CMB Sky Research Articles

COSMOLOGICAL IMPLICATIONS OF THE CMB LARGE-SCALE STRUCTURE

WMAP and Planck may have uncovered several anomalies in the full CMB sky that could indicate possible new physics driving the growth of density fluctuations in the early Universe. These include an unusually low power at the largest scales and an apparent alignment of the quadrupole and octopole moments. In LCDM, the quadrupole and octopole moments should be statistically independent. These low probability features may simply be due to posterior selections from many such possible effects. If this is not the case, however, their combined statistical significance would be equal to the product of their individual significances. Ignoring the biasing due to posterior selection, the missing large-angle correlations would have a probability as low as ~0.1% and the low-l multipole alignment would be unlikely at the ~4.9% level; under the least favourable conditions, their simultaneous observation in the context of the standard model could then be likely at only the ~0.005% level. In this paper, we explore the possibility that these features are indeed anomalous, and show that the corresponding probability of CMB multipole alignment in the R_h=ct Universe would then be ~7-10%, depending on the number of large-scale Sachs-Wolfe induced fluctuations. Since the low power at the largest spatial scales is reproduced in this cosmology without the need to invoke cosmic variance, the overall likelihood of observing both of these features in the CMB is > 7%, much more likely than in LCDM. The key physical ingredient responsible for this difference is the existence in the former of a maximum fluctuation size at the time of recombination, which is absent in the latter because of inflation.

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.

Extreme-Value Statistics for Testing Dark Energy

AbstractThe integrated Sachs-Wolfe effect was recently detected at a level of 4.4σ by [Granett et al. (2008)], by stacking compensated CMB temperature patches corresponding to superstructures in the universe. We test the reported signal using realistic gaussian random realizations of the CMB sky, based on the temperature power spectrum predicted by the concordance ΛCDM model. Such simulations provide a complementary approach to the largely used N-body simulations and allow to include the contaminant effects due to small-scale temperature fluctuations. We also apply our pipeline to foreground-cleaned CMB sky maps using the [Granett et al. (2008)] voids/clusters catalog. We confirm the detection of a signal, which depart from the null hypothesis by 3.5σ, and we report a tension with our theoretical estimates at a significance of about 2.5σ.

Cosmic microwave background anomalies from imperfect dark energy

We test anisotropic dark energy models with the 7-year WMAP temperature observations data. In the presence of imperfect sources, due to large-scale gradients or anisotropies in the dark energy field, the CMB sky will be distorted anisotropically on its way to us by the ISW effect. The signal covariance matrix then becomes nondiagonal for small multipoles, but at $\ell \gtrsim 20$ the anisotropy is negligible. We parametrize possible violations of rotational invariance in the late universe by the magnitude of a post-Friedmannian deviation from isotropy and its scale dependence. This allows to obtain hints on possible imperfect nature of dark energy and the large-angle anomalous features in the CMB. A robust statistical analysis, subjected to various tests and consistency checks, is performed to compare the predicted correlations with those obtained from the satellite-measured CMB full sky maps. The preferred axis point towards $(l,b) = (168^\circ, -31^\circ)$ and the amplitude of the anisotropy is $\varpi_0 = (0.51\pm 0.94)$ (1$\sigma$ deviation quoted). The best-fit model has a steep blue anisotropic spectrum ($n_{\mathrm{de}} = 3.1\pm1.5$).

CMB aberration and Doppler effects as a source of hemispherical asymmetries

Our peculiar motion with respect to the CMB rest frame represents a preferred direction in the observed CMB sky since it induces an apparent deflection of the observed CMB photons (aberration) and a shift in their frequency (Doppler). Both effects distort the multipoles aℓm's at all ℓ's. Such effects are real as it has been recently measured for the first time by Planck according to what was forecast in some recent papers. However, the common lore when estimating a power spectrum from CMB is to consider that Doppler affects only the ℓ = 1 multipole, neglecting any other corrections. In this work we use simulations of the CMB sky in a boosted frame with a peculiar velocity β≡v/c = 1.23 × 10−3 in order to assess the impact of such effect on power spectrum estimations in different regions of the sky. We show that the boost induces a north-south asymmetry in the power spectrum which is highly significant and non-negligible, of about (0.58±0.10)% for half-sky cuts when going up to ℓ ≈ 2500. We suggest that these effects are relevant and may account for some of the north-south asymmetries seen in the Planck data, being especially important at small scales. Finally we analyze the particular case of the ACT experiment, which observed only a small fraction of the sky and show that it suffers a bias of about 1% on the power spectrum and of similar size on some cosmological parameters: for example the position of the peaks shifts by 0.5% and the overall amplitude of the spectrum is about 0.4% lower than a full-sky case.

A MULTI-LEVEL SOLVER FOR GAUSSIAN CONSTRAINED COSMIC MICROWAVE BACKGROUND REALIZATIONS

We present a multi-level solver for drawing constrained Gaussian realizations or finding the maximum likelihood estimate of the CMB sky, given noisy sky maps with partial sky coverage. The method converges substantially faster than existing Conjugate Gradient (CG) methods for the same problem. For instance, for the 143 GHz Planck frequency channel, only 3 multi-level W-cycles result in an absolute error smaller than 1 microKelvin in any pixel. Using 16 CPU cores, this translates to a computational expense of 6 minutes wall time per realization, plus 8 minutes wall time for a power spectrum-dependent precomputation. Each additional W-cycle reduces the error by more than an order of magnitude, at an additional computational cost of 2 minutes. For comparison, we have never been able to achieve similar absolute convergence with conventional CG methods for this high signal-to-noise data set, even after thousands of CG iterations and employing expensive preconditioners. The solver is part of the Commander 2 code, which is available with an open source license at http://commander.bitbucket.org/.

Deep redshift topological lensing: strategies for the T3 candidate

The 3-torus (T^3) FLRW model better fits the nearly zero large-scale auto-correlation of the WMAP CMB sky maps than the infinite flat model. The T^3 model's WMAP parameters imply approximately equal-redshift topological lensing at z \sim 6. We investigate observational strategies for rejecting the T^3 solution or providing candidate topologically lensed galaxy pairs. T^3 holonomies are applied to (i) existing z \sim 6 observations and (ii) simulated observations, creating multiply connected catalogues. Corresponding simply connected catalogues are generated. Each catalogue is analysed using a successive filter method and collecting matched quadruples. Quadruple statistics between the multiply and simply connected catalogues are compared. The expected rejection of the hypothesis, or detection of candidate topologically lensed galaxies, is possible at a significance of 5% for a pair of T^3 axis-centred northern and southern surveys if photometric redshift accuracy is \sigma(\zphot) < 0.01 for a pair of nearly complete 100 deg^2 surveys with a total of > 500 galaxies over 4.3 < z < 6.6, or for a pair of 196 deg^2 surveys with > 400 galaxies and \sigma(\zphot) < 0.02 over 4<z<7. Dropping the maximum time interval in a pair from \Delta t =1 Gyr/h to \Delta t =0.1 Gyr/h yields a requirement of \sigma(\zphot) < 0.005 or \sigma(\zphot) < 0.01, respectively. Millions of z \sim 6 galaxies will be observed over fields of these sizes during the coming decades, implying much stronger constraints. The question is not if the hypothesis will be rejected or confirmed, it is when.

Low variance at large scales of WMAP 9 year data

We use an optimal estimator to study the variance of the WMAP 9 CMB field at low resolution, in both temperature and polarization. Employing realistic Monte Carlo simulation, we find statistically significant deviations from the ΛCDM model in several sky cuts for the temperature field. For the considered masks in this analysis, which cover at least the 54% of the sky, the WMAP 9 CMB sky and ΛCDM are incompatible at ⩾ 99.94% C.L. at large angles ( > 5°). We find instead no anomaly in polarization. As a byproduct of our analysis, we present new, optimal estimates of the WMAP 9 CMB angular power spectra from the WMAP 9 year data at low resolution.

Consistency tests for Planck and WMAP in the low multipole domain

Recently, full sky maps from Planck have been made publicly available. In this paper, we do consistency tests for the three Planck CMB sky maps. We assume that the difference between two maps represents the contributions from systematics, noise, foregrounds and other sources, and that a precise representation of the Cosmic Microwave Background should be uncorrelated with it. We investigate the cross correlation in pixel space between the difference maps and the various Planck maps and find no significant correlations, in comparison to 10000 random Gaussian simulated maps. Additionally we investigate the difference map between the WMAP ILC 9 year map and the ILC 7 year map. We perform cross correlations between this difference map, and the ILC9 and ILC7, and find significant correlations only for the ILC9, at more than the 99.99% level. Likewise, a comparison between the Planck NILC map and the WMAP ILC9 map, shows a strong correlation for the ILC9 map with the difference map, also at more than the 99.99% level. Thus the ILC9 appears to be more contaminated than the ILC7, which should be taken into consideration when using WMAP maps for cosmological analyses.

New constraints on anisotropic rotation of CMB polarization

The coupling of a scalar field to electromagnetic field via the Chern-Simons term will rotate the polarization directions of thecosmic microwave background radiation. The rotation angle which relies on the distribution of the scalar field on the CMB sky isdirection dependent. Such anisotropies will give rise to new distortions to the power spectra of CMB polarization and it can be used toprobe the detailed physics of the scalar field. In this paper we use the updated observational data to constrain the anisotropic rotationangle in a model independent way. We find that the dominant effect of the anisotropic rotation on CMB comes from its variance and it isconstrained tightly by the current data.

On CCC-predicted concentric low-variance circles in the CMB sky

A new analysis of the CMB, using WMAP data, supports earlier indications of non-Gaussian features of concentric circles of low temperature variance. Conformal cyclic cosmology (CCC) predicts such features from supermassive black-hole encounters in an aeon preceding our Big Bang. The significance of individual low-variance circles in the true data has been disputed; yet a recent independent analysis has confirmed CCC's expectation that CMB circles have a non-Gaussian temperature distribution. Here we examine concentric sets of low-variance circular rings in the WMAP data, finding a highly non-isotropic distribution. A new "sky-twist" procedure, directly analysing WMAP data, without appeal to simulations, shows that the prevalence of these concentric sets depends on the rings being circular, rather than even slightly elliptical, numbers dropping off dramatically with increasing ellipticity. This is consistent with CCC's expectations; so also is the crucial fact that whereas some of the rings' radii are found to reach around $15^\circ$, none exceed $20^\circ$. The non-isotropic distribution of the concentric sets may be linked to previously known anomalous and non-Gaussian CMB features.

Constraints on the topology of the Universe: Extension to general geometries

We present an update to the search for a non-trivial topology of the universe by searching for matching circle pairs in the cosmic microwave background using the WMAP 7 year data release. We extend the exisiting bounds to encompass a wider range of possible topologies by searching for matching circle pairs with opening angles 10 degree < \alpha < 90 degree and separation angles 11 degree < \theta < 180 degree. The extended search reveal two small anomalous regions in the CMB sky. Numerous pairs of well-matched circles are found where both circles pass through one or the other of those regions. As this is not the signature of any known manifold, but is a likely consequence of contamination in those sky regions, we repeat the search excluding circle pairs where both pass through either of the two regions. We then find no statistically significant pairs of matched circles, and so no hints of a non-trivial topology. The absence of matched circles increases the lower limit on the length of the shortest closed null geodesic that self-intersects at our location in the universe (equivalently the injectivity radius at our location) to 98.5% of the diameter of the last scattering surface or approximately 26 Gpc. It extends the limit to any manifolds in which the intersecting arcs of said geodesic form an angle greater than 10^o.

HARMONIC IN-PAINTING OF COSMIC MICROWAVE BACKGROUND SKY BY CONSTRAINED GAUSSIAN REALIZATION

The presence of astrophysical emissions between the last scattering surface and our vantage point requires us to apply a foreground mask on CMB sky map, leading to large cut around the Galactic equator and numerous holes. Since many CMB analyses, including non-Gaussianity study may be performed on a whole sky map in a more straightforward and reliable manner, it is of utmost importance to develop an efficient method to in-paint the CMB sky map, while still preserving statistical properties. In this letter, we consider Monte-Carlo simulation of constrained Gaussian field and derive it for CMB anisotropy in harmonic space, where a feasible implementation is possible with good approximation. We applied our method to the simulated data, which confirms the masked area is in-painted in a way compliant with the expected statistical properties. Subsequently, we applied our method to the WMAP foreground-reduced maps and investigated the anomalous alignment between quadrupole and octupole components. From our investigation, we find the alignment in the foreground-reduced maps is even higher than the ILC map. In particular, we find the highest alignment in the V band map, which has less foreground contamination than other bands. Therefore, we find it hard to attribute the alignment to residual foregrounds. Our method will be complementary to other efforts on in-painting or reconstructing the masked CMB data, and of great use to Planck surveyor and future missions.

Can we detect hot/cold spots in the CMB with Minkowski Functionals?

In this paper, we investigate the utility of Minkowski Functionals as a probe of cold/hot disk-like structures in the CMB. In order to construct an accurate estimator, we resolve a long-standing issue with the use of Minkowski Functionals as probes of the CMB sky — namely that of systematic differences (``residuals'') when numerical and analytical MF are compared. We show that such residuals are in fact by-products of binning, whereas it was originally attributed to pixelation or masking effects. We then derive a map-independent estimator that encodes the effects of binning, applicable to beyond our present work. Using this residual-free estimator, we show that small disk-like effects (as claimed by Vielva et al. [1,2]) can be detected only when a large sample of such maps are averaged over. In other words, our estimator is noise-dominated for small disk sizes at WMAP resolution. To confirm our suspicion, we apply our estimator to the WMAP7 data to obtain a null result.

A COMPARATIVE STUDY OF NON-GAUSSIANITY IN ILC–7YR CMB MAP

A detection or non detection of primordial non–Gaussianity (NG) by using the cosmic microwave background radiation (CMB) is a possible way to break the degeneracy of early universe models. Since a single statistical estimator hardly can be sensitive to all possible forms of NG which may be present in the data, it is important to use different statistical estimators to study NG in CMB. Recently, two new large-angle NG indicators based on skewness and kurtosis of spherical caps or spherical cells of CMB sky have been proposed and used in both CMB data and simulated maps. Here, we make a comparative study of these two different procedures by examining the NG in the WMAP seven years ILC map. We show that the spherical cells procedure detects a higher level of NG than that obtained by the method with overlapping spherical caps.

The morphology of the thermal Sunyaev-Zel’dovich sky

At high angular frequencies the thermal Sunyaev-Zel'dovich (tSZ) effect constitutes the dominant signal in the CMB sky. The tSZ effect is caused by large scale pressure fluctuations in the baryonic distribution in the Universe so its statistical properties provide estimates of corresponding properties of the projected 3D pressure fluctuations. It's power spectrum is a sensitive probe of the density fluctuations, and the bispectrum can be used to separate the bias associated with pressure. The bispectrum is often probed with a one-point real-space analogue, the skewness. In addition to the skewness the morphological properties, as probed by the well known Minkowski Functionals (MFs), also require the generalized one-point statistics, which at the lowest order are identical to the skewness parameters. The concept of generalized skewness parameters can be extended to define a set of three associated generalized skew-spectra. We use these skew-spectra to probe the morphology of the tSZ sky or the y-sky. We show how these power spectra can be recovered from the data in the presence of arbitrary mask and noise templates using the well known Pseudo-Cl (PCL) approach for arbitrary beam shape. We also employ an approach based on the halo model to compute the tSZ bispectrum. The bispectrum from each of these models is then used to construct the generalized skew-spectra. We consider the performance of an all-sky survey with Planck-type noise and compare the results against a noise-free ideal experiment using a range of smoothing angles. We find that the skew-spectra can be estimated with very high signal-to-noise ratio from future frequency cleaned tSZ maps that will be available from experiments such as Planck. This will allow their mode by mode estimation for a wide range of angular frequencies and will help us to differentiate them from various other sources of non-Gaussianity.

ARE THERE ECHOES FROM THE PRE-BIG-BANG UNIVERSE? A SEARCH FOR LOW-VARIANCE CIRCLES IN THE COSMIC MICROWAVE BACKGROUND SKY

The existence of concentric low variance circles in the CMB sky, generated by black-hole encounters in an aeon preceding our big bang, is a prediction of the Conformal Cyclic Cosmology. Detection of three families of such circles in WMAP data was recently reported by Gurzadyan & Penrose (2010). We reassess the statistical significance of those circles by comparing with Monte Carlo simulations of the CMB sky with realistic modeling of the anisotropic noise in WMAP data. We find that the circles are not anomalous and that all three groups are consistent at 3sigma level with a Gaussian CMB sky as predicted by inflationary cosmology model.

Symmetry of the CMB sky as a new test of its statistical isotropy. Non cosmological octupole?

In this article we propose a novel test for statistical anisotropy of the CMB ΔT(n̂ = (θ,ϕ)). The test is based on the fact, that the Galactic foregrounds have a remarkably strong symmetry with respect to their antipodal points S1: = n̂↔−n̂,n̂ = (θ,ϕ) and with respect to the Galactic plane, while the cosmological signal should not be symmetric or asymmetric under these transitions.We have applied the test for the octupole component of the WMAP ILC 7 map, by looking at a3,1 and a3,3, and their ratio to a3,2 both for real and imaginary values. We find abnormal symmetry of the octupole component at the level of 0.58%, compared to Monte Carlo simulations. By using the analysis of the phases of the octupole we found remarkably strong cross-correlations between the phases of the kinematic dipole and the ILC 7 octupole, in full agreement with previous results. We further test the multipole range 2 < l < 100, by investigating the ratio between the l+m = even and l+m = odd parts of power spectra. We compare the results to simulations of a Gaussian random sky, and find significant departure from the statistically isotropic and homogeneous case, for a very broad range of multipoles. We found that for the most prominent peaks of our estimator, the phases of the corresponding harmonics are coherent with phases of the octupole. We believe, our test would be very useful for detections of various types of residuals of the foreground and systematic effects at a very broad range of multipoles 2 ⩽ l ⩽ 1500−3000 for the forthcoming PLANCK CMB map, before any conclusions about primordial non-Gaussianity and statistical anisotropy of the CMB.

Measuring our peculiar velocity on the CMB with high-multipole off-diagonal correlations

Our peculiar velocity with respect to the CMB rest frame is knownto induce a large dipole in the CMB. However, the motion of an observerhas also the effect of distorting the anisotropies at all scales,as shown by Challinor and Van Leeuwen (2002), due to aberration andDoppler effects. We propose to measure independently our local motionby using off-diagonal two-point correlation functions for high multipoles.We study the observability of the signal for temperature and polarizationanisotropies. We point out that Planck can measure the velocityβ with an error of about 30% and the direction with anerror of about 20°. This method constitutes a cross-check,which can be useful to verify that our CMB dipole is due mainly toour velocity or to disentangle the velocity from other possible intrinsicsources.Although in this paper we focus on our peculiar velocity, a similareffect would result also from other intrinsic vectorial distortion ofthe CMB which would induce a dipolar lensing. Measuringthe off-diagonal correlation terms is therefore a test for a preferreddirection on the CMB sky.

Secondary non-Gaussianity and cross-correlation analysis

We develop optimised estimators of two sorts of power spectra for fields defined on the sky, in the presence of partial sky coverage. The first is the cross-power spectrum of two fields on the sky; the second is the skew spectrum of three fields. These can probe the Integrated Sachs Wolfe Effect (ISW) at large angular scales and the Sunyaev Z\'eldovich (SZ) effect from hot gas in clusters at small angular scales. The skew spectrum, recently introduced by Munshi & Heavens (2009), is an optimised statistic which can be tuned to study a particular form of non-Gaussianity, such as may arise in the early Universe, but which retains information on the nature of non-Gaussianity. In this paper we develop the mathematical formalism for the skew spectrum of 3 different fields. When applied to the CMB, this allows us to explore the contamination of the skew spectrum by secondary sources of CMB fluctuations. Considering the three-point function, the study of the bispectrum provides valuable information regarding cross-correlation of secondaries with lensing of CMB with much higher significance compared to just the study involving CMB sky alone. We use our analytical models to study specific cases of cosmological interest which include cross-correlating CMB with various large scale tracers to probe ISW and SZ effects for cross spectral analysis and use the formalism to study the signal-to-noise ratio for detection of the weak lensing of the CMB by cross-correlating it with different tracers as well as point sources for CMB experiments such as Planck (abridged).