arXiv subjects

Benjamin D. Wandelt

Publications and source records attributed to Benjamin D. Wandelt.

At least 181 records · Page 10Linked to original sources

arXiv2008

Cosmic (super)string constraints from 21 cm radiation

We calculate the contribution of cosmic strings arising from a phase transition in the early universe, or cosmic superstrings arising from brane inflation, to the cosmic 21 cm power spectrum at redshifts z > 30. Future experiments can exploit this effect to constrain the cosmic string tension Gu and probe virtually the entire brane inflation model space allowed by current observations. Although current experiments with a collecting area of ~ 1 km^2 will not provide any useful constraints, future experiments with a collecting area of 10^4-10^6 km^2 covering the cleanest 10% of the sky can in principle constrain cosmic strings with tension Gu > 10^(-10) to 10^(-12) (superstring/phase transition mass scale >10^13 GeV).

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arXiv2007

Computing High Accuracy Power Spectra with Pico

This paper presents the second release of Pico (Parameters for the Impatient COsmologist). Pico is a general purpose machine learning code which we have applied to computing the CMB power spectra and the WMAP likelihood. For this release, we have made improvements to the algorithm as well as the data sets used to train Pico, leading to a significant improvement in accuracy. For the 9 parameter nonflat case presented here Pico can on average compute the TT, TE and EE spectra to better than 1% of cosmic standard deviation for nearly all $\ell$ values over a large region of parameter space. Performing a cosmological parameter analysis of current CMB and large scale structure data, we show that these power spectra give very accurate 1 and 2 dimensional parameter posteriors. We have extended Pico to allow computation of the tensor power spectrum and the matter transfer function. Pico runs about 1500 times faster than CAMB at the default accuracy and about 250,000 times faster at high accuracy. Training Pico can be done using massively parallel computing resources, including distributed computing projects such as Cosmology@Home. On the homepage for Pico, located at http://cosmos.astro.uiuc.edu/pico, we provide new sets of regression coefficients and make the training code available for public use.

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arXiv2007

Fast Estimator of Primordial Non-Gaussianity from Temperature and Polarization Anisotropies in the Cosmic Microwave Background II: Partial Sky Coverage and Inhomogeneous Noise

In our recent paper (Yadav et al. 2007) we described a fast cubic (bispectrum) estimator of the amplitude of primordial non-Gaussianity of local type, f_{NL}, from a combined analysis of the Cosmic Microwave Background (CMB) temperature and E-polarization observations. In this paper we generalize the estimator to deal with a partial sky coverage as well as inhomogeneous noise. Our generalized estimator is still computationally efficient, scaling as O(N^3/2) compared to the O(N^5/2) scaling of the brute force bispectrum calculation for sky maps with N pixels. Upcoming CMB experiments are expected to yield high-sensitivity temperature and E-polarization data. Our generalized estimator will allow us to optimally utilize the combined CMB temperature and E-polarization information from these realistic experiments, and to constrain primordial non-Gaussianity.

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arXiv2007

21 cm radiation - a new probe of variation in the fine structure constant

We investigate the effect of variation in the value of the fine structure constant at high redshifts (recombination > z > 30) on the absorption of the cosmic microwave background (CMB) at 21 cm hyperfine transition of the neutral atomic hydrogen. We find that the 21 cm signal is very sensitive to the variations in the fine structure constant and it is so far the only probe of the fine structure constant in this redshift range. A change in the value of the fine structure constant by 1% changes the mean brightness temperature decrement of the CMB due to 21 cm absorption by > 5% over the redshift range z < 50. There is an effect of similar magnitude on the amplitude of the fluctuations in the brightness temperature. The redshift of maximum absorption also changes by ~ 5%.

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arXiv2007

Fast Estimator of Primordial Non-Gaussianity from Temperature and Polarization Anisotropies in the Cosmic Microwave Background

Measurements of primordial non-Gaussianity ($f_{NL}$) open a new window onto the physics of inflation. We describe a fast cubic (bispectrum) estimator of $f_{NL}$, using a combined analysis of temperature and polarization observations. The speed of our estimator allows us to use a sufficient number of Monte Carlo simulations to characterize its statistical properties in the presence of real world issues such as instrumental effects, partial sky coverage, and foreground contamination. We find that our estimator is optimal, where optimality is defined by saturation of the Cramer Rao bound, if noise is homogeneous. Our estimator is also computationally efficient, scaling as $O(N^{3/2})$ compared to the $O(N^{5/2})$ scaling of the brute force bispectrum calculation for sky maps with $N$ pixels. For Planck this translates into a speed-up by factors of millions, reducing the required computing time from thousands of years to just hours and thus making $f_{NL}$ estimation feasible for future surveys. Our estimator in its current form is optimal if noise is homogeneous. In future work our fast polarized bispectrum estimator should be extended to deal with inhomogeneous noise in an analogous way to how the existing fast temperature estimator was generalized.

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arXiv2006

Pico: Parameters for the Impatient Cosmologist

We present a fast, accurate, robust and flexible method of accelerating parameter estimation. This algorithm, called Pico, can compute the CMB power spectrum and matter transfer function as well as any computationally expensive likelihoods in a few milliseconds. By removing these bottlenecks from parameter estimation codes, Pico decreases their computational time by 1 or 2 orders of magnitude. Pico has several important properties. First, it is extremely fast and accurate over a large volume of parameter space. Furthermore, its accuracy can continue to be improved by using a larger training set. This method is generalizable to an arbitrary number of cosmological parameters and to any range of l-values in multipole space. Pico is approximately 3000 times faster than CAMB for flat models, and approximately 2000 times faster then the WMAP 3 year likelihood code. In this paper, we demonstrate that using Pico to compute power spectra and likelihoods produces parameter posteriors that are very similar to those using CAMB and the official WMAP3 code, but in only a fraction of the time. Pico and an interface to CosmoMC are made publicly available at http://www.astro.uiuc.edu/~bwandelt/pico/.

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arXiv2006

Optimal Image Reconstruction in Radio Interferometry

We introduce a method for analyzing radio interferometry data which produces maps which are optimal in the Bayesian sense of maximum posterior probability density, given certain prior assumptions. It is similar to maximum entropy techniques, but with an exact accounting of the multiplicity instead of the usual approximation involving Stirling's formula. It also incorporates an Occam factor, automatically limiting the effective amount of detail in the map to that justified by the data. We use Gibbs sampling to determine, to any desired degree of accuracy, the multi-dimensional posterior density distribution. From this we can construct a mean posterior map and other measures of the posterior density, including confidence limits on any well-defined function of the posterior map.

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arXiv2005

A Beginner's Guide to the Theory of CMB Temperature and Polarization Power Spectra in the Line-of-Sight Formalism

We present here a detailed, self--contained treatment of the mathematical formalism for describing the theory of polarized anisotropy in the cosmic microwave background. This didactic review is aimed at researchers who are new to the field. We first develop the mathematical tools for describing polarized scattering of CMB photons. Then we take the reader through a detailed derivation of the line-of-sight formalism, explaining the calculation of both temperature and polarization power spectra due to the scalar and tensor perturbations in a flat Universe.

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arXiv2005

Measuring primordial non-Gaussianity in the cosmic microwave background

We derive a fast way for measuring primordial non-Gaussianity in a nearly full-sky map of the cosmic microwave background. We find a cubic combination of sky maps combining bispectrum configurations to capture a quadratic term in primordial fluctuations. Our method takes only N^1.5 operations rather than N^2.5 of the bispectrum analysis (1000 times faster for l=512), retaining the same sensitivity. A key component is a map of underlying primordial fluctuations, which can be more sensitive to the primordial non-Gaussianity than a temperature map. We also derive a fast and accurate statistic for measuring non-Gaussian signals from foreground point sources. The statistic is 10^6 times faster than the full bispectrum analysis, and can be used to estimate contamination from the sources. Our algorithm has been successfully applied to the Wilkinson Microwave Anisotropy Probe sky maps by Komatsu et al. (2003).

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arXiv2005

A Statistically Robust 3-Sigma Detection of Non-Gaussianity in the WMAP Data Using Hot and Cold Spots

We present a careful frequentist analysis of one- and two-point statistics of the hot and cold spots in the cosmic microwave background (CMB) data obtained by the Wilkinson Microwave Anisotropy Probe (WMAP). Our main result is the detection of a new anomaly at the 3-sigma level using temperature-weighted extrema correlation functions. We obtain this result using a simple hypothesis test which reduces the maximum risk of a false detection to the same level as the claimed significance of the test. We further present a detailed study of the robustness of our earlier claim (Larson and Wandelt 2004) under variations in the noise model and in the resolution of the map. Free software which implements our test is available online.

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arXiv2004

Precision Primordial $^4$He Measurement with CMB Experiments

Big bang nucleosynthesis (BBN) and the cosmic microwave background (CMB) are two major pillars of cosmology. Standard BBN accurately predicts the primordial light element abundances ($^4$He, D, $^3$He and $^7$Li), depending on one parameter, the baryon density. Light element observations are used as a baryometers. The CMB anisotropies also contain information about the content of the universe which allows an important consistency check on the Big Bang model. In addition CMB observations now have sufficient accuracy to not only determine the total baryon density, but also resolve its principal constituents, H and $^4$He. We present a global analysis of all recent CMB data, with special emphasis on the concordance with BBN theory and light element observations. We find $Ω_{B}h^{2}=0.025+0.0019-0.0026$ and $Y_{p}=0.250+0.010-0.014$ (fraction of baryon mass as $^4$He) using CMB data alone, in agreement with $^4$He abundance observations. With this concordance established we show that the inclusion of BBN theory priors significantly reduces the volume of parameter space. In this case, we find $Ω_{B}h^2=0.0244+0.00137-0.00284$ and $Y_p = 0.2493+0.0006-0.001$. We also find that the inclusion of deuterium abundance observations reduces the $Y_p$ and $Ω_{B}h^2$ ranges by a factor of $\sim $2. Further light element observations and CMB anisotropy experiments will refine this concordance and sharpen BBN and the CMB as tools for precision cosmology.

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arXiv2004

The Hot and Cold Spots in the WMAP Data are Not Hot and Cold Enough

This paper presents a frequentist analysis of the hot and cold spots of the cosmic microwave background data collected by the Wilkinson Microwave Anisotropy Probe (WMAP). We compare the WMAP temperature statistics of extrema (number of extrema, mean excursion, variance, skewness and kurtosis of the excursion) to Monte-Carlo simulations. We find that, on average, the local maxima (high temperatures in the anisotropy) are too cold and the local minima are too warm. In order to quantify this claim we describe a two-sided statistical hypothesis test which we advocate for other investigations of the Gaussianity hypothesis. Using this test we reject the isotropic Gaussian hypothesis at more than 99% confidence in a well-defined way. Our claims are based only on regions that are outside the most conservative WMAP foreground mask. We perform our test separately on maxima and minima, and on the north and south ecliptic and Galactic hemispheres and reject Gaussianity at above 95% confidence for almost all tests of the mean excursions. The same test also shows the variance of the maxima and minima to be low in the ecliptic north (99% confidence), but consistent in the south; this effect is not as pronounced in the Galactic north and south hemispheres.

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arXiv2004

Deconvolution Map-Making for Cosmic Microwave Background Observations

We describe a new map-making code for cosmic microwave background (CMB) observations. It implements fast algorithms for convolution and transpose convolution of two functions on the sphere (Wandelt & Górski 2001). Our code can account for arbitrary beam asymmetries and can be applied to any scanning strategy. We demonstrate the method using simulated time-ordered data for three beam models and two scanning patterns, including a coarsened version of the WMAP strategy. We quantitatively compare our results with a standard map-making method and demonstrate that the true sky is recovered with high accuracy using deconvolution map-making.

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arXiv2004

Interacting Quintessence, Cosmic Acceleration and the Coincidence Problem

Faced by recent evidence for a flat universe dominated by dark energy, cosmologists grapple with deep cosmic enigmas such as the cosmological constant problem, extreme fine-tuning and the cosmic coincidence problem. The extent to which we observe the dimming of distant supernovae suggests that the cosmic acceleration is as least as severe as in cosmological constant models. Extrapolating this to our cosmic future implies terrifying visions of either a cold and empty universe or an explosive demise in a ``Big Rip.'' We construct a class of dynamical scalar field models of dark energy and dark matter. Within this class we can explain why supernovae imply a cosmic equation of state $w\lesssim-1$, address fine tuning issues, protect the universe from premature acceleration and predict a constant fraction of dark energy to dark matter in the future (thus solving the coincidence problem), satisfy the dominant energy condition, and ensure that gravitationally bound objects remain so forever (avoid a Big Rip). This is achieved with a string theory inspired Lagrangian containing standard kinetic terms, exponential potentials and couplings, and parameters of order unity.

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arXiv2004

Statistical Challenges of Cosmic Microwave Background Analysis

The Cosmic Microwave Background (CMB) is an abundant source of cosmological information. However, this information is encoded in non-trivial ways in a signal that is difficult to observe. The resulting challenges in extracting this information from CMB data sets have created a new frontier. In this talk I will discuss the challenges of CMB data analysis. I review what cosmological information is contained in the CMB data and the problem of extracting it. CMB analyses can be divided into two types: ``canonical'' parameter extraction which seeks to obtain the best possible estimates of cosmological parameters within a pre-defined theory space and "hypothesis testing" which seeks to test the assumption on which the canonical tests rest. Both of these activities are fundamentally important. In addition to mining the CMB for cosmological information cosmologists would like to strengthen the analysis with data from other cosmologically interesting observations as well as physical constraints. This gives an opportunity 1) to test the results from these separate probes for concordance and 2) if concordance is established to sharpen the constraints on theory space by combining the information from these separate sources.

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arXiv2004

MAGIC: Exact Bayesian Covariance Estimation and Signal Reconstruction for Gaussian Random Fields

In this talk I describe MAGIC, an efficient approach to covariance estimation and signal reconstruction for Gaussian random fields (MAGIC Allows Global Inference of Covariance). It solves a long-standing problem in the field of cosmic microwave background (CMB) data analysis but is in fact a general technique that can be applied to noisy, contaminated and incomplete or censored measurements of either spatial or temporal Gaussian random fields. In this talk I will phrase the method in a way that emphasizes its general structure and applicability but I comment on applications in the CMB context. The method allows the exploration of the full non-Gaussian joint posterior density of the signal and parameters in the covariance matrix (such as the power spectrum) given the data. It generalizes the familiar Wiener filter in that it automatically discovers signal correlations in the data as long as a noise model is specified and priors encode what is known about potential contaminants. The key methodological difference is that instead of attempting to evaluate the likelihood (or posterior density) or its derivatives, this method generates an asymptotically exact Monte Carlo sample from it. I present example applications to power spectrum estimation and signal reconstruction from measurements of the CMB. For these applications the method achieves speed-ups of many orders of magnitude compared to likelihood maximization techniques, while offering greater flexibility in modeling and a full characterization of the uncertainty in the estimates.

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arXiv2003

The CMB Power Spectrum from the Background Emission Anisotropy Scanning Telescope (BEAST) Experiment

The Background Emission Anisotropy Scanning Telescope (BEAST) is a 2.2m off-axis telescope with an 8 element mixed Q (38-45GHz) and Ka (26-36GHz) band focal plane, designed for balloon borne and ground based studies of the Cosmic Microwave Background. Here we present the Cosmic Microwave Background (CMB) angular power spectrum calculated from 682 hours of data observed with the BEAST instrument. We use a binned pseudo-Cl estimator (the MASTER method). We find results that are consistent with other determinations of the CMB anisotropy for angular wavenumber l between 100 and 600. We also perform cosmological parameter estimation. The BEAST data alone produces a good constraint on Omega_k = 1-Omega_tot=-0.074 +/- 0.070, consistent with a flat Universe. A joint parameter estimation analysis with a number of previous CMB experiments produces results consistent with previous determinations.

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arXiv2003

Global, Exact Cosmic Microwave Background Data Analysis Using Gibbs Sampling

We describe an efficient and exact method that enables global Bayesian analysis of cosmic microwave background (CMB) data. The method reveals the joint posterior density (or likelihood for flat priors) of the power spectrum $C_\ell$ and the CMB signal. Foregrounds and instrumental parameters can be simultaneously inferred from the data. The method allows the specification of a wide range of foreground priors. We explicitly show how to propagate the non-Gaussian dependency structure of the $C_\ell$ posterior through to the posterior density of the parameters. If desired, the analysis can be coupled to theoretical (cosmological) priors and can yield the posterior density of cosmological parameter estimates directly from the time-ordered data. The method does not hinge on special assumptions about the survey geometry or noise properties, etc. It is based on a Monte Carlo approach and hence parallelizes trivially. No trace or determinant evaluations are necessary. The feasibility of this approach rests on the ability to solve the systems of linear equations which arise. These are of the same size and computational complexity as the map-making equations. We describe a pre-conditioned conjugate gradient technique that solves this problem and demonstrate in a numerical example that the computational time required for each Monte Carlo sample scales as $n_p^{3/2}$ with the number of pixels $n_p$. We test our method using the COBE-DMR data and explore the non-Gaussian joint posterior density of the COBE-DMR $C_\ell$ in several projections.

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