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All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Precise and accurate cosmology with CMB×LSS power spectra and bispectra

With the advent of a new generation of cosmological experiments that will provide high-precision measurements of the cosmic microwave background (CMB) and galaxies in the large-scale structure, it is pertinent to examine the potential of performing a joint analysis of multiple cosmological probes. In this paper, we study the cosmological information content contained in the one-loop power spectra and tree bispectra of galaxies cross-correlated with CMB lensing. We use the FFTLog method to compute angular correlations in spherical harmonic space, applicable for wide angles that can be accessed by forthcoming galaxy surveys. Here, we find that adding the bispectra and cross-correlations with CMB lensing offers a significant improvement in parameter constraints, including those on the total neutrino mass, M ν , and local non-Gaussianity amplitude, ƒ NL . In particular, our results suggest that the combination of the Vera C. Rubin Observatory's Legacy Survey of Space and Time (LSST) and CMB-S4 will be able to achieve σ(M ν )=42 meV from galaxy and CMB lensing correlations, and σ(M ν )=12 meV when further combined with the CMB temperature and polarization data, without any prior on the optical depth.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2021

Constraints on Λ CDM extensions from the SPT-3G 2018 $EE$ and $TE$ power spectra

Here, we present constraints on extensions to the Λ CDM cosmological model from measurements of the E-mode polarization autopower spectrum and the temperature-E-mode cross-power spectrum of the cosmic microwave background (CMB) made using 2018 SPT-3G data. The extensions considered vary the primordial helium abundance, the effective number of relativistic degrees of freedom, the sum of neutrino masses, the relativistic energy density and mass of a sterile neutrino, and the mean spatial curvature. We do not find clear evidence for any of these extensions, from either the SPT-3G 2018 dataset alone or in combination with baryon acoustic oscillation and Planck data. None of these model extensions significantly relax the tension between Hubble-constant, H 0 , constraints from the CMB and from distance-ladder measurements using Cepheids and supernovae. The addition of the SPT-3G 2018 data to Planck reduces the square-root of the determinants of the parameter covariance matrices by factors of 1.3–2.0 across these models, signaling a substantial reduction in the allowed parameter volume. We also explore CMB-based constraints on H 0 from combined SPT, Planck, and ACT DR4 datasets. While individual experiments see some indications of different H 0 values between the TT, TE, and EE spectra, the combined H 0 constraints are consistent between the three spectra. For the full combined datasets, we report H 0 = 67.49 ± 0.53 km s -1 Mpc -1 , which is the tightest constraint on H0 from CMB power spectra to date and in 4.1σ tension with the most precise distance-ladder-based measurement of H 0 . The SPT-3G survey is planned to continue through at least 2023, with existing maps of combined 2019 and 2020 data already having ~ 3.5 x lower noise than the maps used in this analysis.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2021

Cosmic shear power spectra in practice

Cosmic shear is one of the most powerful probes of Dark Energy, targeted by several current and future galaxy surveys. Lensing shear, however, is only sampled at the positions of galaxies with measured shapes in the catalog, making its associated sky window function one of the most complicated amongst all projected cosmological probes of inhomogeneities, as well as giving rise to inhomogeneous noise. Partly for this reason, cosmic shear analyses have been mostly carried out in real-space, making use of correlation functions, as opposed to Fourier-space power spectra. Since the use of power spectra can yield complementary information and has numerical advantages over real-space pipelines, it is important to develop a complete formalism describing the standard unbiased power spectrum estimators as well as their associated uncertainties. Building on previous work, this paper contains a study of the main complications associated with estimating and interpreting shear power spectra, and presents fast and accurate methods to estimate two key quantities needed for their practical usage: the noise bias and the Gaussian covariance matrix, fully accounting for survey geometry, with some of these results also applicable to other cosmological probes. Here, we demonstrate the performance of these methods by applying them to the latest public data releases of the Hyper Suprime-Cam and the Dark Energy Survey collaborations, quantifying the presence of systematics in our measurements and the validity of the covariance matrix estimate. We make the resulting power spectra, covariance matrices, null tests and all associated data necessary for a full cosmological analysis publicly available.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2025

The Atacama Cosmology Telescope: DR6 power spectra, likelihoods and ΛCDM parameters

We present power spectra of the cosmic microwave background (CMB) anisotropy in temperature and polarization, measured from the Data Release 6 maps made from Atacama Cosmology Telescope (ACT) data. These cover 19,000 deg 2 of sky in bands centered at 98, 150 and 220 GHz, with white noise levels three times lower than Planck in polarization. We find that the ACT angular power spectra estimated over 10,000 deg 2 , and measured to arcminute scales in TT, TE and EE, are well fit by the sum of CMB and foregrounds, where the CMB spectra are described by the ΛCDM model. Combining ACT with larger-scale Planck data, the joint P-ACT dataset provides tight limits on the ingredients, expansion rate, and initial conditions of the universe. We find similar constraining power, and consistent results, from either the Planck power spectra or from ACT combined with WMAP data, as well as from either temperature or polarization in the joint P-ACT dataset. When combined with CMB lensing from ACT and Planck, and baryon acoustic oscillation data from the Dark Energy Spectroscopic Instrument (DESI DR1), we measure a baryon density of Ω b h 2 = 0.0226 ± 0.0001, a cold dark matter density of Ω c h 2 = 0.118 ± 0.001, a Hubble constant of H 0 = 68.22 ± 0.36 km/s/Mpc, a spectral index of n s = 0.974 ± 0.003, and an amplitude of density fluctuations of σ 8 = 0.813 ± 0.005. Including the DESI DR2 data tightens the Hubble constant to H 0 = 68.43 ± 0.27 km/s/Mpc; ΛCDM parameters agree between the P-ACT and DESI DR2 data at the 1.6σ level. We find no evidence for excess lensing in the power spectrum, and no departure from spatial flatness. The contribution from Sunyaev-Zel'dovich (SZ) anisotropy is detected at high significance; we find evidence for a tilt with suppressed small-scale power compared to our baseline SZ template spectrum, consistent with hydrodynamical simulations with feedback.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2023

Hyper Suprime-Cam Year 3 results: Cosmology from cosmic shear power spectra

Here, we measure weak lensing cosmic shear power spectra from the 3-year galaxy shear catalog of the Hyper Suprime-Cam (HSC) Subaru Strategic Program imaging survey. The shear catalog covers 416 deg 2 of the northern sky, with a mean i-band seeing of 0.59 arcsec and an effective galaxy number density of 15 arcmin —2 within our adopted redshift range. With an i-band magnitude limit of 24.5 mag, and four tomographic redshift bins spanning 0.3 ≤ z ph ≤ 1.5 based on photometric redshifts, we obtain a high-significance measurement of the cosmic shear power spectra, with a signal-to-noise ratio of approximately 26.4 in the multipole range 300 < ℓ < 1800. The accuracy of our power spectrum measurement is tested against realistic mock shear catalogs, and we use these catalogs to get a reliable measurement of the covariance of the power spectrum measurements. We use a robust blinding procedure to avoid confirmation bias, and model various uncertainties and sources of bias in our analysis, including point spread function systematics, redshift distribution uncertainties, the intrinsic alignment of galaxies and the modeling of the matter power spectrum. For a flat Λ CDM model, we find S 8 ≡ σ 8 (Ω m /0.3) 0.5 = ${0.776}_{—0.033}^{+0.032}$, which is in excellent agreement with the constraints from the other HSC Year 3 cosmology analyses, as well as those from a number of other cosmic shear experiments. This result implies a ~2σ-level tension with the Planck 2018 cosmology. We study the effect that various systematic errors and modeling choices could have on this value, and find that they can shift the best-fit value of S 8 by no more than ~ 0.5σ, indicating that our result is robust to such systematics.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2026

First constraints from marked angular power spectra with Subaru Hyper Suprime-Cam Survey First-Year Data

We present the first application of marked power spectra to weak lensing data, using maps from the Subaru Hyper Suprime-Cam Year 1 (HSC-Y1) survey. Marked convergence fields, constructed by weighting the convergence field with non-linear functions of its smoothed version, are designed to encode higher-order information while remaining computationally tractable. Using simulations tailored to the HSC-Y1 data, we test three mark functions that up- or down-weight different density environments. Our results show that combining multiple types of marked auto and cross-spectra improves constraints on the clustering amplitude parameter S8≡σ8Ωm/0.3 by ≈43 per cent compared to standard two-point power spectra. When applied to the HSC-Y1 data, this translates into a constraint on S8=0.807±0.024⁠. We assess the sensitivity of the marked power spectra to systematics, including baryonic effects, intrinsic alignment, photometric redshifts, and multiplicative shear bias. We note that some of the additional information introduced by the marked field originates from scales smaller than the scale cut, and is partly Gaussian in nature. This does not invalidate our systematic tests. These results demonstrate the promise of marked statistics as a practical and powerful tool for extracting non-Gaussian information from weak lensing surveys.

Cowell, Jessica A. [Oxford U.; Tokyo U., IPMU] (OR↗
DOE OSTI2020

Blazar variability power spectra from radio up to TeV photon energies: Mrk 421 and PKS 2155−304

ABSTRACT We present the results of the power spectral density (PSD) analysis for the blazars Mrk 421 and PKS 2155−304, using good-quality, densely sampled light curves at multiple frequencies, covering 17 decades of the electromagnetic spectrum, and variability time-scales from weeks up to a decade. The data were collected from publicly available archives of observatories at radio from Owens Valley Radio Observatory, optical and infrared (B, V, R, I, J, H, and Kbands), X-rays from the Swift and the Rossi X-ray Timing Explorer, high and very high energy (VHE) γ-rays from the Fermi and Very Energetic Radiation Imaging Telescope Array System as well as the High Energy Stereoscopic System. Our results are: (1) the power-law form of the variability power spectra at radio, infrared, and optical frequencies have slopes ∼1.8, indicative of random-walk-type noise processes; (2) the power-law form of the variability power spectra at higher frequencies, from X-rays to VHE γ-rays, however, have slopes ∼1.2, suggesting a flicker noise-type process; and (3) there is significantly more variability power at X-rays, high and VHE γ-rays on time-scales ≲ 100 d, as compared to lower energies. Our results do not easily fit into a simple model, in which a single compact emission zone is dominating the radiative output of the blazars across all the time-scales probed in our analysis. Instead, we argue that the frequency-dependent shape of the variability power spectra points out a more complex picture, with highly inhomogeneous outflow producing non-thermal emission over an extended, stratified volume.

Goyal, Arti↗
DOE OSTI2026

Nonlinear Information from DESI Luminous Red Galaxies: An Emulator-Based Analysis of Pre- and Post-Reconstruction Power Spectra

We present joint measurements of the pre- and post-reconstruction power spectra, $P_{\rm pre}$ and $P_{\rm post}$, together with their cross-power spectrum, $P_{\rm cross}$, for the Luminous Red Galaxies (LRGs) in the DESI Data Release 1 (DR1). We jointly analyse these observables with an emulator-based full-shape modeling framework, thereby, for the first time, we extract complementary nonlinear information from the galaxy density field before and after reconstruction in real survey data. Specifically, including $P_{\rm post}$ and $P_{\rm cross}$ in addition to $P_{\rm pre}$ (hereafter $P_{\rm all}$) yields an improvement of approximately $18$-$27\%$ in the $σ_8$ constraint in both $Λ$CDM and $w$CDM, depending on the redshift bin, relative to the $P_{\rm pre}$-only analysis with the cosmic microwave background distance priors (hereafter CMB). In $w$CDM, the joint CMB+$P_{\rm all}$ analysis can tighten the constraints on $w$ by approximately $5$-$15\%$ across the two LRG redshift bins, compared to the CMB+$P_{\rm pre}$ combination. Further incorporating the Type Ia supernova dataset and comparing the cosmological constraints in $w$CDM from each individual power-spectrum component with those from the full combination, we find that $P_{\rm all}$ consistently provides the tightest constraints. From the joint CMB+$P_{\rm all}$+DES-Dovekie dataset, we obtain $Ω_m = 0.314 \pm 0.0048$ and $w = -0.988 \pm 0.023$ for the \texttt{LRG1} sample, and $Ω_m = 0.318 \pm 0.0046$ and $w = -0.988 \pm 0.025$ for \texttt{LRG2}. These results demonstrate that combining pre- and post-reconstruction power spectra with their cross-correlation enables DESI to harvest additional nonlinear information, leading to tighter constraints on cosmological parameters.

Wang, Yuting [NAOC, Beijing; Beijing, GUCAS] (ORCI↗
DOE OSTI2024

Constraining multi-field inflation using the SPHEREx all-sky survey power spectra

Abstract We investigate how well the SPHEREx all-sky survey can constrain local primordial non-Gaussianity beyond the parameterf NL using galaxy power spectra. We forecast joint constraints on the parametersf NL ,g NL andτ NL obtained assuming a simple two-field curvaton model of inflation. The parametersf NL andg NL characterise the squeezed limits of the primordial bispectrum and trispectrum respectively, and lead to a characteristic scale-dependence of the galaxy bias that increases out to arbitrarily large scales. Values of the parameterτ NL > (6/5f NL ) 2 cause the galaxy power spectrum to have a stochastic component which also increases out to arbitrarily large scales. Our MCMC forecasts indicate that SPHEREx can provide joint constraints on any two of the three parametersf NL ,g NL andτ NL . Due to strong degeneracies among these parameters, measurements of the galaxy power spectra alone may not be sufficient to jointly constrain all three. Constraints onf NL ,g NL andτ NL obtained from galaxy power spectrum observations depend on the modelling of underlying nuisance parameters. We study the robustness of our forecast constraints to modelling choices and note that even with relatively conservative modelling assumptions, SPHEREx galaxy power spectra can provide strong evidence of local non-Gaussianity, even if the particular values off NL andg NL cannot be measured precisely.

Astronomy & Astrophysics↗
DOE OSTI2026

SPT-3G D1: CMB temperature and polarization power spectra and cosmology from 2019 and 2020 observations of the SPT-3G main field

Here, we present measurements of the temperature and E-mode polarization angular power spectra of the cosmic microwave background (CMB) from observations of 4% of the sky with SPT-3G, the current camera on the South Pole Telescope (SPT). The maps used in this analysis are the deepest used in a CMB TT / TE / EE analysis to date. The maps and resulting power spectra have been validated through blind and unblind tests. The measurements of the lensed EE and TE spectra are the most precise to date at ℓ = 1800 – 4000 and ℓ = 2200 – 4000 , respectively. Combining our TT / TE / EE spectra with previously published SPT-3G CMB lensing results, we find parameters for the standard Λ cold dark matter ( Λ CDM ) model consistent with Planck and ACT DR6 with comparable constraining power. We report a Hubble constant of H 0 = 66.66 ± 0.60 km s - 1 Mpc - 1 from SPT-3G alone, 6.2 σ away from local measurements from SH0ES. For the first time, combined ground-based ( SPT + ACT ) CMB primary and lensing data have reached Planck’s constraining power on some parameters, a milestone for CMB cosmology. The combination of these three CMB experiments yields the tightest CMB constraints to date, with H 0 = 67.19 ± 0.38 km s - 1 Mpc - 1 , and the amplitude of clustering σ 8 = 0.8137 ± 0.0037 . CMB data alone show no evidence for physics beyond Λ CDM , however, we observe a 2.8 σ difference in Λ CDM between CMB and baryon acoustic oscillation (BAO) results from DESI-DR2, which is relaxed in extended models. The combination of CMB and BAO yields 2 − 3 σ shifts from Λ CDM in the curvature of the Universe, the amplitude of CMB lensing, or the dark energy equation of state. It also drives mild preferences for models that address the Hubble tension through modified recombination or variations in the electron mass in a nonflat Universe. This work highlights the growing power of ground-based CMB experiments and lays a foundation for further cosmological analyses with SPT-3G.

Camphuis, Etienne [Sorbonne Université; CNRS; Inst↗
DOE OSTI2025

Quantifying bias due to non-Gaussian foregrounds in an optimal reconstruction of CMB lensing and temperature power spectra

We estimate the magnitude of the bias due to non-Gaussian extragalactic foregrounds on the optimal reconstruction of the cosmic microwave background (CMB) lensing potential and temperature power spectra. The reconstruction is performed using a Bayesian inference method known as the marginal unbiased score expansion (MUSE). We apply MUSE to a minimum variance combination of multifrequency maps drawn from the Agora publicly available simulations of the lensed CMB and correlated extragalactic foreground emission. Taking noise levels appropriate to the SPT-3G D1 release, we find non-Gaussian foregrounds may bias the MUSE reconstruction of the lensing potential amplitude at the level of (0.7 ± 0.3)σ when using modes up to ℓ max = 3500. We do not detect a statistically significant bias, finding a value of (-0.4 ± 0.3)σ, when restricted to lower angular multipoles, ℓ max = 3000. This work is a first step toward understanding the impact of extragalactic foregrounds on optimal reconstructions of CMB temperature and lensing potential power spectra.

Statistical sampling techniques↗
DOE OSTI2024

Planck Dust Polarization Power Spectra Are Consistent with Strongly Supersonic Turbulence

Abstract The polarization of the cosmic microwave background is rich in information but obscured by foreground emission from the Milky Way’s interstellar medium (ISM). To uncover relationships between the underlying turbulent ISM and the foreground power spectra, we simulated a suite of driven, magnetized, turbulent models of the ISM, varying the fluid properties via the sonic Mach number, M S , and magnetic (Alfvén) Mach number, M A . We measure the power spectra of density ( ρ ), velocity ( v ), magnetic field ( H ), total projected intensity ( T ), parity-even polarization ( E ), and parity-odd polarization ( B ). We find that the slopes of all six quantities increase with M S . Most increase with M A , while the magnetic field spectrum steepens with M A . By comparing spectral slopes of E and B to those measured by Planck, we infer typical values of M S and M A for the ISM. As the fluid velocity increases, M S > 4 , the ratio of BB power to EE power increases to approach a constant value near the Planck-observed value of ∼0.5, regardless of the magnetic field strength. We also examine correlation coefficients between projected quantities, and find that r TE ≈ 0.3, in agreement with Planck, for appropriate combinations of M S and M A . Finally, we consider parity-violating correlations r TB and r EB .

Astronomy & Astrophysics↗
DOE OSTI2020

Beyond Limber: efficient computation of angular power spectra for galaxy clustering and weak lensing

Angular two-point statistics of large-scale structure observables are important cosmological probes. To reach the high accuracy required by the statistical precision of future surveys, some of these statistics may need to be computed without the commonly employed Limber approximation; the exact computation however requires integration over Bessel functions, and a brute-force evaluation is slow to converge. Here, we present a new method based on our generalized FFTLog algorithm for the efficient computation of angular power spectra beyond the Limber approximation. The new method significantly simplifies the calculation and improves the numerical speed and stability. It is easily extended to handle integrals involving derivatives of Bessel functions, making it equally applicable to numerically more challenging cases such as contributions from redshift-space distortions and Doppler effects. We implement our method for galaxy clustering and galaxy-galaxy lensing power spectra. We find that using the Limber approximation for galaxy clustering in future analyses like LSST Year 1 and DES Year 6 may cause significant biases in cosmological parameters, indicating that going beyond the Limber approximation is necessary for these analyses.

weak gravitational lensing↗
DOE OSTI2021

The Atacama Cosmology Telescope: delensed power spectra and parameters

We present ΛCDM cosmological parameter constraints obtained from delensed microwave background power spectra. Lensing maps from a subset of DR4 data from the Atacama Cosmology Telescope (ACT) are used to undo the lensing effect in ACT spectra observed at 150 and 98 GHz. At 150 GHz, we remove the lensing distortion with an effective efficiency of 30% (TT), 30% (EE), 26% (TE) and 20% (BB); this results in detections of the delensing effect at 8.7σ (TT), 5.1σ (EE), 2.6σ (TE), and 2.4σ (BB) significance. The combination of 150 and 98 GHz TT, EE, and TE delensed spectra is well fit by a standard ΛCDM model. We also measure the shift in best-fit parameters when fitting delensed versus lensed spectra; while this shift does not inform our ability to measure cosmological parameters, it does provide a three-way consistency check among the lensing inferred from the best-fit parameters, the lensing in the CMB power spectrum, and the reconstructed lensing map. This shift is predicted to be zero when fitting with the correct model since both lensed and delensed spectra originate from the same region of sky. Furthermore, fitting with a ΛCDM model and marginalizing over foregrounds, we find that the shift in cosmological parameters is consistent with zero. Our results show that gravitational lensing of the microwave background is internally consistent within the framework of the standard cosmological model.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2020

Theory of molecular emission power spectra. I. Macroscopic quantum electrodynamics formalism

In this work, we study the emission power spectrum of a molecular emitter with multiple vibrational modes in the framework of macroscopic quantum electrodynamics. The theory we present is general for a molecular spontaneous emission spectrum in the presence of arbitrary inhomogeneous, dispersive, and absorbing media. Moreover, the theory shows that the molecular emission power spectra can be decomposed into the electromagnetic environment factor and lineshape function. In order to demonstrate the validity of the theory, we investigate the lineshape function in two limits. In the incoherent limit (single molecules in a vacuum), the lineshape function exactly corresponds to the Franck–Condon principle. In the coherent limit (single molecules strongly coupled with single polaritons or photons) together with the condition of high vibrational frequency, the lineshape function exhibits a Rabi splitting, the spacing of which is exactly the same as the magnitude of exciton–photon coupling estimated by our previous theory [S. Wang et al., J. Chem. Phys. 151, 014105 (2019)]. Finally, we explore the influence of exciton–photon and electron–phonon interactions on the lineshape function of a single molecule in a cavity. The theory shows that the vibronic structure of the lineshape function does not always disappear as the exciton–photon coupling increases, and it is related to the loss of a dielectric environment.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

The Atacama Cosmology Telescope: a measurement of the Cosmic Microwave Background power spectra at 98 and 150 GHz

We present the temperature and polarization angular power spectra of the CMB measured by the Atacama Cosmology Telescope (ACT) from 5400 deg2 of the 2013–2016 survey, which covers >15000 deg2 at 98 and 150 GHz. For this analysis we adopt a blinding strategy to help avoid confirmation bias and, related to this, show numerous checks for systematic error done before unblinding. Using the likelihood for the cosmological analysis we constrain secondary sources of anisotropy and foreground emission, and derive a “CMB-only” spectrum that extends to ℓ=4000. At large angular scales, foreground emission at 150 GHz is ∼1% of TT and EE within our selected regions and consistent with that found by Planck. Using the same likelihood, we obtain the cosmological parameters for ΛCDM for the ACT data alone with a prior on the optical depth of τ=0.065±0.015. ΛCDM is a good fit. The best-fit model has a reduced χ2 of 1.07 (PTE=0.07) with H0=67.9±1.5 km/s/Mpc. We show that the lensing BB signal is consistent with ΛCDM and limit the celestial EB polarization angle to ψP =−0.07ˆ±0.09ˆ. We directly cross correlate ACT with Planck and observe generally good agreement but with some discrepancies in TE. All data on which this analysis is based will be publicly released.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2022

CMB power spectra and cosmological parameters from Planck PR4 with CamSpec

ABSTRACT We present angular power spectra and cosmological parameter constraints derived from the Planck PR4 (NPIPE) maps of the cosmic microwave background. NPIPE, released by the Planck Collaboration in 2020, is a new processing pipeline for producing calibrated frequency maps from Planck data. We have created new versions of the CamSpec likelihood using these maps and applied them to constrain the lambda cold dark matter (ΛCDM) model and single-parameter extensions. We find excellent consistency between NPIPE and the Planck 2018 maps at the parameter level, showing that the Planck cosmology is robust to substantial changes in the mapmaking. The lower noise of NPIPE leads to ~10 per cent tighter constraints, and we see both smaller error bars and a shift towards the ΛCDM values for beyond-ΛCDM parameters including ΩK and AL.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2022

A Simulation-based Method for Correcting Mode Coupling in CMB Angular Power Spectra

Modern cosmic microwave background (CMB) analysis pipelines regularly employ complex time-domain filters, beam models, masking, and other techniques during the production of sky maps and their corresponding angular power spectra. However, these processes can generate couplings between multipoles from the same spectrum and from different spectra, in addition to the typical power attenuation. Within the context of pseudo-C ℓ based, MASTER-style analyses, the net effect of the time-domain filtering is commonly approximated by a multiplicative transfer function, F ℓ , that can fail to capture mode mixing and is dependent on the spectrum of the signal. To address these shortcomings, we have developed a simulation-based spectral correction approach that constructs a two-dimensional transfer matrix, ${J}_{{\ell }{\ell }^{\prime} }$, which contains information about mode mixing in addition to mode attenuation. We demonstrate the application of this approach on data from the first flight of the Spider balloon-borne CMB experiment.

79 ASTRONOMY AND ASTROPHYSICS↗