Cosmic Microwave Background Data Sets Research Articles

Principal components of CMB non-Gaussianity

The skew-spectrum statistic introduced by Munshi & Heavens has recently been used in studies of non-Gaussianity from diverse cosmological data sets including the detection of primary and secondary non-Gaussianity of cosmic microwave background (CMB) radiation. Extending previous work, focused on independent estimation, here we deal with the question of joint estimation of multiple skew-spectra from the same or correlated data sets. We consider the optimum skew-spectra for various models of primordial non-Gaussianity as well as secondary bispectra that originate from the cross-correlation of secondaries and lensing of CMB: coupling of lensing with the Integrated Sachs–Wolfe effect, coupling of lensing with thermal Sunyaev–Zeldovich, as well as from unresolved point sources. For joint estimation of various types of non-Gaussianity, we use the principal component analysis (PCA) to construct the linear combinations of amplitudes of various models of non-Gaussianity, e.g. |$f^{\rm loc}_{\rm NL},f^{\rm eq}_{\rm NL},f^{\rm ortho}_{\rm NL}$| that can be estimated from CMB maps. We describe how the bias induced in the estimation of primordial non-Gaussianity due to secondary non-Gaussianity may be evaluated for arbitrary primordial models using a PCA analysis. The PCA approach allows one to infer approximate (but generally accurate) constraints using CMB data sets on any reasonably smooth model by use of a look-up table and performing a simple computation. This principle is validated by computing constraints on the Dirac–Born–Infeld bispectrum using a PCA analysis of the standard templates.

TESTING CPT SYMMETRY WITH CURRENT AND FUTURE CMB MEASUREMENTS

In this paper we use the current and future cosmic microwave background (CMB) experiments to test the Charge-Parity-Time Reversal (CPT) symmetry. We consider a CPT-violating interaction in the photon sector $\mathcal{L}_{\rm cs}\sim p_\mu A_\nu \tilde{F}^{\mu\nu}$ which gives rise to a rotation of the polarization vectors of the propagating CMB photons. By combining the nine-year WMAP, BOOMERanG 2003 and BICEP1 observations, we obtain the current constraint on the isotropic rotation angle $\bar{\alpha} = -2.12 \pm 1.14$ ($1\sigma$), indicating an about $2\sigma$ significance of the CPT violation. Here, we particularly take the systematic errors of CMB measurements into account. Then, we study the effects of the anisotropies of the rotation angle [$\Delta{\alpha}({\bf \hat{n}})$] on the CMB polarization power spectra in detail. Due to the small effects, the current CMB polarization data can not constrain the related parameters very well. We obtain the 95\% C.L. upper limit of the variance of the anisotropies of the rotation angle $C^\alpha(0) < 0.035$ from all the CMB datasets. More interestingly, including the anisotropies of rotation angle could lower the best fit value of $r$ and relax the tension on the constraints of $r$ between BICEP2 and Planck. Finally, we investigate the capabilities of future Planck polarization measurements on $\bar{\alpha}$ and $\Delta{\alpha}({\bf \hat{n}})$. Benefited from the high precision of Planck data, the constraints of the rotation angle can be significantly improved.

Accelerating the cosmic microwave background map-making procedure through preconditioning

Estimation of the sky signal from sequences of time ordered data is one of the key steps in Cosmic Microwave Background (CMB) data analysis, commonly referred to as the map-making problem. Some of the most popular and general methods proposed for this problem involve solving generalised least squares (GLS) equations with non-diagonal noise weights given by a block-diagonal matrix with Toeplitz blocks. In this work we study new map-making solvers potentially suitable for applications to the largest anticipated data sets. They are based on iterative conjugate gradient (CG) approaches enhanced with novel, parallel, two-level preconditioners. We apply the proposed solvers to examples of simulated non-polarised and polarised CMB observations, and a set of idealised scanning strategies with sky coverage ranging from nearly a full sky down to small sky patches. We discuss in detail their implementation for massively parallel computational platforms and their performance for a broad range of parameters characterising the simulated data sets. We find that our best new solver can outperform carefully-optimised standard solvers used today by a factor of as much as 5 in terms of the convergence rate and a factor of up to $4$ in terms of the time to solution, and to do so without significantly increasing the memory consumption and the volume of inter-processor communication. The performance of the new algorithms is also found to be more stable and robust, and less dependent on specific characteristics of the analysed data set. We therefore conclude that the proposed approaches are well suited to address successfully challenges posed by new and forthcoming CMB data sets.

Weighing the giants – IV. Cosmology and neutrino mass

We employ robust weak gravitational lensing measurements to improve cosmological constraints from measurements of the galaxy cluster mass function and its evolution, using X-ray selected clusters detected in the ROSAT All-Sky Survey. Our lensing analysis constrains the absolute mass scale of such clusters at the 8 per cent level, including both statistical and systematic uncertainties. Combining it with the survey data and X-ray follow-up observations, we find a tight constraint on a combination of the mean matter density and late-time normalization of the matter power spectrum, σ8(Ωm/0.3)0.17 = 0.81 ± 0.03, with marginalized, one-dimensional constraints of Ωm = 0.26 ± 0.03 and σ8 = 0.83 ± 0.04. For these two parameters, this represents a factor of 2 improvement in precision with respect to previous work, primarily due to the reduced systematic uncertainty in the absolute mass calibration provided by the lensing analysis. Our new results are in good agreement with constraints from cosmic microwave background (CMB) data, both Wilkinson Microwave Anisotropy Probe (WMAP) and Planck (plus WMAP polarization), under the assumption of a flat ΛCDM cosmology with minimal neutrino mass. Consequently, we find no evidence for non-minimal neutrino mass from the combination of cluster data with CMB, supernova and baryon acoustic oscillation measurements, regardless of which all-sky CMB data set is used (and independent of the recent claimed detection of B modes on degree scales). We also present improved constraints on models of dark energy (both constant and evolving), modifications of gravity, and primordial non-Gaussianity. Assuming flatness, the constraints for a constant dark energy equation of state from the cluster data alone are at the 15 per cent level, improving to ∼6 per cent when the cluster data are combined with other leading probes.

Neutrino constraints: what large-scale structure and CMB data are telling us?

We discuss the reliability of neutrino mass constraints, either active or sterile, from the combination of different low redshift Universe probes with measurements of CMB anisotropies. In our analyses we consider WMAP 9-year or Planck Cosmic Microwave Background (CMB) data in combination with Baryonic Acoustic Oscillations (BAO) measurements from BOSS DR11, galaxy shear measurements from CFHTLenS, SDSS Ly α forest constraints and galaxy cluster mass function from Chandra observations. At odds with recent similar studies, to avoid model dependence of the constraints we perform a full likelihood analysis for all the datasets employed. As for the cluster data analysis we rely on to the most recent calibration of massive neutrino effects in the halo mass function and we explore the impact of the uncertainty in the mass bias and re-calibration of the halo mass function due to baryonic feedback processes on cosmological parameters. We find that none of the low redshift probes alone provide evidence for massive neutrino in combination with CMB measurements, while a larger than 2σ detection of non zero neutrino mass, either active or sterile, is achieved combining cluster or shear data with CMB and BAO measurements. Yet, the significance of the detection exceeds 3σ if we combine all four datasets. For a three active neutrino scenario, from the joint analysis of CMB, BAO, shear and cluster data including the uncertainty in the mass bias we obtain ∑ mν =0.29+0.18-0.21 eV and ∑ mν =0.22+0.17-0.18 eV 95%CL) using WMAP9 or Planck as CMB dataset, respectively. The preference for massive neutrino is even larger in the sterile neutrino scenario, for which we get mseff=0.44+0.28-0.26 eV and Δ Neff=0.78+0.60-0.59 95%CL) from the joint analysis of Planck, BAO, shear and cluster datasets. For this data combination the vanilla ΛCDM model is rejected at more than 3σ and a sterile neutrino mass as motivated by accelerator anomaly is within the 2σ errors. Conversely, the Ly α data favour vanishing neutrino masses and from the data combination Planck+BAO+Ly α we get the tight upper limits ∑ mν <0.14 eV and mseff<0.22 eV—Δ Neff<1.11 95%CL) for the active and sterile neutrino model, respectively. Finally, results from the full data combination reflect the tension between the σ8 constraints obtained from cluster and shear data and that inferred from Ly α forest measurements; in the active neutrino scenario for both CMB datasets employed, the full data combination yields only an upper limits on ∑ mν, while assuming an extra sterile neutrino we still get preference for non-vanishing mass, mseff=0.26+0.22-0.24 eV, and dark contribution to the radiation content, Δ Neff=0.82±0.55.

THE 1% CONCORDANCE HUBBLE CONSTANT

The determination of the Hubble constant has been a central goal in observational astrophysics for nearly 100 years. Extraordinary progress has occurred in recent years on two fronts: the cosmic distance ladder measurements at low redshift and cosmic microwave background (CMB) measurements at high redshift. The CMB is used to predict the current expansion rate through a best-fit cosmological model. Complementary progress has been made with baryon acoustic oscillation (BAO) measurements at relatively low redshifts. While BAO data do not independently determine a Hubble constant, they are important for constraints on possible solutions and checks on cosmic consistency. A precise determination of the Hubble constant is of great value, but it is more important to compare the high and low redshift measurements to test our cosmological model. Significant tension would suggest either uncertainties not accounted for in the experimental estimates, or the discovery of new physics beyond the standard model of cosmology. In this paper we examine in detail the tension between the CMB, BAO, and cosmic distance ladder data sets. We find that these measurements are consistent within reasonable statistical expectations, and we combine them to determine a best-fit Hubble constant of 69.6+/-0.7 km/s/Mpc. This value is based upon WMAP9+SPT+ACT+6dFGS+BOSS/DR11+H_0/Riess; we explore alternate data combinations in the text. The combined data constrain the Hubble constant to 1%, with no compelling evidence for new physics.

Fast calculation of the Fisher matrix for cosmic microwave background experiments

The Fisher information matrix of the cosmic microwave background (CMB) radiation power spectrum coefficients is a fundamental quantity that specifies the information content of a CMB experiment. In the most general case, its exact calculation scales with the third power of the number of data points N and is therefore computationally prohibitive for state-of-the-art surveys. Applicable to a very large class of CMB experiments without special symmetries, we show how to compute the Fisher matrix in only O(N^2 log N) operations as long as the inverse noise covariance matrix can be applied to a data vector in time O(l_max^3 log l_max). This assumption is true to a good approximation for all CMB data sets taken so far. The method takes into account common systematics such as arbitrary sky coverage and realistic noise correlations. As a consequence, optimal quadratic power spectrum estimation also becomes feasible in O(N^2 log N) operations for this large group of experiments. We discuss the relevance of our findings to other areas of cosmology where optimal power spectrum estimation plays a role.

IS THE COSMIC MICROWAVE BACKGROUND ASYMMETRY DUE TO THE KINEMATIC DIPOLE?

Parity violation found in the Cosmic Microwave Background (CMB) radiation is a crucial clue for the non-standard cosmological model or the possible contamination of various foreground residuals and/or calibration of the CMB data sets. In this paper, we study the directional properties of the CMB parity asymmetry by excluding the $m=0$ modes in the definition of parity parameters. We find that the preferred directions of the parity parameters coincide with the CMB kinematic dipole, which implies that the CMB parity asymmetry may be connected with the possible contamination of the residual dipole component. We also find that such tendency is not only localized at $l=2,3$, but in the extended multipole ranges up to $l\sim 22$.

Joint quasar-cosmic microwave background constraints on reionization history

Based on the work by Mitra, Choudhury & Ferrara (2010), we obtain model-independent constraints on reionization from cosmic microwave background (CMB) and QSO absorption line data by decomposing the function N_{ion}(z) (the number of photons entering the IGM per baryon in collapsed objects) into its principal components. The main addition in this work is that for the CMB data set, we explicitly include the angular power spectra C_l for TT, TE and EE modes in our analysis which seem to contain somewhat more information than taking the electron scattering optical depth tau_{el} as a single data point. Using Markov Chain Monte Carlo methods, we find that all the quantities related to reionization can be severely constrained at z < 6 whereas a broad range of reionization histories at z > 6 are still permitted by the current data sets. With currently available data from WMAP7, we constrain 0.080 < tau_{el} < 0.112 (95% CL) and also conclude that reionization is 50% complete between 9.0 < z(Q_{HII} = 0.5) < 11.8 (95% CL) and is 99% complete between 5.8 < z(Q_{HII} = 0.99) < 10.4 (95% CL). With the forthcoming PLANCK data on large-scale polarization (ignoring effect of foregrounds), the z > 6 constraints will be improved considerably, e.g., the 2-sigma error on tau_{el} will be reduced to 0.009 and the uncertainties on z(Q_{HII} = 0.5) and z(Q_{HII} = 0.99) would be \sim 1 and 3 (95% CL), respectively. For more stringent constraints on reionization at z > 6, one has to rely on data sets other than CMB. Our method will be useful in such case since it can be used for non-parametric reconstruction of reionization history with arbitrary data sets.

PARAMETER ESTIMATION FROM IMPROVED MEASUREMENTS OF THE COSMIC MICROWAVE BACKGROUND FROM QUaD

We evaluate the contribution of cosmic microwave background (CMB) polarization spectra to cosmological parameter constraints. We produce cosmological parameters using high-quality CMB polarization data from the ground-based QUaD experiment and demonstrate for the majority of parameters that there is significant improvement on the constraints obtained from satellite CMB polarization data. We split a multi-experiment CMB dataset into temperature and polarization subsets and show that the best-fit confidence regions for the LCDM 6-parameter cosmological model are consistent with each other, and that polarization data reduces the confidence regions on all parameters. We provide the best limits on parameters from QUaD EE/BB polarization data and we find best-fit parameters from the multi-experiment CMB dataset using the optimal pivot scale of k_p=0.013 Mpc-1 to be {omch2, ombh2, H_0, A_s, n_s, tau}= {0.113, 0.0224, 70.6, 2.29 times 10^-9, 0.960, 0.086}.

MADmap: A MASSIVELY PARALLEL MAXIMUM LIKELIHOOD COSMIC MICROWAVE BACKGROUND MAP-MAKER

MADmap is a software application used to produce maximum-likelihood images of the sky from time-ordered data which include correlated noise, such as those gathered by Cosmic Microwave Background (CMB) experiments. It works efficiently on platforms ranging from small workstations to the most massively parallel supercomputers. Map-making is a critical step in the analysis of all CMB data sets, and the maximum-likelihood approach is the most accurate and widely applicable algorithm; however, it is a computationally challenging task. This challenge will only increase with the next generation of ground-based, balloon-borne and satellite CMB polarization experiments. The faintness of the B-mode signal that these experiments seek to measure requires them to gather enormous data sets. MADmap is already being run on up to $O(10^{11})$ time samples, $O(10^8)$ pixels and $O(10^4)$ cores, with ongoing work to scale to the next generation of data sets and supercomputers. We describe MADmap's algorithm based around a preconditioned conjugate gradient solver, fast Fourier transforms and sparse matrix operations. We highlight MADmap's ability to address problems typically encountered in the analysis of realistic CMB data sets and describe its application to simulations of the Planck and EBEX experiments. The massively parallel and distributed implementation is detailed and scaling complexities are given for the resources required. MADmap is capable of analysing the largest data sets now being collected on computing resources currently available, and we argue that, given Moore's Law, MADmap will be capable of reducing the most massive projected data sets.

Simulating weak lensing of CMB maps

<i>Aims. <i/>Accurate predictions of cosmic microwave background (CMB) anisotropies and polarization are required for analyzing future CMB data sets, which ultimately require accurately simulated lensed maps.<i>Methods. <i/>We present a fast, arbitrarily accurate method to simulate the effect of gravitational lensing of the CMB anisotropies and polarization fields by large-scale structures on arbitrarily spaced grid points over a unit sphere using a non-equispaced fast Fourier transform (NFFT).<i>Results. <i/>The angular power spectrum of the simulated lensed CMB map, particularly the B-mode of polarization, agrees extremely well with analytical predictions. The analytical derivation of CMB-lensed spectra is based on non-trivial, partially resummed perturbative expansions of the correlation functions, for which our simulations therefore provide an accurate numerical validation. We demonstrate the efficiency and accuracy of the method and exhibit their dependence on the algorithm parameters. Lensed CMB maps simulated in this method are a useful tool for the analysis and interpretation of upcoming CMB experiments, such as PLANCK and ACT. Our code is available on request.

SUBDEGREE SUNYAEV-ZEL'DOVICH SIGNAL FROM MULTIFREQUENCY BOOMERANG OBSERVATIONS

The Sunyaev-Zel'dovich (SZ) effect is the inverse Compton-scattering of cosmic microwave background (CMB) photons by hot electrons in the intervening gas throughout the universe. The effect has a distinct spectral signature that allows its separation from other signals in multifrequency CMB data sets. Using CMB anisotropies measured at three frequencies by the BOOMERANG 2003 flight we constrain SZ fluctuations in the 10 arcmin to 1 deg angular range. Propagating errors and potential systematic effects through simulations, we obtain an overall upper limit of 15.3 μK (2σ) for rms SZ fluctuations in a broad bin between multipoles of 250 and 1200 at the Rayleigh-Jeans (RJ) end of the spectrum. The resulting upper limit on the local universe normalization of the density perturbations with BOOMERANG SZ data alone is σSZ 8 < 1.14 at the 95% confidence level. When combined with other CMB anisotropy and SZ measurements, we find σSZ 8 < 0.92 (95% c.l.).

Forecasts for dark energy measurements with future H i surveys

We use two independent methods to forecast the dark energy measurements achievable by combining future galaxy redshift surveys based on the radio HI emission line with Cosmic Microwave Background (CMB) data from the {\sl Planck} satellite. In the first method we focus on the `standard ruler' provided by the baryon acoustic oscillation (BAO) length scale. In the second method we utilize additional information encoded in the galaxy power spectrum including galaxy bias from velocity-space distortions and the growth of cosmic structure. We find that a radio synthesis array with about 10 per cent of the collecting area of the Square Kilometre Array (SKA), equipped with a wide ($10-100 ~ {\rm deg}^2$) field-of-view, would have the capacity to perform a $20{,}000 ~ {\rm deg}^2$ redshift survey to a maximum redshift $z_{\rm max} \sim 0.8$ and thereby produce dark energy measurements that are competitive with surveys likely to be undertaken by optical telescopes around 2015. There would then be powerful arguments for adding collecting area to such a `Phase-1' SKA because of the square-law scaling of survey speed with telescope sensitivity for HI surveys, compared to the linear scaling for optical redshift surveys. The full SKA telescope should, by performing a $20{,}000 ~ {\rm deg}^2$ HI redshift survey to $z_{\rm max} \sim 2$ around 2020, yield an accurate measurement of cosmological parameters independent of CMB datasets. Combining CMB ({\sl Planck}) and galaxy power spectrum (SKA) measurements will drive errors in the dark energy equation-of-state parameter $w$ well below the 1 per cent level. The major systematic uncertainty in these forecasts is the lack of direct information about the mass function of high-redshift HI-emitting galaxies.

Maximum likelihood algorithm for parametric component separation in cosmic microwave background experiments

We discuss an approach to the component separation of microwave, multifrequency sky maps as those typically produced from cosmic microwave background (CMB) anisotropy data sets. The algorithm is based on the two-step, parametric, likelihood-based technique recently elaborated on by Eriksen et al., where the foreground spectral parameters are estimated prior to the actual separation of the components. In contrast with the previous approaches, we accomplish the former task with help of an analytically derived likelihood function for the spectral parameters, which, we show, yields estimates equal to the maximum likelihood values of the full multidimensional data problem. We then use these estimates to perform the second step via the standard, generalized-least-squares-like procedure. We demonstrate that the proposed approach is equivalent to a direct maximization of the full data likelihood, which is recast in a computationally tractable form. We use the corresponding curvature matrices to characterize statistical properties of the recovered parameters. We incorporate in the formalism some of the essential features of the CMB data sets, such as inhomogeneous pixel domain noise, unknown map offsets as well as calibration errors and study their consequences for the separation. We find that the calibration is likely to have a dominant effect on the precision of the spectral parameter determination for a realistic CMB experiment. We apply the algorithm to simulated data and discuss the results. Our focus is on partial sky, total intensity and polarization, CMB experiments such as planned balloon-borne and ground-based efforts, however, the techniques presented here should be also applicable to the full-sky data as for instance, those produced by the Wilkinson Microwave Anisotropy Probe (WMAP) satellite and anticipated from the Planck mission.

Cosmic microwave background temperature and polarization pseudo-Cℓestimators and covariances

We develop the pseudo-Cl method for reconstructing the cosmic microwave background (CMB) temperature and polarization auto- and cross-power spectra, and estimate the pseudo-Cl covariance matrix for a realistic experiment on the cut sky. We calculate the full coupling equations for all six possible CMB power spectra, relating the observed pseudo-Cl values to the underlying all-sky Cl values, and test the reconstruction on both full-sky and cut-sky simulated CMB data sets. In particular we consider the reconstruction of the Cl from upcoming ground-based polarization experiments covering areas of a few hundred deg2 and find that the method is fast, unbiased and performs well over a wide range of multipoles from l= 2 to l= 2500. We then calculate the full covariance matrix between the modes of the pseudo-temperature and polarization power spectra, assuming that the underlying CMB fields are Gaussian randomly distributed. The complexity of the covariance matrix prohibits its rapid calculation, required for parameter estimation. Hence we present an approximation for the covariance matrix in terms of convolutions of the underlying power spectra. The coupling matrices in these expressions can be estimated by fitting to numerical simulations, circumventing direct and slow calculation, and further, inaccurate analytic approximations. We show that these coupling matrices are mostly independent of cosmology, and that the full covariance matrix for all six pseudo-Cl power spectra can be quickly and accurately calculated for any given cosmological model using this method. We compare these semi-analytic covariance matrices against simulations and find good agreement, the accuracy of which depends mainly on survey area and the range of cosmological parameters considered.

Joint cosmological parameters forecast from CFHTLS-cosmic shear and CMB data

We present a prospective analysis of a combined cosmic shear and cosmic microwave background data sets, focusing on a Canada France Hawaii Telescope Legacy Survey (CFHTLS) type lensing survey and the current WMAP-1 year and CBI data. We investigate the parameter degeneracies and error estimates of a seven parameter model, for the lensing alone as well as for the combined experiments. The analysis is performed using a Monte Carlo Markov Chain calculation, allowing for a more realistic estimate of errors and degeneracies than a Fisher matrix approach. After a detailed discussion of the relevant statistical techniques, the set of the most relevant 2 and 3-dimensional lensing contours are given. It is shown that the combined cosmic shear and CMB is particularly efficient to break some parameter degeneracies. The principal component directions are computed and it is found that the most orthogonal contours between the two experiments are for the parameter pairs , and , where ns and are, respectively, the slope of the primordial mass power spectrum and the running of the spectral index. It is shown, under the assumption of perfectely controlled systematics, that an improvement of a factor of 2 is expected on the running of the spectral index from the combined data sets. Forecasts for error improvements from a wide field space telescope lensing survey are also given.

Goodness–of–fit statistics and CMB data sets

Application of a Goodness–of–fit (GOF) statistic is an essential element in parameter estimation. We discuss the computation of GOF when estimating parameters from anisotropy measurements of the cosmic microwave background (CMB), and we propose two GOF statistics to be used when employing approximate band–power likelihood functions. They are based on an approximate form for the distribution of band–power estimators that requires only minimal experimental information to construct. Monte Carlo simulations of CMB experiments show that the proposed form describes the true distributions quite well. We apply these GOF statistics to current CMB anisotropy data and discuss the results.

Cosmic Microwave Background as a Gravity Probe

We show that cosmic microwave background (CMB) observations have a strong potentiality not only as a test of cosmic kinematics but also as a gravity probe. We compare the recent high-resolution CMB data to models with a direct coupling of dark energy to dark matter. This extra interaction violates the equivalence principle, acts as an additional scalar gravity on dark matter fluctuations, and imprints a characteristic signature on the CMB spectra. Defining the ratio β of the dark energy interaction to gravity, we that β < 0.16 (95% confidence level [c.l.]) from the current CMB data set, regardless of the potential. This implies that the effective equation of state between equivalence and tracking has been close to the pure matter equation of state within 1% and that scalar gravity is at least 40 times weaker than tensor gravity. Furthermore, we show that an ideal CMB experiment limited by cosmic variance only can put an upper bound β < 0.05 (95% c.l.), comparable to the best limits provided by local gravity experiments on the coupling to baryons.

MASTER of the Cosmic Microwave Background Anisotropy Power Spectrum: A Fast Method for Statistical Analysis of Large and Complex Cosmic Microwave Background Data Sets

We describe a fast and accurate method for estimation of the cosmic microwave background (CMB) anisotropy angular power spectrum --- Monte Carlo Apodised Spherical Transform EstimatoR. Originally devised for use in the interpretation of the Boomerang experimental data, MASTER is both a computationally efficient method suitable for use with the currently available CMB data sets (already large in size, despite covering small fractions of the sky, and affected by inhomogeneous and correlated noise), and a very promising application for the analysis of very large future CMB satellite mission products.