CMB Maps Research Articles

Scale-dependent hemispherical asymmetry from general initial state during inflation

We consider a general initial state for inflation as the mechanism for generating scale-dependent hemispherical asymmetry. An observable scale-dependent non-Gaussianity is generated that leads to observable hemispherical asymmetry from the super-horizon long mode modulation. We show that the amplitude of dipole asymmetry falls off exponentially on small angular scales which can address the absence of dipole asymmetry at these scales. In addition, depending on the nature of non-vaccum initial state, the amplitude of the dipole asymmetry has oscillatory features which can be detected in a careful CMB map analysis. Furthermore, we show that the non-vacuum initial state provides a natural mechanism for enhancing the super horizon long mode perturbation as required to generate the dipole asymmetry.

Planck2013 results. XIV. Zodiacal emission

The Planck satellite provides a set of all-sky maps at nine frequencies from 30 GHz to 857 GHz. Planets, minor bodies, and diffuse interplanetary dust emission (IPD) are all observed. The IPD can be separated from Galactic and other emissions because Planck views a given point on the celestial sphere multiple times, through different columns of IPD. We use the Planck data to investigate the behaviour of zodiacal emission over the whole sky at sub-millimetre and millimetre wavelengths. We fit the Planck data to find the emissivities of the various components of the COBE zodiacal model -- a diffuse cloud, three asteroidal dust bands, a circumsolar ring, and an Earth-trailing feature. The emissivity of the diffuse cloud decreases with increasing wavelength, as expected from earlier analyses. The emissivities of the dust bands, however, decrease less rapidly, indicating that the properties of the grains in the bands are different from those in the diffuse cloud. We fit the small amount of Galactic emission seen through the telescope's far sidelobes, and place limits on possible contamination of the CMB results from both zodiacal and far-sidelobe emission. When necessary, the results are used in the Planck pipeline to make maps with zodiacal emission and far sidelobes removed. We show that the zodiacal correction to the CMB maps is small compared to the Planck CMB temperature power spectrum and give a list of flux densities for small Solar System bodies.

Planck2013 results. XV. CMB power spectra and likelihood

We present the Planck likelihood, a complete statistical description of the two-point correlation function of the CMB temperature fluctuations. We use this likelihood to derive the Planck CMB power spectrum over three decades in l, covering 2 <= l <= 2500. The main source of error at l <= 1500 is cosmic variance. Uncertainties in small-scale foreground modelling and instrumental noise dominate the error budget at higher l's. For l < 50, our likelihood exploits all Planck frequency channels from 30 to 353 GHz through a physically motivated Bayesian component separation technique. At l >= 50, we employ a correlated Gaussian likelihood approximation based on angular cross-spectra derived from the 100, 143 and 217 GHz channels. We validate our likelihood through an extensive suite of consistency tests, and assess the impact of residual foreground and instrumental uncertainties on cosmological parameters. We find good internal agreement among the high-l cross-spectra with residuals of a few uK^2 at l <= 1000. We compare our results with foreground-cleaned CMB maps, and with cross-spectra derived from the 70 GHz Planck map, and find broad agreement in terms of spectrum residuals and cosmological parameters. The best-fit LCDM cosmology is in excellent agreement with preliminary Planck polarisation spectra. The standard LCDM cosmology is well constrained by Planck by l <= 1500. For example, we report a 5.4 sigma deviation from n_s /= 1. Considering various extensions beyond the standard model, we find no indication of significant departures from the LCDM framework. Finally, we report a tension between the best-fit LCDM model and the low-l spectrum in the form of a power deficit of 5-10% at l <~ 40, significant at 2.5-3 sigma. We do not elaborate further on its cosmological implications, but note that this is our most puzzling finding in an otherwise remarkably consistent dataset. (Abridged)

North-South non-Gaussian asymmetry in Planck CMB maps

We report the results of a statistical analysis performed with the four foreground-cleaned Planck maps by means of a suitably defined local-variance estimator. Our analysis shows a clear dipolar structure in Planck's variance map pointing in the direction (l,b) ≃ (220°,-32°), thus consistent with the North-South asymmetry phenomenon. Surprisingly, and contrary to previous findings, removing the CMB quadrupole and octopole makes the asymmetry stronger. Our results show a maximal statistical significance, of 98.1% CL, in the scales ranging from ℓ=4 to ℓ=500. Additionally, through exhaustive analyses of the four foreground-cleaned and individual frequency Planck maps, we find unlikely that residual foregrounds could be causing this dipole variance asymmetry. Moreover, we find that the dipole gets lower amplitudes for larger masks, evidencing that most of the contribution to the variance dipole comes from a region near the galactic plane. Finally, our results are robust against different foreground cleaning procedures, different Planck masks, pixelization parameters, and the addition of inhomogeneous real noise.

Statistical anisotropies in gravitational waves in solid inflation

Solid inflation can support a long period of anisotropic inflation. We calculate the statistical anisotropies in the scalar and tensor power spectra and their cross-correlation in anisotropic solid inflation. The tensor-scalar cross-correlation can either be positive or negative, which impacts the statistical anisotropies of the TT and TB spectra in CMB map more significantly compared with the tensor self-correlation. The tensor power spectrum contains potentially comparable contributions from quadrupole and octopole angular patterns, which is different from the power spectra of scalar, the cross-correlation or the scalar bispectrum, where the quadrupole type statistical anisotropy dominates over octopole.

Testing cosmic microwave background polarization data using position angles

We consider a novel null test for contamination which can be applied to CMB polarization data that involves analysis of the statistics of the polarization position angles. Specifically, we will concentrate on using histograms of the measured position angles to illustrate the idea. Such a test has been used to identify systematics in the NVSS point source catalogue with an amplitude well below the noise level. We explore the statistical properties of polarization angles in CMB maps. If the polarization angle is not correlated between pixels, then the errors follow a simple $\sqrt{N_{pix}}$ law. However this is typically not the case for CMB maps since these have correlations which result in an increase in the variance since the effective number of independent pixels is reduced. Then we illustrate how certain classes of systematic errors can result in very obvious patterns in these histograms, and thus that these errors could possibly be identified using this method. We discuss how this idea might be applied in a realistic context, and make a preliminary analysis of the WMAP7 data, finding evidence of a systematic error in the Q and W band data, consistent with a constant offset in Q and U.

Planck CMB anomalies: astrophysical and cosmological secondary effects and the curse of masking

Large-scale anomalies have been reported in CMB data with both WMAP and Planck data. These could be due to foreground residuals and or systematic effects, though their confirmation with Planck data suggests they are not due to a problem in the WMAP or Planck pipelines. If these anomalies are in fact primordial, then understanding their origin is fundamental to either validate the standard model of cosmology or to explore new physics. We investigate three other possible issues: 1) the trade-off between minimising systematics due to foreground contamination (with a conservative mask) and minimising systematics due to masking, 2) astrophysical secondary effects (the kinetic Doppler quadrupole and kinetic Sunyaev-Zel'dovich effect), and 3) secondary cosmological signals (the integrated Sachs-Wolfe effect). We address the masking issue by considering new procedures that use both WMAP and Planck to produce higher quality full-sky maps using the sparsity methodology (LGMCA maps). We show the impact of masking is dominant over that of residual foregrounds, and the LGMCA full-sky maps can be used without further processing to study anomalies. We consider four official Planck PR1 and two LGMCA CMB maps. Analysis of the observed CMB maps shows that only the low quadrupole and quadrupole-octopole alignment seem significant, but that the planar octopole, Axis of Evil, mirror parity and cold spot are not significant in nearly all maps considered. After subtraction of astrophysical and cosmological secondary effects, only the low quadrupole may still be considered anomalous, meaning the significance of only one anomaly is affected by secondary effect subtraction out of six anomalies considered. In the spirit of reproducible research all reconstructed maps and codes will be made available for download here http://www.cosmostat.org/anomaliesCMB.html.

CMB hemispherical asymmetry: long mode modulation and non-Gaussianity

The observed hemispherical asymmetry in CMB map can be explained by modulation from a long wavelength super horizon mode which non-linearly couples to the CMB modes. We address the criticism in [1] about the role of non-Gaussianities in squeezed and equilateral configurations in generating hemispherical asymmetry from the long mode modulation. We stress that the modulation is sensitive to the non-Gaussianity in the squeezed limit. In addition, we demonstrate the validity of our approach in providing a consistency condition relating the amplitude of dipole asymmetry to fNL in the squeezed limit.

Viability of the matter bounce scenario in Loop Quantum Cosmology from BICEP2 last data

The CMB map provided by the Planck project constrains the value of the ratio of tensor-to-scalar perturbations, namely r, to be smaller than 0.11 (95 % CL). This bound rules out the simplest models of inflation. However, recent data from BICEP2 is in strong tension with this constrain, as it finds a value r=0.20+0.07-0.05 with 0r= disfavored at 7.0 σ, which allows these simplest inflationary models to survive. The remarkable fact is that, even though the BICEP2 experiment was conceived to search for evidence of inflation, its experimental data matches correctly theoretical results coming from the matter bounce scenario (the alternative model to the inflationary paradigm). More precisely, most bouncing cosmologies do not pass Planck's constrains due to the smallness of the value of the tensor/scalar ratio r⩽ 0.11, but with new BICEP2 data some of them fit well with experimental data. This is the case with the matter bounce scenario in the teleparallel version of Loop Quantum Cosmology.

The TT, TB, EB and BB correlations in anisotropic inflation

The ongoing and future experiments will measure the B-mode from different sky coverage and frequency bands, with the potential to reveal non-trivial features in polarization map. In this work we study the TT, TB, EB and BB correlations associated with the B-mode polarization of CMB map in models of charged anisotropic inflation. The model contains a chaotic-type large field complex inflaton which is charged under the U(1) gauge field. We calculate the statistical anisotropies generated in the power spectra of the curvature perturbation, the tensor perturbation and their cross-correlation. It is shown that the asymmetry in tensor power spectrum is a very sensitive probe of the gauge coupling. While the level of statistical anisotropy in temperature power spectrum can be small and satisfy the observational bounds, the interactions from the gauge coupling can induce large directional dependence in tensor modes. This will leave interesting anisotropic fingerprints in various correlations involving the B-mode polarization such as the TB cross-correlation which may be detected in upcoming Planck polarization data. In addition, the TT correlation receives an anisotropic contribution from the tensor sector which naturally decays after l ≳ 100. We expect that the mechanism of using tensor sector to induce asymmetry at low l to be generic which can also be applied to address other low l CMB anomalies.

Scalar-tensor anticross-correlation does not help to reconcile the tension between BICEP2 and Planck

We examine the recent proposal [1] that the anti-cross-correlation of the scalar and tensor primordial fluctuations reconciles the tension between BICEP2 and Planck observations. We show that unfortunately the contribution from the scalar-tensor correlation to the CMB temperature power spectrum vanishes once summed over the angular mode $m$ so the tension between BICEP2 and Planck can not be reconciled. The reason is that one has to use the spin-weighted spherical harmonics when projecting fields with nonzero spins into the CMB sky. These nonzero spin-weighted spherical harmonics are subject to orthogonality conditions when summed over the angular direction and thus the desired cross-correlation between the scalar and tensor perturbations in CMB map vanishes.

Residual foreground contamination in the WMAP data

We have studied whether there is any residual foreground contamination in the foreground reduced WMAP-7 data for the differential assemblies (DAs) Q, V and W. We have calculated the correlation between the foreground map, from which long wavelength correlations have been subtracted, and the foreground reduced map for each DA. We have found positive correlations for all the channels. The statistical significance of the resulting values has been tested by comparing with correlations between the cleaned CMB maps and 1000 simulated Gaussian maps to which instrumental effects have been added. We have found high statistical significance of the observed correlations, implying the presence of residual contamination in the cleaned data, and found that, for Q and V channels, a large fraction of the contamination comes from pixels, where the foreground maps have positive values larger than three times its rms value, which shows the presence of unresolved point sources that contribute significantly to the contamination.

Power spectrum distortions in CMB map one-dimensional cross-sections depending on the cosmological model. II

Power spectrum distortions in CMB map one-dimensional cross-sections depending on the cosmological model. II

On the signature of z 0.6 superclusters and voids in the Integrated Sachs-Wolfe effect

Through a large ensemble of Gaussian realisations and a suite of large-volume N-body simulations, we show that in a standard LCDM scenario, supervoids and superclusters in the redshift range $z\in[0.4,0.7]$ should leave a {\em small} signature on the ISW effect of the order $\sim 2 \mu$K. We perform aperture photometry on WMAP data, centred on such superstructures identified from SDSS LRGs, and find amplitudes at the level of 8 -- 11$ \mu$K -- thus confirming the earlier work of Granett et al 2008. If we focus on apertures of the size $\sim3.6\degr$, then our realisations indicate that LCDM is discrepant at the level of $\sim4 \sigma$. If we combine all aperture scales considered, ranging from 1\degr--20\degr, then the discrepancy becomes $\sim2\sigma$, and it further lowers to $\sim 0.6 \sigma$ if only 30 superstructures are considered in the analysis (being compatible with no ISW signatures at $1.3\sigma$ in this case). Full-sky ISW maps generated from our N-body simulations show that this discrepancy cannot be alleviated by appealing to Rees-Sciama mechanisms, since their impact on the scales probed by our filters is negligible. We perform a series of tests on the WMAP data for systematics. We check for foreground contaminants and show that the signal does not display the correct dependence on the aperture size expected for a residual foreground tracing the density field. The signal also proves robust against rotation tests of the CMB maps, and seems to be spatially associated to the angular positions of the supervoids and superclusters. We explore whether the signal can be explained by the presence of primordial non-Gaussianities of the local type. We show that for models with $\FNL=\pm100$, whilst there is a change in the pattern of temperature anisotropies, all amplitude shifts are well below $<1\mu$K.

Statistics of general functions of a Gaussian field-application to non-Gaussianity from preheating

We provide a general formula for calculating correlators of arbitrary function of a Gaussian field. This work extends the standard leading-order approximation based on the δN formalism to the case where truncation of the δN at some low order does not yield the correct answer. As an application of this formula, we investigate 2, 3 and 4-point functions of the primordial curvature perturbation generated in the massless preheating model by approximating the mapping between the curvature perturbation and the Gaussian field as a sum of the many spiky normal distribution functions as suggested by lattice calculations. We also discuss observational consequences of this case and show that trispectrum would be a key observable to search signature of preheating in the CMB map. It is found the forms of the curvature correlation functions for any δN, at the leading order in the correlator of the Gaussian field, coincide with the standard local type ones. Within this approximation, it is also found that the standard formula for the non-linearity parameters given by the product of the derivatives of the e-folding number still holds after we replace the bare e-folding number appearing in the original δN expansion with the one smoothed in the field space with a Gaussian window function.

Power spectrum distortions in CMB map one-dimensional cross-sections depending on the cosmological model

We examine the effect produced by the variation of parameters of the cosmological model on the power spectrum of one-dimensional cross-sections of the cosmic microwave background maps. We also investigate the possibility of determining these parameters in the analysis of one-dimensional data. The features of the component separation procedure, leading to additional restrictions on the accuracy of reconstruction of the original spectrum are discussed. When the low harmonics remain in the map, the power spectrum of a one-dimensional cross-section is poorly sensitive to the variations of a number of cosmological parameters. Still, the analysis of one-dimensional data could be useful in the search and study of anomalous effects.

Motion induced second order temperature and y-type anisotropies after the subtraction of linear dipole in the CMB maps

y-type spectral distortions of the cosmic microwave background allow usto detect clusters and groups of galaxies, filaments of hot gas and thenon-uniformities in the warm hot intergalactic medium. Several CMBexperiments (on small areas of sky) and theoretical groups (for full sky)have recently published y-type distortion maps. We propose to search fortwo artificial hot spots in such y-type maps resulting from theincomplete subtraction of the effect of the motion induced dipole on the cosmic microwavebackground sky. This dipole introduces, at second order, additionaltemperature and y-distortion anisotropy on the sky of amplitude few μK which couldpotentially be measured by Planck HFI and Pixie experiments and can be used as a source of crosschannel calibration by CMB experiments. This y-type distortion is present inevery pixel and is not the result of averaging the whole sky. Thisdistortion, calculated exactly from the known linear dipole, can besubtracted from the final y-type maps, if desired.

CMB maximum temperature asymmetry axis: Alignment with other cosmic asymmetries

We use a global pixel based estimator to identify the axis of the residual Maximum Temperature Asymmetry (MTA) (after the dipole subtraction) of the WMAP 7 year Internal Linear Combination (ILC) CMB temperature sky map. The estimator is based on considering the temperature differences between opposite pixels in the sky at various angular resolutions (4 degrees-15 degrees and selecting the axis that maximizes this difference. We consider three large scale Healpix resolutions (N_{side}=16 (3.7 degrees), N_{side}=8 (7.3 degrees) and N_{side}=4 (14.7 degrees)). We compare the direction and magnitude of this asymmetry with three other cosmic asymmetry axes (\alpha dipole, Dark Energy Dipole and Dark Flow) and find that the four asymmetry axes are abnormally close to each other. We compare the observed MTA axis with the corresponding MTA axes of 10^4 Gaussian isotropic simulated ILC maps (based on LCDM). The fraction of simulated ILC maps that reproduces the observed magnitude of the MTA asymmetry and alignment with the observed \alpha dipole is in the range of 0.1%-0.5%$ (depending on the resolution chosen for the CMB map). The corresponding magnitude+alignment probabilities with the other two asymmetry axes (Dark Energy Dipole and Dark Flow) are at the level of about 1%. We propose Extended Topological Quintessence as a physical model qualitatively consistent with this coincidence of directions.

Residual foreground contamination in the WMAP data and bias in non-Gaussianity estimation

We analyze whether there is any residual foreground contamination inthe cleaned WMAP 7 years data for the differentialassemblies, Q, V and W. We calculate the correlation between theforeground map, from which long wavelength correlations have beensubtracted, and the foreground reduced map for each differentialassembly after applying the Galaxy and point sources masks. We find positive correlations forall the differential assemblies, with high statistical significance.For Q and V, we find that a large fraction of thecontamination comes frompixels where the foreground maps have positive values larger thanthree times the rms values. These findings imply the presence ofresidual contamination from Galactic emissions and unresolved pointsources. We redo the analysis after masking the extended point sourcescataloque of Scodeller et al. [7] and find a drop in the correlation and corresponding significancevalues. To quantify the effect of the residualcontamination on the search for primordial non-Gaussianity in theCMB we add estimated contaminant fraction to simulatedGaussian CMB maps and calculate the characteristic non-Gaussiandeviation shapes of Minkowski Functionals that arise due to thecontamination. We find remarkable agreement of these deviation shapeswith those measured from WMAP data, which imply that a major fractionof the observed non-Gaussian deviation comes from residual foregroundcontamination. We also compute non-Gaussian deviations of MinkowskiFunctionals after applying the point sources mask of Scodeller et al. and find a decrease in the overall amplitudes of the deviationswhich is consistent with a decrease in the level of contamination.

Low-ℓCMB analysis and inpainting

Reconstruction of the CMB in the Galactic plane is extremely difficult due to the dominant foreground emissions such as Dust, Free-Free or Synchrotron. For cosmological studies, the standard approach consists in masking this area where the reconstruction is not good enough. This leads to difficulties for the statistical analysis of the CMB map, especially at very large scales (to study for e.g., the low quadrupole, ISW, axis of evil, etc). We investigate in this paper how well some inpainting techniques can recover the low-$\ell$ spherical harmonic coefficients. We introduce three new inpainting techniques based on three different kinds of priors: sparsity, energy and isotropy, and we compare them. We show that two of them, sparsity and energy priors, can lead to extremely high quality reconstruction, within 1% of the cosmic variance for a mask with Fsky larger than 80%.