arXiv subjects

Emory F. Bunn

Publications and source records attributed to Emory F. Bunn.

At least 37 records · Page 2Linked to original sources

arXiv2013

Systematic Effects in Interferometric Observations of the CMB Polarization

The detection of the primordial $B$-mode spectrum of the polarized cosmic microwave background (CMB) signal may provide a probe of inflation. However, observation of such a faint signal requires excellent control of systematic errors. Interferometry proves to be a promising approach for overcoming such a challenge. In this paper we present a complete simulation pipeline of interferometric observations of CMB polarization, including systematic errors. We employ two different methods for obtaining the power spectra from mock data produced by simulated observations: the maximum likelihood method and the method of Gibbs sampling. We show that the results from both methods are consistent with each other, as well as, within a factor of 6, with analytical estimates. Several categories of systematic errors are considered: instrumental errors, consisting of antenna gain and antenna coupling errors, and beam errors, consisting of antenna pointing errors, beam cross-polarization and beam shape (and size) errors. In order to recover the tensor-to-scalar ratio, $r$, within a 10% tolerance level, which ensures the experiment is sensitive enough to detect the $B$-signal at $r=0.01$ in the multipole range $28 < \ell < 384$, we find that, for a QUBIC-like experiment, Gaussian-distributed systematic errors must be controlled with precisions of $|g_{rms}| = 0.1$ for antenna gain, $|ε_{rms}| = 5 \times 10^{-4}$ for antenna coupling, $δ_{rms} \approx 0.7^\circ$ for pointing, $ζ_{rms} \approx 0.7^\circ$ for beam shape, and $μ_{rms} = 5 \times 10^{-4}$ for beam cross-polarization.

astro-ph.CO↗

arXiv2013

Bayesian Inference of Polarized CMB Power Spectra from Interferometric Data

Detection of B-mode polarization of the cosmic microwave background (CMB) radiation is one of the frontiers of observational cosmology. Because they are an order of magnitude fainter than E-modes, it is quite a challenge to detect B-modes. Having more manageable systematics, interferometers prove to have a substantial advantage over imagers in detecting such faint signals. Here, we present a method for Bayesian inference of power spectra and signal reconstruction from interferometric data of the CMB polarization signal by using the technique of Gibbs sampling. We demonstrate the validity of the method in the flat-sky approximation for a simulation of an interferometric observation on a finite patch with incomplete uv-plane coverage, a finite beam size and a realistic noise model. With a computational complexity of O(n^{3/2}), n being the data size, Gibbs sampling provides an efficient method for analyzing upcoming cosmology observations.

astro-ph.CO↗

arXiv2011

Efficient decomposition of cosmic microwave background polarization maps into pure E, pure B, and ambiguous components

Separation of the B component of a cosmic microwave background (CMB) polarization map from the much larger E component is an essential step in CMB polarimetry. For a map with incomplete sky coverage, this separation is necessarily hampered by the presence of "ambiguous" modes which could be either E or B modes. I present an efficient pixel-space algorithm for removing the ambiguous modes and separating the map into "pure" E and B components. The method, which works for arbitrary geometries, does not involve generating a complete basis of such modes and scales the cube of the number of pixels on the boundary of the map.

astro-ph.CO↗

arXiv2010

Cosmic microwave background constraints on cosmological models with large-scale isotropy breaking

Several anomalies appear to be present in the large-angle cosmic microwave background (CMB) anisotropy maps of WMAP, including the alignment of large-scale multipoles. Models in which isotropy is spontaneously broken (e.g., by a scalar field) have been proposed as explanations for these anomalies, as have models in which a preferred direction is imposed during inflation. We examine models inspired by these, in which isotropy is broken by a multiplicative factor with dipole and/or quadrupole terms. We evaluate the evidence provided by the multipole alignment using a Bayesian framework, finding that the evidence in favor of the model is generally weak. We also compute approximate changes in estimated cosmological parameters in the broken-isotropy models. Only the overall normalization of the power spectrum is modified significantly.

astro-ph.CO↗

arXiv2010

Large-Angle Anomalies in the Microwave Background

Several claims have been made of anomalies in the large-angle properties of the cosmic microwave background anisotropy as measured by WMAP. In most cases, the statistical significance of these anomalies is hard or even impossible to assess, due to the fact that the statistics used to quantify the anomalies were chosen a posteriori. On the other hand, the possibility of detecting new physics on the largest observable scales is so exciting that, in my opinion, it is worthwhile to examine the claims carefully. I will focus on three particular claims: the lack of large-angle power, the north-south power asymmetry, and multipole alignments. In all cases, the problem of a posteriori statistics can best be solved by finding a new data set that probes similar physical scales to the large-angle CMB. This is a difficult task, but there are some possible routes to achieving it.

astro-ph.CO↗

arXiv2009

The kinematic origin of the cosmological redshift

A common belief about big-bang cosmology is that the cosmological redshift cannot be properly viewed as a Doppler shift (that is, as evidence for a recession velocity), but must be viewed in terms of the stretching of space. We argue that, contrary to this view, the most natural interpretation of the redshift is as a Doppler shift, or rather as the accumulation of many infinitesimal Doppler shifts. The stretching-of-space interpretation obscures a central idea of relativity, namely that it is always valid to choose a coordinate system that is locally Minkowskian. We show that an observed frequency shift in any spacetime can be interpreted either as a kinematic (Doppler) shift or a gravitational shift by imagining a suitable family of observers along the photon's path. In the context of the expanding universe the kinematic interpretation corresponds to a family of comoving observers and hence is more natural.

physics.pop-ph↗

arXiv2009

Evolution and the second law of thermodynamics

Skeptics of biological evolution often claim that evolution requires a decrease in entropy, giving rise to a conflict with the second law of thermodynamics. This argument is fallacious because it neglects the large increase in entropy provided by sunlight striking the Earth. A recent article provided a quantitative assessment of the entropies involved and showed explicitly that there is no conflict. That article rests on an unjustified assumption about the amount of entropy reduction involved in evolution. I present a refinement of the argument that does not rely on this assumption.

physics.pop-ph↗

arXiv2008

E/B mode mixing

In future microwave background polarization experiments, particularly those that aim to characterize the B component, careful attention will have to be paid to the mixing of E and B components due to finite sky coverage and pixelization. Any polarization map can be decomposed into "pure E," "pure B," and "ambiguous" components. In practice, since the B component is expected to be much weaker than the E component, nearly all of the recoverable $B$ information is contained in the pure B component. The amount of B information lost to ambiguous modes can be estimated in simple ways from the survey geometry and pixelization. Separation of any given map into pure and ambiguous components can be done by finding a basis of pure and ambiguous modes, but it is often more efficient to "purify" the map directly in real space by solving a certain differential equation to find the ambiguous component. This method may be useful in conjunction with power spectrum estimation techniques such as the pseudo-Cl method.

astro-ph↗

arXiv2008

Phase Shift Sequences for an Adding Interferometer

Cosmic microwave background (CMB) polarimetry has the potential to provide revolutionary advances in cosmology. Future experiments to detect the very weak B mode signal in CMB polarization maps will require unprecedented sensitivity and control of systematic errors. Bolometric interferometry may provide a way to achieve these goals. In a bolometric interferometer (or other adding interferometer), phase shift sequences are applied to the inputs in order to recover the visibilities. Noise is minimized when the phase shift sequences corresponding to all visibilities are orthogonal. We present a systematic method for finding sequences that produce this orthogonality, approximately minimizing both the length of the time sequence and the number of discrete phase shift values required. When some baselines are geometrically equivalent, we can choose sequences that read out those baselines simultaneously, which has been shown to improve signal to noise ratio.

astro-ph↗

arXiv2008

Contamination cannot explain the lack of large-scale power in the cosmic microwave background radiation

Several anomalies appear to be present in the large-angle cosmic microwave background (CMB) anisotropy maps of WMAP. One of these is a lack of large-scale power. Because the data otherwise match standard models extremely well, it is natural to consider perturbations of the standard model as possible explanations. We show that, as long as the source of the perturbation is statistically independent of the source of the primary CMB anisotropy, no such model can explain this large-scale power deficit. On the contrary, any such perturbation always reduces the probability of obtaining any given low value of large-scale power. We rigorously prove this result when the lack of large-scale power is quantified with a quadratic statistic, such as the quadrupole moment. When a statistic based on the integrated square of the correlation function is used instead, we present strong numerical evidence in support of the result. The result applies to models in which the geometry of spacetime is perturbed (e.g., an ellipsoidal Universe) as well as explanations involving local contaminants, undiagnosed foregrounds, or systematic errors. Because the large-scale power deficit is arguably the most significant of the observed anomalies, explanations that worsen this discrepancy should be regarded with great skepticism, even if they help in explaining other anomalies such as multipole alignments.

astro-ph↗

arXiv2007

Directionality in the WMAP Polarization Data

Polarization is the next frontier of CMB analysis, but its signal is dominated over much of the sky by foregrounds which must be carefully removed. To determine the efficacy of this cleaning it is necessary to have sensitive tests for residual foreground contamination in polarization sky maps. The dominant Galactic foregrounds introduce a large-scale anisotropy on to the sky, so it makes sense to use a statistic sensitive to overall directionality for this purpose. Here we adapt the rapidly computable D statistic of Bunn and Scott to polarization data, and demonstrate its utility as a foreground monitor by applying it to the low resolution WMAP 3-yr sky maps. With a thorough simulation of the maps' noise properties, we find no evidence for contamination in the foreground cleaned sky maps.

astro-ph↗

arXiv2006

Constraining f(R) Gravity as a Scalar Tensor Theory

We search for viable f(R) theories of gravity, making use of the equivalence between such theories and scalar-tensor gravity. We find that models can be made consistent with solar system constraints either by giving the scalar a high mass or by exploiting the so-called chameleon effect. However, in both cases, it appears likely that any late-time cosmic acceleration will be observationally indistinguishable from acceleration caused by a cosmological constant. We also explore further observational constraints from, e.g., big bang nucleosynthesis and inflation.

astro-ph↗

arXiv2006

Systematic Errors in Cosmic Microwave Background Interferometry

Cosmic microwave background (CMB) polarization observations will require superb control of systematic errors in order to achieve their full scientific potential, particularly in the case of attempts to detect the B modes that may provide a window on inflation. Interferometry may be a promising way to achieve these goals. This paper presents a formalism for characterizing the effects of a variety of systematic errors on interferometric CMB polarization observations, with particular emphasis on estimates of the B-mode power spectrum. The most severe errors are those that couple the temperature anisotropy signal to polarization; such errors include cross-talk within detectors, misalignment of polarizers, and cross-polarization. In a B mode experiment, the next most serious category of errors are those that mix E and B modes, such as gain fluctuations, pointing errors, and beam shape errors. The paper also indicates which sources of error may cause circular polarization (e.g., from foregrounds) to contaminate the cosmologically interesting linear polarization channels, and conversely whether monitoring of the circular polarization channels may yield useful information about the errors themselves. For all the sources of error considered, estimates of the level of control that will be required for both E and B mode experiments are provided. Both experiments that interfere linear polarizations and those that interfere circular polarizations are considered. The fact that circular experiments simultaneously measure both linear polarization Stokes parameters in each baseline mitigates some sources of error.

astro-ph↗

arXiv2006

Mosaicking with cosmic microwave background interferometers

Measurements of cosmic microwave background (CMB) anisotropies by interferometers offer several advantages over single-dish observations. The formalism for analyzing interferometer CMB data is well developed in the flat-sky approximation, valid for small fields of view. As the area of sky is increased to obtain finer spectral resolution, this approximation needs to be relaxed. We extend the formalism for CMB interferometry, including both temperature and polarization, to mosaics of observations covering arbitrarily large areas of the sky, with each individual pointing lying within the flat-sky approximation. We present a method for computing the correlation between visibilities with arbitrary pointing centers and baselines and illustrate the effects of sky curvature on the l-space resolution that can be obtained from a mosaic.

astro-ph↗

arXiv2006

Probing the Universe on Gigaparsec Scales with Remote Cosmic Microwave Background Quadrupole Measurements

Scattering of cosmic microwave background (CMB) radiation in galaxy clusters induces a polarization signal proportional to the CMB quadrupole anisotropy at the cluster's location and look-back time. A survey of such remote quadrupole measurements provides information about large-scale cosmological perturbations. This paper presents a formalism for calculating the correlation function of remote quadrupole measurements in spherical harmonic space. The number of independent modes probed by both single-redshift and volume-limited surveys is presented, along with the length scales probed by these modes. In a remote quadrupole survey sparsely covering a large area of sky, the largest-scale modes probe the same length scales as the quadrupole but with much narrower Fourier-space window functions. The largest-scale modes are significantly correlated with the local CMB, but even when this correlation is projected out the largest remaining modes probe gigaparsec scales (comparable to the CMB at l=2-10) with narrow window functions. These modes may provide insight into the possible anomalies in the large-scale CMB anisotropy. At fixed redshift, the data from such a survey form an E-type spin-2 field on the sphere to a good approximation; the near-absence of B modes will provide a valuable check on systematic errors. A survey of only a few low-redshift clusters allows an independent reconstruction of the five coefficients of the local CMB quadrupole, providing a test for contamination in the WMAP quadrupole. The formalism presented here is also useful for analyzing smaller-scale surveys to probe the late integrated Sachs-Wolfe effect and hence the properties of dark energy

astro-ph↗

arXiv2003

Separating E from B

In a microwave background polarization map that covers only part of the sky, it is impossible to separate the E and B components perfectly. This difficulty in general makes it more difficult to detect the B component in a data set. Any polarization map can be separated in a unique way into "pure E," "pure B," and "ambiguous" components. Power that resides in the pure E (B) component is guaranteed to be produced by E (B) modes, but there is no way to tell whether the ambiguous component comes from E or B modes. A polarization map can be separated into the three components either by finding an orthonormal basis for each component, or directly in real space by using Green functions or other methods.

astro-ph↗

arXiv2002

Detectability of Microwave Background Polarization

[NOTE: Previous versions of this paper (both on astro-ph and published in Phys. Rev. D) contain results that are in error. The power spectra C_l were normalized incorrectly by a factor of 2 pi. All observing times in detector-years in those versions are too large by a factor of 2 pi. The main place these numbers appear is on the vertical axes of Figures 4 and 5. Note that because all calculations were based on the same power spectra, all conclusions pertaining to comparisons of different techniques remain unchanged. This error has been corrected in the present version of the paper. An erratum is being sent to Phys. Rev. D. I apologize for the error.] Using a Fisher-matrix formalism, we calculate the required sensitivities and observing times for an experiment to measure the amplitudes of both E and B components as a function of sky coverage, taking full account of the fact that the two components cannot be perfectly separated in an incomplete sky map. We also present a simple approximation scheme that accounts for mixing of E and B components in computing predicted errors in the E-component power spectrum amplitude. In an experiment with small sky coverage, mixing of the two components increases the difficulty of detecting the subdominant B component by a factor of two or more in observing time; however, for larger survey sizes the effect of mixing is less pronounced. Surprisingly, mixing of E and B components can enhance the detectability of the E component by increasing the effective number of independent modes that probe this component

astro-ph↗

arXiv2002

E/B decomposition of finite pixelized CMB maps

Separation of the E and B components of a microwave background polarization map or a weak lensing map is an essential step in extracting science from it, but when the map covers only part of the sky and/or is pixelized, this decomposition cannot be done perfectly. We present a method for decomposing an arbitrary sky map into a sum of three orthogonal components that we term ``pure E'', ``pure B'' and ``ambiguous''. This method is useful both for providing intuition for experimental design and for analyzing data sets in practice. We show how to find orthonormal bases for all three components in terms of bilaplacian eigenfunctions. The number of ambiguous modes is proportional to the length of the map boundary so fairly round maps are preferred. For real-world data analysis, we present a simple matrix eigenvalue method for calculating nearly pure E and B modes in pixelized maps. We find that the dominant source of leakage between E and B is aliasing of small-scale power caused by the pixelization. This problem can be eliminated by heavily oversampling the map, but is exacerbated by the fact that the E power spectrum is expected to be much larger than the B power spectrum and extremely blue. We found that a factor of 2 to 3 more pixels are needed in a polarization map to achieve the same level of contamination by aliased power than in a temperature map.

astro-ph↗