The effect of systematics on polarized spectral indices

We study four particularly bright polarized compact objects (Tau A, Virgo A, 3C273 and Fornax A) in the 7-year WMAP sky maps, with the goal of understanding potential systematics involved in estimation of foreground spectral indices. We estimate the spectral index, the polarization angle, the polarization fraction and apparent size and shape of these objects when smoothed to a nominal resolution of 1 degree FWHM. Second, we compute the spectral index as a function of polarization orientation, alpha. Because these objects are approximately point sources with constant polarization angle, this function should be constant in the absence of systematics. However, computing it for the K- and Ka-band WMAP data we find strong index variations for all four sources. For Tau A, we find a spectral index beta=-2.59+-0.03 for alpha=30 degrees, and beta=-2.03+-0.01 for alpha=50 degrees. On the other hand, the spectral index between Ka and Q band is found to be stable. A simple elliptical Gaussian toy model with parameters matching those observed in Tau A reproduces the observed signal, and shows that the spectral index is in particular sensitive to the detector polarization angle. Based on these findings, we first conclude that estimation of spectral indices with the WMAP K-band polarization data at 1 degree scales is not robust. Second, we note that these issues may be of concern for ground-based and sub-orbital experiments that use the WMAP polarization measurements of Tau A for calibration of gain and polarization angles.Comment: 5 pages, 6 figures, submitted to ApJ; new figure and expanded conclusio

Measuring primordial gravitational waves from CMB B-modes in cosmologies with generalized expansion histories

We evaluate our capability to constrain the abundance of primordial tensor perturbations in cosmologies with generalized expansion histories in the epoch of cosmic acceleration. Forthcoming satellite and sub-orbital experiments probing polarization in the CMB are expected to measure the B-mode power in CMB polarization, coming from PGWs on the degree scale, as well as gravitational lensing on arcmin scales; the latter is the main competitor for the measurement of PGWs, and is directly affected by the underlying expansion history, determined by the presence of a DE component. In particular, we consider early DE possible scenarios, in which the expansion history is substantially modified at the epoch in which the CMB lensing is most relevant. We show that the introduction of a parametrized DE may induce a variation as large as 30% in the ratio of the power of lensing and PGWs on the degree scale. We find that adopting the nominal specifications of upcoming satellite measurements the constraining power on PGWs is weakened by the inclusion of the extra degrees of freedom, resulting in a reduction of about 10% of the upper limits on r in fiducial models with no GWs, as well as a comparable increase in the error bars in models with non-zero r. Moreover, we find that the inclusion of sub-orbital CMB experiments, capable of mapping the B-mode power up to the angular scales affected by lensing, can restore the forecasted performances with a cosmological constant. Finally, we show how the combination of CMB data with Type Ia SNe, BAO and Hubble constant allows to constrain simultaneously r and the DE quantities in the parametrization we consider, consisting of present abundance and first redshift derivative of the energy density. We compare this study with results obtained using the forecasted lensing potential measurement precision from CMB satellite observations, finding consistent results.Comment: 17 pages, 9 figures, accepted for publication by JCAP. Modified version after the referee's comment

Estimating the tensor-to-scalar ratio and the effect of residual foreground contamination

We consider future balloon-borne and ground-based suborbital experiments designed to search for inflationary gravitational waves, and investigate the impact of residual foregrounds that remain in the estimated cosmic microwave background maps. This is achieved by propagating foreground modelling uncertainties from the component separation, under the assumption of a spatially uniform foreground frequency scaling, through to the power spectrum estimates, and up to measurement of the tensor to scalar ratio in the parameter estimation step. We characterize the error covariance due to subtracted foregrounds, and find it to be subdominant compared to instrumental noise and sample variance in our simulated data analysis. We model the unsubtracted residual foreground contribution using a two-parameter power law and show that marginalization over these foreground parameters is effective in accounting for a bias due to excess foreground power at low $\ell$. We conclude that, at least in the suborbital experimental setups we have simulated, foreground errors may be modeled and propagated up to parameter estimation with only a slight degradation of the target sensitivity of these experiments derived neglecting the presence of the foregrounds.Comment: 19 pages, 12 figures, accepted for publication in JCA

Single-field inflation constraints from CMB and SDSS data

We present constraints on canonical single-field inflation derived from WMAP five year, ACBAR, QUAD, BICEP data combined with the halo power spectrum from SDSS LRG7. Models with a non-scale-invariant spectrum and a red tilt n_s < 1 are now preferred over the Harrison-Zel'dovich model (n_s = 1, tensor-to-scalar ratio r = 0) at high significance. Assuming no running of the spectral indices, we derive constraints on the parameters (n_s, r) and compare our results with the predictions of simple inflationary models. The marginalised credible intervals read n_s = 0.962^{+0.028}_{-0.026} and r < 0.17 (at 95% confidence level). Interestingly, the 68% c.l. contours favour mainly models with a convex potential in the observable region, but the quadratic potential model remains inside the 95% c.l. contours. We demonstrate that these results are robust to changes in the datasets considered and in the theoretical assumptions made. We then consider a non-vanishing running of the spectral indices by employing different methods, non-parametric but approximate, or parametric but exact. With our combination of CMB and LSS data, running models are preferred over power-law models only by a Delta chi^2 ~ 5.8, allowing inflationary stages producing a sizable negative running -0.063^{+0.061}_{-0.049} and larger tensor-scalar ratio r < 0.33 at the 95% c.l. This requires large values of the third derivative of the inflaton potential within the observable range. We derive bounds on this derivative under the assumption that the inflaton potential can be approximated as a third order polynomial within the observable range.Comment: 32 pages, 7 figures. v2: additional references, some typos corrected, passed to JCAP style. v3: minor changes, matches published versio

SPIDER: Probing the Early Universe with a Suborbital Polarimeter

We evaluate the ability of SPIDER, a balloon-borne polarimeter, to detect a divergence-free polarization pattern ("B-modes") in the Cosmic Microwave Background (CMB). In the inflationary scenario, the amplitude of this signal is proportional to that of the primordial scalar perturbations through the tensor-to-scalar ratio r. We show that the expected level of systematic error in the SPIDER instrument is significantly below the amplitude of an interesting cosmological signal with r=0.03. We present a scanning strategy that enables us to minimize uncertainty in the reconstruction of the Stokes parameters used to characterize the CMB, while accessing a relatively wide range of angular scales. Evaluating the amplitude of the polarized Galactic emission in the SPIDER field, we conclude that the polarized emission from interstellar dust is as bright or brighter than the cosmological signal at all SPIDER frequencies (90 GHz, 150 GHz, and 280 GHz), a situation similar to that found in the "Southern Hole." We show that two ~20-day flights of the SPIDER instrument can constrain the amplitude of the B-mode signal to r<0.03 (99% CL) even when foreground contamination is taken into account. In the absence of foregrounds, the same limit can be reached after one 20-day flight.Comment: 29 pages, 8 figures, 4 tables; v2: matches published version, flight schedule updated, two typos fixed in Table 2, references and minor clarifications added, results unchange

Measuring our Peculiar Velocity by "Pre-deboosting" the CMB

It was recently shown that our peculiar velocity \beta with respect to the CMB induces mixing among multipoles and off-diagonal correlations at all scales which can be used as a measurement of \beta, which is independent of the standard measurement using the CMB temperature dipole. The proposed techniques rely however on a perturbative expansion which breaks down for \ell \gtrsim 1/(\beta) \approx 800. Here we propose a technique which consists of deboosting the CMB temperature in the time-ordered data and show that it extends the validity of the perturbation analysis multipoles up to \ell \sim 10000. We also obtain accurate fitting functions for the mixing between multipoles valid in a full non-linear treatment. Finally we forecast the achievable precision with which these correlations can be measured in a number of current and future CMB missions. We show that Planck could measure the velocity with a precision of around 60 km/s, ACTPol in 4 years around 40 km/s, while proposed future experiments could further shrink this error bar by over a factor of around 2.Comment: 14 pages, 7 figures. Revised projections for ACTPol, SPTPol and ACBAR; included projections for BICEP2; extended conclusions; typos correcte

Making maps of cosmic microwave background polarization for B-mode studies: The POLARBEAR example

Analysis of cosmic microwave background (CMB) datasets typically requires some filtering of the raw time-ordered data. For instance, in the context of ground-based observations, filtering is frequently used to minimize the impact of low frequency noise, atmospheric contributions and/or scan synchronous signals on the resulting maps. In this work we have explicitly constructed a general filtering operator, which can unambiguously remove any set of unwanted modes in the data, and then amend the map-making procedure in order to incorporate and correct for it. We show that such an approach is mathematically equivalent to the solution of a problem in which the sky signal and unwanted modes are estimated simultaneously and the latter are marginalized over. We investigated the conditions under which this amended map-making procedure can render an unbiased estimate of the sky signal in realistic circumstances. We then discuss the potential implications of these observations on the choice of map-making and power spectrum estimation approaches in the context of B-mode polarization studies. Specifically, we have studied the effects of time-domain filtering on the noise correlation structure in the map domain, as well as impact it may haveon the performance of the popular pseudo-spectrum estimators. We conclude that although maps produced by the proposed estimators arguably provide the most faithful representation of the sky possible given the data, they may not straightforwardly lead to the best constraints on the power spectra of the underlying sky signal and special care may need to be taken to ensure this is the case. By contrast, simplified map-makers which do not explicitly correct for time-domain filtering, but leave it to subsequent steps in the data analysis, may perform equally well and be easier and faster to implement. We focused on polarization-sensitive measurements targeting the B-mode component of the CMB signal and apply the proposed methods to realistic simulations based on characteristics of an actual CMB polarization experiment, POLARBEAR. Our analysis and conclusions are however more generally applicable. \ua9 ESO, 2017

The Q/U Imaging Experiment: Polarization Measurements of Radio Sources at 43 and 95 GHz

We present polarization measurements of extragalactic radio sources observed during the Cosmic Microwave Background polarization survey of the Q/U Imaging Experiment (QUIET), operating at 43 GHz (Q-band) and 95 GHz (W-band). We examine sources selected at 20 GHz from the public, $>$40 mJy catalog of the Australia Telescope (AT20G) survey. There are $\sim$480 such sources within QUIET's four low-foreground survey patches, including the nearby radio galaxies Centaurus A and Pictor A. The median error on our polarized flux density measurements is 30--40 mJy per Stokes parameter. At S/N $> 3$ significance, we detect linear polarization for seven sources in Q-band and six in W-band; only $1.3 \pm 1.1$ detections per frequency band are expected by chance. For sources without a detection of polarized emission, we find that half of the sources have polarization amplitudes below 90 mJy (Q-band) and 106 mJy (W-band), at 95% confidence. Finally, we compare our polarization measurements to intensity and polarization measurements of the same sources from the literature. For the four sources with WMAP and Planck intensity measurements $>1$ Jy, the polarization fraction are above 1% in both QUIET bands. At high significance, we compute polarization fractions as much as 10--20% for some sources, but the effects of source variability may cut that level in half for contemporaneous comparisons. Our results indicate that simple models---ones that scale a fixed polarization fraction with frequency---are inadequate to model the behavior of these sources and their contributions to polarization maps.Comment: 16 pages, 10 figures. Submitted to Ap

Second Season QUIET Observations: Measurements of the CMB Polarization Power Spectrum at 95 GHz

The Q/U Imaging ExperimenT (QUIET) has observed the cosmic microwave background (CMB) at 43 and 95GHz. The 43-GHz results have been published in QUIET Collaboration et al. (2011), and here we report the measurement of CMB polarization power spectra using the 95-GHz data. This data set comprises 5337 hours of observations recorded by an array of 84 polarized coherent receivers with a total array sensitivity of 87 uK sqrt(s). Four low-foreground fields were observed, covering a total of ~1000 square degrees with an effective angular resolution of 12.8', allowing for constraints on primordial gravitational waves and high-signal-to-noise measurements of the E-modes across three acoustic peaks. The data reduction was performed using two independent analysis pipelines, one based on a pseudo-Cl (PCL) cross-correlation approach, and the other on a maximum-likelihood (ML) approach. All data selection criteria and filters were modified until a predefined set of null tests had been satisfied before inspecting any non-null power spectrum. The results derived by the two pipelines are in good agreement. We characterize the EE, EB and BB power spectra between l=25 and 975 and find that the EE spectrum is consistent with LCDM, while the BB power spectrum is consistent with zero. Based on these measurements, we constrain the tensor-to-scalar ratio to r=1.1+0.9-0.8 (r<2.8 at 95% C.L.) as derived by the ML pipeline, and r=1.2+0.9-0.8 (r<2.7 at 95% C.L.) as derived by the PCL pipeline. In one of the fields, we find a correlation with the dust component of the Planck Sky Model, though the corresponding excess power is small compared to statistical errors. Finally, we derive limits on all known systematic errors, and demonstrate that these correspond to a tensor-to-scalar ratio smaller than r=0.01, the lowest level yet reported in the literature.Comment: 10 pages, 6 figures, 3 tables, submitted to ApJ, This paper should be cited as "QUIET Collaboration (2012)." v2: updated to reflect published versio

Spider Optimization II: Optical, Magnetic and Foreground Effects

Spider is a balloon-borne instrument designed to map the polarization of the cosmic microwave background (CMB) with degree-scale resolution over a large fraction of the sky. Spider's main goal is to measure the amplitude of primordial gravitational waves through their imprint on the polarization of the CMB if the tensor-to-scalar ratio, r, is greater than 0.03. To achieve this goal, instrumental systematic errors must be controlled with unprecedented accuracy. Here, we build on previous work to use simulations of Spider observations to examine the impact of several systematic effects that have been characterized through testing and modeling of various instrument components. In particular, we investigate the impact of the non-ideal spectral response of the half-wave plates, coupling between focal plane components and the Earth's magnetic field, and beam mismatches and asymmetries. We also present a model of diffuse polarized foreground emission based on a three-dimensional model of the Galactic magnetic field and dust, and study the interaction of this foreground emission with our observation strategy and instrumental effects. We find that the expected level of foreground and systematic contamination is sufficiently low for Spider to achieve its science goals.Comment: submitted to APJ, 15 pages, 12 figure