Inflationary B-mode Research Articles

Impact of Galactic dust non-Gaussianity on searches for B-modes from inflation

ABSTRACT A key challenge in the search for primordial B-modes is the presence of polarized Galactic foregrounds, especially thermal dust emission. Power-spectrum-based analysis methods generally assume the foregrounds to be Gaussian random fields when constructing a likelihood and computing the covariance matrix. In this paper, we investigate how non-Gaussianity in the dust field instead affects CMB and foreground parameter inference in the context of inflationary B-mode searches, capturing this effect via modifications to the dust power-spectrum covariance matrix. For upcoming experiments such as the Simons Observatory, we find no dependence of the tensor-to-scalar ratio uncertainty $\sigma (r)$ on the degree of dust non-Gaussianity or the nature of the dust covariance matrix. We provide an explanation of this result, noting that when frequency decorrelation is negligible, dust in mid-frequency channels is cleaned using high-frequency data in a way that is independent of the spatial statistics of dust. We show that our results hold also for non-zero levels of frequency decorrelation that are compatible with existing data. We find, however, that neglecting the impact of dust non-Gaussianity in the covariance matrix can lead to inaccuracies in goodness-of-fit metrics. Care must thus be taken when using such metrics to test B-mode spectra and models, although we show that any such problems can be mitigated by using only cleaned spectrum combinations when computing goodness-of-fit statistics.

New Probe of Inflationary Gravitational Waves: Cross-Correlations of Lensed Primary CMB B-Modes with Large-Scale Structure.

We propose a new probe of inflationary gravitational waves (IGWs): the cross-correlation of the lensing of inflationary B-mode polarization with a large-scale structure (LSS) tracer, which can also be a cosmic microwave background (CMB) lensing map. This is equivalent to measuring a three-point function of two CMB B-modes and an LSS tracer. We forecast expected 1σ constraints on the tensor-to-scalar ratio r, albeit with a simplistic foreground treatment, and find constraints of σ_{r}≃7×10^{-3} from the correlation of CMB-S4-Deep B-mode lensing and LSST galaxies, σ_{r}≃5×10^{-3} from the correlation of CMB-S4-Deep B-mode lensing and CMB-S4-Deep CMB lensing, and σ_{r}≃10^{-2} from the correlation of LiteBIRD B-mode lensing and CMB-S4-Wide lensing. Because this probe is inherently non-Gaussian, simple Gaussian foregrounds will not produce any biases to the measurement of r. While a detailed investigation of non-Gaussian foreground contamination for different cross-correlations will be essential, this observable has the potential to be a useful probe of IGWs, which, due to different sensitivity to many potential sources of systematic errors, can be complementary to standard methods for constraining r.

Cosmic birefringence tomography and calibration independence with reionization signals in the CMB

ABSTRACTThe search for cosmic polarization rotation or birefringence in the cosmic microwave background (CMB) is well motivated because it can provide powerful constraints on parity-violating new physics, such as axion-like particles. In this paper, we point out that since the CMB polarization is produced at two very different redshifts – it is generated at both reionization and recombination – new parity-violating physics can generically rotate the polarization signals from these different sources by different amounts. We explore two implications of this. First, measurements of CMB birefringence are challenging because the effect is degenerate with a miscalibration of CMB polarization angles; however, by taking the difference of the reionization and recombination birefringence angles (measured from different CMB angular scales), we can obtain a cosmological signal that is immune to instrumental angle miscalibration. Secondly, we note that the combination with other methods for probing birefringence can give tomographic information, constraining the redshift origin of any physics producing birefringence. We forecast that the difference of the reionization and recombination birefringence angles can be competitively determined to within ∼0.05 deg for future CMB satellites such as LiteBIRD. Although much further work is needed, we argue that foreground mitigation for this measurement should be less challenging than for inflationary B-mode searches on similar scales due to larger signals and lower foregrounds.

Mitigating Bias in CMB B-modes from Foreground Cleaning Using a Moment Expansion

One of the primary challenges facing upcoming cosmic microwave background (CMB) polarization experiments aiming to measure the inflationary B-mode signal is the removal of polarized foregrounds. The thermal dust foreground is often modeled as a single modified blackbody; however, overly simplistic foreground models can bias measurements of the tensor-to-scalar ratio r. As CMB polarization experiments become increasingly sensitive, thermal dust emission models must account for greater complexity in the dust foreground while making minimal assumptions about the underlying distribution of dust properties within a beam. We use Planck dust temperature data to estimate the typical variation in dust properties along the line of sight and examine the impact of these variations on the bias in r if a single modified blackbody model is assumed. We then assess the ability of the moment method to capture the effects of spatial averaging and to reduce bias in the tensor-to-scalar ratio for different possible toy models of dust emission. We find that the expected bias due to temperature variations along the line of sight is significant compared to the target sensitivities of future CMB experiments, and that the use of the moment method could reduce bias as well as shed light into the distribution of dust physical parameters.

Peeling off foregrounds with the constrained moment ILC method to unveil primordial CMB B modes

ABSTRACT Galactic foregrounds are the main obstacle to observations of the cosmic microwave background (CMB) B-mode polarization. In addition to obscuring the inflationary B-mode signal by several orders of magnitude, Galactic foregrounds have non-trivial spectral signatures that are partially unknown and distorted by averaging effects along the line of sight, within the pixel/beam window, and by various analysis choices (e.g. spherical harmonic transforms and filters). Statistical moment expansion methods provide a powerful tool for modelling the effective Galactic foreground emission resulting from these averaging effects in CMB observations, while blind component separation treatments can handle unknown foregrounds. In this work, we combine these two approaches to develop a new semiblind component separation method at the intersection of parametric and blind methods, called constrained moment ILC (cMILC). This method adds several constraints to the standard ILC method to deproject the main statistical moments of the Galactic foreground emission. Applications to maps are performed in needlet space and when compared to the NILC method, this helps in significantly reducing residual foreground contamination (bias, variance, and skewness) in the reconstructed CMB B-mode map, power spectrum, and tensor-to-scalar ratio. We consider sky simulations for experimental settings similar to those of LiteBIRD and PICO, illustrating which trade-offs between residual foreground biases and degradation of the constraint on r can be expected within the new cMILC framework. We also outline several directions that require more work in preparation for the coming analysis challenges.

Polarization of the Cosmic Infrared Background Fluctuations

Abstract The cosmic infrared background (CIB) is slightly polarized. Polarization directions of individual galaxies could be aligned with tidal fields around galaxies, resulting in nonzero CIB polarization. We use a linear intrinsic alignment model to theoretically predict angular correlations of the CIB polarization fluctuations and find that electriclike and curl-like (B-mode) polarization modes are equally generated with power four orders of magnitude less than their intensity. The CIB B-mode signal is negligible and not a concerning foreground for the inflationary B-mode searches at nominal frequencies for cosmic microwave background measurements, but could be detected at submillimeter wavelengths by future space missions.

Optical Design and Characterization of 40-GHz Detector and Module for the BICEP Array

Families of cosmic inflation models predict a primordial gravitational-wave background that imprints B-mode polarization pattern in the Cosmic Microwave Background (CMB). High sensitivity instruments with wide frequency coverage and well-controlled systematic errors are needed to constrain the faint B-mode amplitude. We have developed antenna-coupled Transition Edge Sensor (TES) arrays for high-sensitivity polarized CMB observations over a wide range of millimeter-wave bands. BICEP Array, the latest phase of the BICEP/Keck experiment series, is a multi-receiver experiment designed to search for inflationary B-mode polarization to a precision $\sigma$(r) between 0.002 and 0.004 after 3 full years of observations, depending on foreground complexity and the degree of lensing removal. We describe the electromagnetic design and measured performance of BICEP Array low-frequency 40-GHz detector, their packaging in focal plane modules, and optical characterization including efficiency and beam matching between polarization pairs. We summarize the design and simulated optical performance, including an approach to improve the optical efficiency due to mismatch losses. We report the measured beam maps for a new broad-band corrugation design to minimize beam differential ellipticity between polarization pairs caused by interactions with the module housing frame, which helps minimize polarized beam mismatch that converts CMB temperature to polarization ($T \rightarrow P$) anisotropy in CMB maps.

Pixel space convolution for cosmic microwave background experiments

Cosmic microwave background experiments have experienced an exponential increase in complexity, data size and sensitivity. One of the goals of current and future experiments is to characterize the B-mode power spectrum, which would be considered a strong evidence supporting inflation. The signal associated with inflationary B-modes is very weak, and so a successful detection requires exquisite control over systematic effects, several of which might arise due to the interaction between the electromagnetic properties of the telescope beam, the scanning strategy and the sky model. In this work, we present the Pixel Space COnvolver (PISCO), a new software tool capable of producing mock data streams for a general CMB experiment. PISCO uses a fully polarized representation of the electromagnetic properties of the telescope. PISCO also exploits the massively parallel architecture of Graphic Processing Units to speed-up the main calculation. This work shows the results of applying PISCO in several scenarios, included a realistic simulation of an ongoing experiment, the Cosmology Large Angular Scale Surveyor.

Detection and removal of B-mode dust foregrounds with signatures of statistical anisotropy

Searches for inflationary gravitational wave signals in the CMB B-mode polarisation are expected to reach unprecedented power over the next decade. A major difficulty in these ongoing searches is that galactic foregrounds such as dust can easily mimic inflationary signals. Though typically foregrounds are separated from primordial signals using the foregrounds' different frequency dependence, in this paper we investigate instead the extent to which the galactic dust B-modes' statistical anisotropy can be used to distinguish them from inflationary B-modes, building on the work of Kamionkowski and Kovetz (2014). In our work, we extend existing anisotropy estimators and apply them to simulations of polarised dust to forecast their performance for future experiments. Considering the application of this method as a null-test for dust contamination to CMB-S4, we find that we can detect residual dust levels corresponding to $r\sim0.001$ at $2\sigma$, which implies that statistical anisotropy estimators will be a powerful diagnostic for foreground residuals (though our results show some dependence on the dust simulation used). Finally, considering applications beyond a simple null test, we demonstrate how anisotropy statistics can be used to construct an estimate of the dust B-mode map, which could potentially be used to clean the B-mode sky.

Polarized beam patterns from a multimoded feed for observations of the cosmic microwave background

We measure linearly polarized beam patterns for a multi-moded concentrator and compare the results to a simple model based on geometric optics. We convolve the measured co-polar and cross-polar beams with simulated maps of CMB polarization to estimate the amplitude of the systematic error resulting from the cross-polar beam response. The un-corrected error signal has typical amplitude of 3 nK, corresponding to inflationary B-mode amplitude r ~ 10^{-3}. Convolving the measured cross-polar beam pattern with maps of the CMB E-mode polarization provides a template for correcting the cross-polar response, reducing it to negligible levels.

Demonstration of Cosmic Microwave Background Delensing Using the Cosmic Infrared Background.

Delensing is an increasingly important technique to reverse the gravitational lensing of the cosmic microwave background (CMB) and thus reveal primordial signals the lensing may obscure. We present a first demonstration of delensing on Planck temperature maps using the cosmic infrared background (CIB). Reversing the lensing deflections in Planck CMB temperature maps using a linear combination of the 545 and 857GHz maps as a lensing tracer, we find that the lensing effects in the temperature power spectrum are reduced in a manner consistent with theoretical expectations. In particular, the characteristic sharpening of the acoustic peaks of the temperature power spectrum resulting from successful delensing is detected at a significance of 16σ, with an amplitude of A_{delens}=1.12±0.07 relative to the expected value of unity. This first demonstration on data of CIB delensing, and of delensing techniques in general, is significant because lensing removal will soon be essential for achieving high-precision constraints on inflationary B-mode polarization.

FOREGROUND BIAS FROM PARAMETRIC MODELS OF FAR-IR DUST EMISSION

ABSTRACT We use simple toy models of far-IR dust emission to estimate the accuracy to which the polarization of the cosmic microwave background can be recovered using multi-frequency fits, if the parametric form chosen for the fitted dust model differs from the actual dust emission. Commonly used approximations to the far-IR dust spectrum yield CMB residuals comparable to or larger than the sensitivities expected for the next generation of CMB missions, despite fitting the combined CMB + foreground emission to precision 0.1% or better. The Rayleigh–Jeans approximation to the dust spectrum biases the fitted dust spectral index by and the inflationary B-mode amplitude by . Fitting the dust to a modified blackbody at a single temperature biases the best-fit CMB by if the true dust spectrum contains multiple temperature components. A 13-parameter model fitting two temperature components reduces this bias by an order of magnitude if the true dust spectrum is in fact a simple superposition of emission at different temperatures, but fails at the level for dust whose spectral index varies with frequency. Restricting the observing frequencies to a narrow region near the foreground minimum reduces these biases for some dust spectra but can increase the bias for others. Data at THz frequencies surrounding the peak of the dust emission can mitigate these biases while providing a direct determination of the dust temperature profile.

LiteBIRD: Mission Overview and Focal Plane Layout

LiteBIRD is a proposed CMB polarization satellite project to probe the inflationary B-mode signal. The satellite is designed to measure the tensor-to-scalar ratio with a 68 % confidence level uncertainty of $$\sigma _\mathrm{r}<10^{-3}$$ , including statistical, instrumental systematic, and foreground uncertainties. LiteBIRD will observe the full sky from the second Lagrange point for 3 years. We have a focal plane layout for observing frequency coverage that spans 40–402 GHz to characterize the galactic foregrounds. We have two detector candidates, transition-edge sensor bolometers and microwave kinetic inductance detectors. In both cases, a telecentric focal plane consists of approximately $$2\times 10^3$$ superconducting detectors. We will present the mission overview of LiteBIRD, the project status, and the TES focal plane layout.

Did BICEP2 see vector modes? First B-mode constraints on cosmic defects.

Scaling networks of cosmic defects, such as strings and textures, actively generate scalar, vector, and tensor metric perturbations throughout the history of the Universe. In particular, vector modes sourced by defects are an efficient source of the cosmic microwave background B-mode polarization. We use the recently released BICEP2 and POLARBEAR B-mode polarization spectra to constrain properties of a wide range of different types of cosmic strings networks. We find that in order for strings to provide a satisfactory fit on their own, the effective interstring distance needs to be extremely large--spectra that fit the data best are more representative of global strings and textures. When a local string contribution is considered together with the inflationary B-mode spectrum, the fit is improved. We discuss implications of these results for theories that predict cosmic defects.

DEGREE-SCALE COSMIC MICROWAVE BACKGROUND POLARIZATION MEASUREMENTS FROM THREE YEARS OF BICEP1 DATA

BICEP1 is a millimeter-wavelength telescope designed specifically to measure the inflationary B-mode polarization of the Cosmic Microwave Background (CMB) at degree angular scales. We present results from an analysis of the data acquired during three seasons of observations at the South Pole (2006 to 2008). This work extends the two-year result published in Chiang et al. (2010), with additional data from the third season and relaxed detector-selection criteria. This analysis also introduces a more comprehensive estimation of band-power window functions, improved likelihood estimation methods and a new technique for deprojecting monopole temperature-to-polarization leakage which reduces this class of systematic uncertainty to a negligible level. We present maps of temperature, E- and B-mode polarization, and their associated angular power spectra. The improvement in the map noise level and polarization spectra error bars are consistent with the 52% increase in integration time relative to Chiang et al. (2010). We confirm both self-consistency of the polarization data and consistency with the two-year results. We measure the angular power spectra at 21 <= l <= 335 and find that the EE spectrum is consistent with Lambda Cold Dark Matter (LCDM) cosmology, with the first acoustic peak of the EE spectrum now detected at 15sigma. The BB spectrum remains consistent with zero. From B-modes only, we constrain the tensor-to-scalar ratio to r = 0.03+0.27-0.23, or r < 0.70 at 95% confidence level.

The South Pole Telescope: Latest Results and Future Prospects

AbstractThe South Pole Telescope is a 10 meter telescope optimized for sensitive, high-resolution measurements of the cosmic microwave background (CMB) anisotropy and millimeter-wavelength sky. In November 2011, the SPT completed the 2500 deg2 SPT-SZ survey. The survey has led to several major cosmological results, derived from measurements of the fine angular scale primary and secondary CMB anisotropies, the discovery of galaxy clusters via the Sunyaev-Zel'dovich (SZ) effect and the resulting mass-limited cluster catalog, and the discovery of a population of distant, dusty star forming galaxies (DSFGs). In January 2012, the SPT was equipped with a new polarization sensitive camera, SPTpol, which will enable detection of the contribution to the CMB polarization power spectrum from lensing by large scale structure (the so-called “lensing B-modes”) and, on larger angular scales, a detection or improved upper limit on the primordial inflationary signal (“gravitational-wave B-modes”), thereby constraining the energy scale of Inflation. Development is underway for SPT-3G, the third-generation camera for SPT. The SPT-3G survey will cross the threshold from statistical detection of B-mode CMB lensing to imaging the fluctuations at high signal-to-noise; enabling the separation of lensing and inflationary B-modes and improving the constraint on the sum of the neutrino masses Σmν to a level relevant for exploring the neutrino mass hierarchy.

Three-point statistics of cosmological stochastic gravitational waves

We consider the 3-pt function (i.e. the bispectrum or non-Gaussianity) for stochastic backgrounds of gravitational waves. We estimate the amplitude of this signal for the primordial inflationary background, gravitational waves generated during preheating, and for gravitational waves produced by self-ordering scalar fields following a global phase transition. To assess detectability, we describe how to extract the 3-pt signal from an idealized interferometric experiment and compute the signal to noise ratio as a function of integration time. The 3-pt signal for the stochastic gravitational wave background generated by inflation is unsurprisingly tiny. For gravitational radiation generated by purely causal, classical mechanisms we find that, no matter how non-linear the process is, the 3-pt correlations produced vanish in direct detection experiments. On the other hand, we show that in scenarios where the B-mode of the CMB is sourced by gravitational waves generated by a global phase transition, a strong 3-pt signal among the polarization modes could also be produced. This may provide another method of distinguishing inflationary B-modes. To carry out this computation, we have developed a diagrammatic approach to the calculation of stochastic gravitational waves sourced by scalar fluids, which has applications beyond the present scenario.

MEASUREMENT OF COSMIC MICROWAVE BACKGROUND POLARIZATION POWER SPECTRA FROM TWO YEARS OF BICEP DATA

Background Imaging of Cosmic Extragalactic Polarization (BICEP) is a bolometric polarimeter designed to measure the inflationary B-mode polarization of the cosmic microwave background (CMB) at degree angular scales. During three seasons of observing at the South Pole (2006 through 2008), BICEP mapped ~2% of the sky chosen to be uniquely clean of polarized foreground emission. Here we present initial results derived from a subset of the data acquired during the first two years. We present maps of temperature, Stokes Q and U, E and B modes, and associated angular power spectra. We demonstrate that the polarization data are self-consistent by performing a series of jackknife tests. We study potential systematic errors in detail and show that they are sub-dominant to the statistical errors. We measure the E-mode angular power spectrum with high precision at 21 < ell < 335, detecting for the first time the peak expected at ell ~ 140. The measured E-mode spectrum is consistent with expectations from a LCDM model, and the B-mode spectrum is consistent with zero. The tensor-to-scalar ratio derived from the B-mode spectrum is r = 0.03+0.31-0.26, or r < 0.72 at 95% confidence, the first meaningful constraint on the inflationary gravitational wave background to come directly from CMB B-mode polarization.

CHARACTERIZATION OF THE BICEP TELESCOPE FOR HIGH-PRECISION COSMIC MICROWAVE BACKGROUND POLARIMETRY

The BICEP experiment was designed specifically to search for the signature of inflationary gravitational waves in the polarization of the cosmic microwave background (CMB). Using a novel small-aperture refractor and 49 pairs of polarization-sensitive bolometers, BICEP has completed 3 years of successful observations at the South Pole beginning in 2006 February. To constrain the amplitude of the inflationary B-mode polarization, which is expected to be at least 7 orders of magnitude fainter than the 3 K CMB intensity, precise control of systematic effects is essential. This paper describes the characterization of potential systematic errors for the BICEP experiment, supplementing a companion paper on the initial cosmological results. Using the analysis pipelines for the experiment, we have simulated the impact of systematic errors on the B-mode polarization measurement. Guided by these simulations, we have established benchmarks for the characterization of critical instrumental properties including bolometer relative gains, beam mismatch, polarization orientation, telescope pointing, sidelobes, thermal stability, and timestream noise model. A comparison of the benchmarks with the measured values shows that we have characterized the instrument adequately to ensure that systematic errors do not limit BICEP's 2-year results, and identifies which future refinements are likely necessary to probe inflationary B-mode polarization down to levels below a tensor-to-scalar ratio r = 0.1.