∝ ℓαEE,BB , with αEE = -2.95 ± 0.04 and αBB = -2.85 ± 0.14. The B/E power asymmetry is proved with a B-to-E ratio, computed as the amplitude ratio at the pivot multipole ℓ = 80, of 0.22 ± 0.02. The EB cross-component is compatible with zero at 1σ, with an upper constraint on the EB/EE ratio of 1.2% at the 2σ level. We show that the EE and BB power-law model with null EB cross-correlation describes reasonably well the diffuse synchrotron polarization emission for the full sky if the bright Galactic center and point sources are masked. The recovered SED shows power-law spectral indices βEE = -3.00 ± 0.10 and βBB = -3.05 ± 0.36 compatible between themselves, in the frequency range 23–30 GHz. Results also seem to indicate that the SED gets steeper from low to high Galactic latitude.

The parameter-level performance of covariance matrix conditioning in cosmic microwave background data analyses

ABSTRACT Empirical estimates of the band power covariance matrix are commonly used in cosmic microwave background (CMB) power spectrum analyses. While this approach easily captures correlations in the data, noise in the resulting covariance estimate can systematically bias the parameter fitting. Conditioning the estimated covariance matrix, by applying prior information on the shape of the eigenvectors, can reduce these biases and ensure the recovery of robust parameter constraints. In this work, we use simulations to benchmark the performance of four different conditioning schemes, motivated by contemporary CMB analyses. The simulated surveys measure the TT, TE, and EE power spectra over the angular multipole range 300 ≤ ℓ ≤ 3500 in Δℓ = 50 wide bins, for temperature map-noise levels of 10, 6.4, and $2\, \mu$K arcmin. We divide the survey data into Nreal = 30, 50, or 100 uniform subsets. We show the results of different conditioning schemes on the errors in the covariance estimate, and how these uncertainties on the covariance matrix propagate to the best-fitting parameters and parameter uncertainties. The most significant effect we find is an additional scatter in the best-fitting point, beyond what is expected from the data likelihood. For a minimal conditioning strategy, Nreal = 30, and a temperature map-noise level of 10$\, \mu$K arcmin, we find the uncertainty on the recovered best-fitting parameter to be ×1.3 larger than the apparent posterior width from the likelihood (×1.2 larger than the uncertainty when the true covariance is used). Stronger priors on the covariance matrix reduce the misestimation of parameter uncertainties to $\lt 1{{\ \rm per\ cent}}$. As expected, empirical estimates perform better with higher Nreal, ameliorating the adverse effects on parameter constraints.

Consistency of Planck, ACT, and SPT constraints on magnetically assisted recombination and forecasts for future experiments

Primordial magnetic fields can change the recombination history of the universe by inducing clumping in the baryon density at small scales. They were recently proposed as a candidate model to relieve the Hubble tension. We investigate the consistency of the constraints on a clumping factor parameter $b$ in a simplistic model, using the latest CMB data from Planck, ACT DR4 and SPT-3G 2018. For the combined CMB data alone, we find no evidence for clumping being different from zero, though when adding a prior on $H_0$ based on the latest distance-ladder analysis of the SH0ES team, we report a weak detection of $b$. Our analysis of simulated datasets shows that ACT DR4 has more constraining power with respect to SPT-3G 2018 due to the degeneracy breaking power of the TT band powers (not included in SPT). Simulations also suggest that the TE,EE power spectra of the two datasets should have the same constraining power. However, the ACT DR4 TE,EE constraint is tighter than expectations, while the SPT-3G 2018 one is looser. While this is compatible with statistical fluctuations, we explore systematic effects which may account for such deviations. Overall, the ACT results are only marginally consistent with Planck or SPT-3G, at the $2-3\sigma$ level within $\Lambda$CDM+$b$ and $\Lambda$CDM, while Planck and SPT-3G are in good agreement. Combining the CMB data together with BAO and SNIa provides an upper limit of b<0.4 at 95\% c.l. (b<0.5 without ACT). Adding a SH0ES-based prior on the Hubble constant gives $b = 0.31^{+0.11}_{-0.15}$ and $H_0=69.28 \pm 0.56$ km/s/Mpc ($b = 0.41^{+0.14}_{-018}$ and $H_0=69.70 \pm 0.63$ km/s/Mpc without ACT). Finally, we forecast constraints on $b$ for the full SPT-3G survey, Simons Observatory, and CMB-S4, finding improvements by factors of 1.5 (2.7 with Planck), 5.9 and 7.8, respectively, over Planck alone.

The high-redshift tail of stellar reionization in LCDM is beyond the reach of the low-ℓ CMB

ABSTRACT The first generation (Pop-III) stars can ionize 1–10 per cent of the universe by z = 15, when the metal-enriched (Pop-II) stars may contribute negligibly to the ionization. This low ionization tail might leave detectable imprints on the large-scale CMB E-mode polarization. However, we show that physical models for reionization are unlikely to be sufficiently extended to detect any parameter beyond the total optical depth through reionization. This result is driven in part by the total optical depth inferred by Planck, indicating a reionization midpoint around z = 8, which in combination with the requirement that reionization completes by z ≈ 5.5 limits the amplitude of an extended tail. To demonstrate this, we perform semi-analytic calculations of reionization including Pop-III star formation in minihalos with Lyman-Werner feedback. We find that standard Pop-III models need to produce very extended reionization at z &amp;gt; 15 to be distinguishable at 2-σ from Pop-II-only models, assuming a cosmic variance-limited measurement of the low-ℓ EE power spectrum. However, we show that unless there is a late-time quenching mechanism such as from strong X-ray feedback or some other extreme Pop-III scenario, structure formation makes it quite challenging to produce high enough Thomson scattering optical depth from z &amp;gt; 15, τ(z &amp;gt; 15), and still be consistent with other observational constraints on reionization.

Planck constraints on the tensor-to-scalar ratio

We present constraints on the tensor-to-scalar ratio r using Planck data. We use the latest release of Planck maps, processed with the NPIPE code, which produces calibrated frequency maps in temperature and polarisation for all Planck channels from 30 GHz to 857 GHz using the same pipeline. We computed constraints on r using the BB angular power spectrum, and we also discuss constraints coming from the TT spectrum. Given Planck’s noise level, the TT spectrum gives constraints on r that are cosmic-variance limited (with σr = 0.093), but we show that the marginalised posterior peaks towards negative values of r at about the 1.2σ level. We derived Planck constraints using the BB power spectrum at both large angular scales (the ‘reionisation bump’) and intermediate angular scales (the ‘recombination bump’) from ℓ = 2 to 150 and find a stronger constraint than that from TT, with σr = 0.069. The Planck BB spectrum shows no systematic bias and is compatible with zero, given both the statistical noise and the systematic uncertainties. The likelihood analysis using B modes yields the constraint r &lt; 0.158 at 95% confidence using more than 50% of the sky. This upper limit tightens to r &lt; 0.069 when Planck EE, BB, and EB power spectra are combined consistently, and it tightens further to r &lt; 0.056 when the Planck TT power spectrum is included in the combination. Finally, combining Planck with BICEP2/Keck 2015 data yields an upper limit of r &lt; 0.044.

Propagating residual biases in masked cosmic shear power spectra

In this paper we derive a full expression for the propagation of weak lensing shape measurement biases into cosmic shear power spectra including the effect of missing data. We show using simulations that terms higher than first order in bias parameters can be ignored and the impact of biases can be captured by terms dependent only on the mean of the multiplicative bias field. We identify that the B-mode power contains information on the multiplicative bias. We find that without priors on the residual multiplicative bias $\delta m$ and stochastic ellipticity variance $\sigma_e$ that constraints on the amplitude of the cosmic shear power spectrum are completely degenerate, and that when applying priors the constrained amplitude $A$ is slightly biased low via a classic marginalisation paradox. Using all-sky Gaussian random field simulations we find that the combination of $(1+2\delta m)A$ is unbiased for a joint EE and BB power spectrum likelihood if the error and mean (precision and accuracy) of the stochastic ellipticity variance is known to better than $\sigma(\sigma_e)\leq 0.05$ and $\Delta\sigma_e\leq 0.01$, or the multiplicative bias is known to better than $\sigma(m)\leq 0.07$ and $\Delta m\leq 0.01$.

A Measurement of the CMB E-mode Angular Power Spectrum at Subdegree Scales from 670 Square Degrees of POLARBEAR Data

Abstract We report a measurement of the E-mode polarization power spectrum of the cosmic microwave background (CMB) using 150 GHz data taken from 2014 July to 2016 December with the Polarbear experiment. We reach an effective polarization map noise level of - across an observation area of 670 square degrees. We measure the EE power spectrum over the angular multipole range , tracing the third to seventh acoustic peaks with high sensitivity. The statistical uncertainty on E-mode bandpowers is ∼2.3 at , with a systematic uncertainty of 0.5 . The data are consistent with the standard ΛCDM cosmological model with a probability-to-exceed of 0.38. We combine recent CMB E-mode measurements and make inferences about cosmological parameters in ΛCDM as well as in extensions to ΛCDM. Adding the ground-based CMB polarization measurements to the Planck data set reduces the uncertainty on the Hubble constant by a factor of 1.2 to . When allowing the number of relativistic species ( ) to vary, we find , which is in good agreement with the standard value of 3.046. Instead allowing the primordial helium abundance ( ) to vary, the data favor . This is very close to the expectation of 0.2467 from big bang nucleosynthesis. When varying both and , we find and .

Footprints of Doppler and aberration effects in cosmic microwave background experiments: statistical and cosmological implications

ABSTRACT In the frame of the Solar system, the Doppler and aberration effects cause distortions in the form of mode couplings in the cosmic microwave background (CMB) temperature and polarization power spectra and, hence, impose biases on the statistics derived by the moving observer. We explore several aspects of such biases and pay close attention to their effects on CMB polarization, which, previously, have not been examined in detail. A potentially important bias that we introduce here is boost variance—an additional term in cosmic variance, induced by the observer’s motion. Although this additional term is negligible for whole-sky experiments, in partial-sky experiments it can reach 10 per cent (temperature) to 20 per cent (polarization) of the standard cosmic variance (σ). Furthermore, we investigate the significance of motion-induced power and parity asymmetries in TT, EE, and TE as well as potential biases induced in cosmological parameter estimation performed with whole-sky TTTEEE. Using Planck-like simulations, we find that our local motion induces $\sim 1\!-\!2 {{\ \rm per\ cent}}$ hemispherical asymmetry in a wide range of angular scales in the CMB temperature and polarization power spectra; however, it does not imply any significant amount of parity asymmetry or shift in cosmological parameters. Finally, we examine the prospects of measuring the velocity of the Solar system w.r.t. the CMB with future experiments via the mode coupling induced by the Doppler and aberration effects. Using the CMB TT, EE, and TE power spectra up to ℓ = 4000, the Simons Observatory and CMB-S4 can make a dipole-independent measurement of our local velocity, respectively, at 8.5σ and 20σ.

Analytic Calculation of Covariance between Cosmological Parameters from Correlated Data Sets, with an Application to SPTpol.

Consistency checks of cosmological data sets are an important tool because they may suggest systematic errors or the type of modifications to ΛCDM necessary to resolve current tensions. In this work, we derive an analytic method for calculating the level of correlations between model parameters from two correlated cosmological data sets, which complements more computationally expensive simulations. This method is an extension of the Fisher analysis that assumes a Gaussian likelihood and a known data covariance matrix. We apply this method to the South Pole Telescope Polarimeter (SPTpol) temperature and polarization cosmic microwave background (CMB) spectra (TE and EE). We find weak correlations between ΛCDM parameters with a 9% correlation between the TE-only and EE-only constraints on H 0 and a 25% and 32% correlation for log(A s ) and n s respectively. The TE-EE parameter differences are consistent with zero, with a probability to exceed of 0.53. Using simulations we show that this test is independent of the consistency of the SPTpol TE and EE band powers with the best-fit ΛCDM model spectra. Despite the negative correlations between the TE and EE power spectra, the correlations between TE-only and EE-only ΛCDM parameters are positive. Ignoring correlations in the TT-TE and TE-EE comparisons biases the χ 2 low, artificially making parameters look more consistent. Therefore, we conclude that these correlations need to be accounted for when performing internal consistency checks of the TT versus TE versus EE power spectra for future CMB analyses.

Exact joint likelihood of pseudo-Cℓ estimates from correlated Gaussian cosmological fields

ABSTRACT We present the exact joint likelihood of pseudo-Cℓ power spectrum estimates measured from an arbitrary number of Gaussian cosmological fields. Our method is applicable to both spin-0 fields and spin-2 fields, including a mixture of the two, and is relevant to cosmic microwave background (CMB), weak lensing, and galaxy clustering analyses. We show that Gaussian cosmological fields are mixed by a mask in such a way that retains their Gaussianity and derive exact expressions for the covariance of the cut-sky spherical harmonic coefficients, the pseudo-aℓms, without making any assumptions about the mask geometry. We then show that each auto or cross-pseudo-Cℓ estimator can be written as a quadratic form, and apply the known joint distribution of quadratic forms to obtain the exact joint likelihood of a set of pseudo-Cℓ estimates in the presence of an arbitrary mask. We show that the same formalism can be applied to obtain the exact joint likelihood of quadratic maximum likelihood power spectrum estimates. Considering the polarization of the CMB as an example, we show using simulations that our likelihood recovers the full, exact multivariate distribution of EE, BB, and EB pseudo-Cℓ power spectra. Our method provides a route to robust cosmological constraints from future CMB and large-scale structure surveys in an era of ever-increasing statistical precision.

Axion dark matter detection with CMB polarization

We point out two ways to search for low-mass axion dark matter using cosmic microwave background (CMB) polarization measurements. These appear, in particular, to be some of the most promising ways to directly detect fuzzy dark matter. Axion dark matter causes rotation of the polarization of light passing through it. This gives rise to two novel phenomena in the CMB. First, the late-time oscillations of the axion field today cause the CMB polarization to oscillate in phase across the entire sky. Second, the early-time oscillations of the axion field wash out the polarization produced at last-scattering, reducing the polarized fraction (TE and EE power spectra) compared to the standard prediction. Since the axion field is oscillating, the common (static) `cosmic birefringence' search is not appropriate for axion dark matter. These two phenomena can be used to search for axion dark matter at the lighter end of the mass range, with a reach several orders of magnitude beyond current constraints. We set a limit from the washout effect using existing Planck results, and find significant future discovery potential for CMB detectors searching in particular for the oscillating effect.

Measurements of the Temperature and E-mode Polarization of the CMB from 500 Square Degrees of SPTpol Data

Abstract We present measurements of the E-mode polarization angular auto-power spectrum (EE) and temperature–E-mode cross-power spectrum (TE) of the cosmic microwave background (CMB) using 150 GHz data from three seasons of SPTpol observations. We report the power spectra over the spherical harmonic multipole range and detect nine acoustic peaks in the EE spectrum with high signal-to-noise ratio. These measurements are the most sensitive to date of the EE and TE power spectra at and , respectively. The observations cover 500 , a fivefold increase in area compared to previous SPTpol analyses, which increases our sensitivity to the photon diffusion damping tail of the CMB power spectra enabling tighter constraints on ΛCDM model extensions. After masking all sources with unpolarized flux mJy, we place a 95% confidence upper limit on residual polarized point-source power of at , suggesting that the EE damping tail dominates foregrounds to at least with modest source masking. We find that the SPTpol data set is in mild tension with the ΛCDM model ( ), and different data splits prefer parameter values that differ at the level. When fitting SPTpol data at , we find cosmological parameter constraints consistent with those for Planck temperature. Including SPTpol data at results in a preference for a higher value of the expansion rate ( ) and a lower value for present-day density fluctuations ( ).