Measurements of the Matter Density Perturbation Amplitude from Cosmological Data

The various measurements of the linear matter density perturbation amplitude obtained from the observations of the cosmic microwave background (CMB) anisotropy, weak gravitational lensing, galaxy cluster mass function, matter power spectrum, and redshift space distortions are compared. The Planck data on the CMB temperature anisotropy spectrum at high multipoles, ? > 1000 (where the effect of gravitational lensing is most significant), are shown to give a measurement of the matter density perturbation amplitude that contradicts all other measurements of this quantity from both Planck CMB anisotropy data and other data at a significance level of about 3.7σ. Thus, at present these data should not be combined together for the calculations of constraints on cosmological parameters. Except for the Planck data on the CMB temperature anisotropy spectrum at high multipoles, all the remaining measurements of the density perturbation amplitude agree well between themselves and give the following constraints: σ₈ = 0.792± 0.006 on the linear matter density perturbation amplitude, Ω_m = 0.287± 0.007 on the matter density parameter, and H₀ = 69.4 ± 0.6 km s^?1 Mpc^?1 on the Hubble constant. Various constraints on the sum of neutrino masses and the number of neutrino flavors can be obtained by additionally taking into account the data on baryon acoustic oscillations and (or) direct Hubble constant measurements in the local Universe.     

Understanding the WMAP Cold Spot mystery

The Cold Spot (CS) at galactic coordinates (b = −57°, l = 209°) was discovered in the Wilkinson Microwave Anisotropy Probe (WMAP)data as a cosmic background anomaly. In order to assess the cosmological significance of the Spot, we examine its properties using the cluster analysis of the local extrema in the cosmic microwave background (CMB) signal. We also check the hypothesis that the CMB signal has a non-Gaussian tail, localized in the low-multipole components. We constructed a linear filter, dividing the signal into two parts: non-Gaussian and Gaussian. Using the filter scale as a variable, we can maximize the skewness and kurtosis of the smoothed signal and minimize these statistics. We discovered that the shape of the CS is formed primarily by the components of the CMB signal represented by the multipoles between 10 ≤ ℓ ≤ 20, with a corresponding angular scale of about 5°–10°. This signal leads to the modulation of the CMB on the whole sky, clearly seen at |b| > 30° in both the ILC andWCM maps, rather than in a single localized feature. After subtraction of this modulation, the remaining part of the CMB signal appears to be consistent with statistical homogeneity and Gaussianity. We therefore infer that the mystery of the WMAP Cold Spot reflects directly the peculiarities of low multipoles of the CMB signal, rather than a single local (isolated) defect or the manifestations of a globally anisotropic cosmology.     

Do we need to correct the internal linear combination quadrupole?

The problem of high correlation of the CMB quadrupole with foregrounds is investigated in this paper. We present an analysis of the cross-correlation for the WMAP ILC(III) low multipoles and foregrounds and show that without correction of the sign for m = 0 harmonic of the quadrupole this correlation is very high. By analysis of 10⁴ Monte Carlo simulations of the CMB-foreground separation, presented by Eriksen et al. [1], we show that practically for 50% realizations of the CMB quadrupole with the sign of the m = 0 mode equivalent to the sign of the foreground component, the input quadrupoles have the opposite sign of the output signal. Preserving the WMAP ILC(III) power spectrum of the quadrupole and changing the sign of the ILC (III) m = 0mode, we get the coefficient of cross-correlations |K(? = 2)| < 10%, what decreases the level of cross-correlations by a factor of 5–6. We use themultipole vectors for the renormalized ILC(III) quadrupole and show that these vectors are very sensitive to the sign and amplitude of the m = 0 mode.     

Measuring statistical isotropy of CMB anisotropy

The statistical expectation values of the temperature fluctuations and polarization of cosmic microwave background (CMB) are assumed to be preserved under rotations of the sky. We investigate the statistical isotropy (SI) of the CMB maps recently measured by the Wilkinson microwave anisotropy probe (WMAP) using the bipolar spherical harmonic formalism proposed in Hajian and Souradeep [Hajian, A., Souradeep, T. (2003) Astrophys. J. Lett. 597, L5] for CMB temperature anisotropy and extended to CMB polarization in Basak, Hajian and Souradeep [Basak, S., Hajian, A., Souradeep, T. (2006) Phys. Rev. D74, 02130(R)]. The Bipolar Power Spectrum (BiPS) had been measured for the full sky CMB anisotropy maps of the first year WMAP data and now for the recently released three years of WMAP data. We also introduce and measure directional sensitive reduced Bipolar coefficients on the three year WMAP ILC map. Consistent with our published results from first year WMAP data we have no evidence for violation of statistical isotropy on large angular scales. Preliminary analysis of the recently released first WMAP polarization maps, however, indicate significant violation of SI even when the foreground contaminated regions are masked out. Further work is required to confirm a possible cosmic origin and rule out the (more likely) origin in observational artifact such as foreground residuals at high galactic latitude.     

Statistics of WMAP ILC map temperature fluctuations towards distant radio galaxies

For 2442 galaxies of the catalog, compiled based on the NED, SDSS, and CATS survey data with redshifts z, > 0.3 we conducted an analysis of the amplitude of temperature fluctuations in the cosmic microwave background (CMB) in the points, corresponding to the direction to these objects. To this end, we used the ILC map from the WMAP mission seven-year data release. We have estimated the dipole component of the background and tested the hypothesis of Kashlinsky on the existence of a “dark bulk flow”, determined for the estimated dipole component of the CMB WMAP by the value of the CMB anisotropy in the direction to the clusters of galaxies. We show that the amplitude of this dipole T _max = 0.012mK is located within the σ interval, estimated by Monte Carlo simulations for the Gaussian fluctuations of the CMB signal in the ΛCDM model. The low amplitude of the dipole indicates that it is impossible to confirm this hypothesis from the WMAP data. In addition, we studied the statistics of the fluctuation amplitude of the microwave signal in the direction to radio galaxies. A weakening of the absolute value of the mean signal in the corresponding fields was discovered.     

Intracluster medium through three years of WMAP

Wilkinson microwave anisotropy probe (WMAP) has provided us with the highest resolution all-sky maps of the cosmic microwave background (CMB). As a result of thermal Sunyaev–Zel’dovich effect, clusters of galaxies are imprinted as tiny, poorly resolved dips on top of primary CMB anisotropies in these maps. Here, I describe different efforts to extract the physics of intracluster medium (ICM) from the sea of primary CMB, through combining WMAP with low-redshift galaxy or X-ray cluster surveys. This finally culminates at a mean (universal) ICM pressure profile, which is for the first time directly constrained from WMAP 3 year maps, and leads to interesting constraints on the ICM baryonic budget.     

Bianchi model CMB polarization and its implications for CMB anomalies

We derive the cosmic microwave background (CMB) radiative transfer equation in the form of a multipole hierarchy in the nearly Friedmann–Robertson–Walker limit of homogeneous, but anisotropic, universes classified via their Bianchi type. Compared with previous calculations, this allows a more sophisticated treatment of recombination, produces predictions for the polarization of the radiation and allows for reionization. Our derivation is independent of any assumptions about the dynamical behaviour of the field equations, except that it requires anisotropies to be small back to recombination; this is already demanded by observations.
We calculate the polarization signal in the Bianchi VII _h case, with the parameters recently advocated to mimic the several large-angle anomalous features observed in the CMB. We find that the peak polarization signal is  ∼1.2 μK  for the best-fitting model to the temperature anisotropies, and is mostly confined to multipoles   l < 10  . Remarkably, the predicted large-angle EE and TE power spectra in the Bianchi model are consistent with Wilkinson Microwave Anisotropy Probe ( WMAP ) observations that are usually interpreted as evidence of early reionization. However, the power in B-mode polarization is predicted to be similar to the E-mode power and parity-violating correlations are also predicted by the model; the WMAP non-detection of either of these signals casts further strong doubts on the veracity of attempts to explain the large-angle anomalies with global anisotropy. On the other hand, given that there exist further dynamical degrees of freedom in the VII _h universes that are yet to be compared with CMB observations, we cannot at this time definitively reject the anisotropy explanation.     

Instability of reconstruction of the low CMB multipoles

We discuss the problem of the bias of the Internal Linear Combination (ILC) CMB map and show that it is closely related to the coefficient of cross-correlation K(?) of the true CMB and the foreground for each multipole ?. We present analysis of the cross-correlation for the WMAP ILC quadrupole and octupole from the first (ILC(I)) and the third (ILC(III)) year data releases and show that these correlations are ～ ?0.52–0.6. Analysing 10⁴ Monte Carlo simulations of the random Gaussian CMB signals, we show that the distribution function for the corresponding coefficient of the cross-correlation has a polynomial shape P(K, ?) ∝ (1 ? K ²)^??1. We show that the most probable value of the cross-correlation coefficient of the ILC and foreground quadrupole has two extrema at K ? ±0.58. Thus, the ILC(III) quadrupole represents the most probable value of the coefficient K. We analyze the problem of debiasing of the ILC CMB and pointed out that reconstruction of the bias seems to be very problematic due to statistical uncertainties. In addition, instability of the debiasing illuminates itself for the quadrupole and octupole components through the flip-effect, when the even ? + m modes can be reconstructed with significant error. This error manifests itself as opposite, in respect to the true sign of even low multipole modes, and leads to significant changes of the coefficient of cross-correlation with the foreground. We show that the CMB realizations, whose the sign of quadrupole (2, 0) component is negative (and the same, as for all the foregrounds), the corresponding probability to get the positive sign after implementation of the ILC method is about 40%.     

Search for Candidate Objects with the Sunyaev–Zeldovich Effect in the Radio Source Vicinities—galaxies: clusters: general

Based on the data from the Westerbork Northern Sky Survey performed at a frequency of 325 MHz in the range of right ascensions 0^h ≤ α < 2^h and declinations 29° < δ < 78° and using multi-frequency Planck maps, we selected candidate objects with the Sunyaev–Zeldovich effect. The list of the most probable candidates includes 381 sources. It is shown that the search for such objects can be accelerated by using a priori data on the negative level of fluctuations in the CMB map with removed low multipoles in the direction to radio sources.     

Wilkinson Microwave Anisotropy Probe 5-yr constraints on fnl with wavelets

We present a Gaussianity analysis of the Wilkinson Microwave Anisotropy Probe ( WMAP ) 5-yr cosmic microwave background (CMB) temperature anisotropy data maps. We use several third-order estimators based on the spherical Mexican hat wavelet. We impose constraints on the local non-linear coupling parameter f _nl using well-motivated non-Gaussian simulations. We analyse the WMAP maps at resolution of 6.9 arcmin for the Q , V , and W frequency bands. We use the KQ 75 mask recommended by the WMAP team which masks out 28 per cent of the sky. The wavelet coefficients are evaluated at 10 different scales from 6.9 to 150 arcmin. With these coefficients, we compute the third order estimators which are used to perform a  χ²  analysis. The  χ²  statistic is used to test the Gaussianity of the WMAP data as well as to constrain the f _nl parameter. Our results indicate that the WMAP data are compatible with the Gaussian simulations, and the f _nl parameter is constrained to  −8 < f _nl < +111  at 95 per cent confidence level (CL) for the combined   V + W   map. This value has been corrected for the presence of undetected point sources, which add a positive contribution of  Δ f _nl= 3 ± 5  in the   V + W   map. Our results are very similar to those obtained by the WMAP team using the bispectrum.     

Foreground removal from WMAP 7 yr polarization maps using an MLP neural network

One of the fundamental problems in extracting the cosmic microwave background signal (CMB) from millimeter/submillimeter observations is the pollution by emission from the Milky Way: synchrotron, free-free, and thermal dust emission. To extract the fundamental cosmological parameters from CMB signal, it is mandatory to minimize this pollution since it will create systematic errors in the CMB power spectra. In previous investigations, it has been demonstrated that the neural network method provide high quality CMB maps from temperature data. Here the analysis is extended to polarization maps. As a concrete example, the WMAP 7-year polarization data, the most reliable determination of the polarization properties of the CMB, has been analyzed. The analysis has adopted the frequency maps, noise models, window functions and the foreground models as provided by the WMAP Team, and no auxiliary data is included. Within this framework it is demonstrated that the network can extract the CMB polarization signal with no sign of pollution by the polarized foregrounds. The errors in the derived polarization power spectra are improved compared to the errors derived by the WMAP Team.     

Non-Gaussian foreground residuals of the WMAP first-year maps

We investigate the effect of foreground residuals in the WMAP ( Wilkinson Microwave Anisotropy Probe ) data by adding foreground contamination to Gaussian ensembles of cosmic microwave background (CMB) signal and noise maps. We evaluate a set of non-Gaussian estimators on the contaminated ensembles to determine with what accuracy any residual in the data can be constrained using higher-order statistics. We apply the estimators to the raw and cleaned Q -, V - and W -band first-year maps. The foreground subtraction method applied to clean the data in Bennett et al. appears to have induced a correlation between the power spectra and normalized bispectra of the maps which is absent in Gaussian simulations. It also appears to increase the correlation between the  Δℓ= 1  inter-ℓ bispectrum of the cleaned maps and the foreground templates. In a number of cases the significance of the effect is above the 98 per cent confidence level.     

Comparison of low-harmonics spectra and maps according to the WMAP and Planck space missions

We present a comparison of the angular power spectra and maps represented by the WMAP and Planck mission teams. The spectra are compared in the the multi pole range (2 ≤ ? ≤ 50). The ? =5, 7, 13, 29, 37, 41–46 harmonics have a discrepancy in the angular power spectra. The maps of the microwave background and their phase characteristics are studied at these spatial frequencies. We show that the discrepancy of the spectra is due to a different account of the systematics linked with the Galaxy, the ecliptic, and possibly with the Earth. These effects, leading to a statistical anisotropy, may be responsible for the observed anomalies in both experiments at low harmonics.     

Cross-correlation between WMAP and 2MASS: non-Gaussianity induced by the SZ effect

We study the non-Gaussianity induced by the Sunyaev–Zel'dovich (SZ) effect in cosmic microwave background (CMB) fluctuation maps. If a CMB map is contaminated by the SZ effect of galaxies or galaxy clusters, the CMB maps should have similar non-Gaussian features to the galaxy and cluster fields. Using the WMAP data and 2MASS galaxy catalogue, we show that the non-Gaussianity of the 2MASS galaxies is imprinted on WMAP maps. The signature of non-Gaussianity can be seen with the fourth-order cross-correlation between the wavelet variables of the WMAP maps and 2MASS clusters. The intensity of the fourth-order non-Gaussian features is found to be consistent with the contamination of the SZ effect of 2MASS galaxies. We also show that this non-Gaussianity can not be seen by the high-order autocorrelation of the WMAP . This is because the SZ signals in the autocorrelations of the WMAP data generally are weaker than the WMAP –2MASS cross-correlations by a factor f ², which is the ratio between the powers of the SZ-effect map and the CMB fluctuations on the scale considered. Therefore, the ratio of high-order autocorrelations of CMB maps to cross-correlations of the CMB maps and galaxy field would be effective to constrain the powers of the SZ effect on various scales.     

Angular power spectrum of CMB anisotropy from WMAP

The remarkable improvement in the estimates of different cosmological parameters in recent years has been largely spearheaded by accurate measurements of the angular power spectrum of cosmic microwave background (CMB) radiation. This has required removal of foreground contamination as well as detector noise bias with reliability and precision. Recently, a novel model-independent method for the estimation of CMB angular power spectrum from multi-frequency observations has been proposed and implemented on the first year WMAP (WMAP-1) data by Saha et al. [Saha, R., Jain, P., Souradeep, T., 2006. ApJL, 645, L89]. We review the results from WMAP-1 and also present the new angular power spectrum based on three years of the WMAP data (WMAP-3). Previous estimates have depended on foreground templates built using extraneous observational input to remove foreground contamination. This is the first demonstration that the CMB angular spectrum can be reliably estimated with precision from a self contained analysis of the WMAP data. The primary product of WMAP are the observations of CMB in 10 independent difference assemblies (DA) distributed over five frequency bands that have uncorrelated noise. Our method utilizes maximum information available within WMAP data by linearly combining DA maps from different frequencies to remove foregrounds and estimating the power spectrum from the 24 cross-power spectra of clean maps that have independent noise. An important merit of the method is that the expected residual power from unresolved point sources is significantly tempered to a constant offset at large multipoles (in contrast to the l² contribution expected from a Poisson distribution) leading to a small correction at large multipoles. Hence, the power spectrum estimates are less susceptible to uncertainties in the model of point sources.     

Maximum likelihood algorithm for parametric component separation in cosmic microwave background experiments

We discuss an approach to the component separation of microwave, multifrequency sky maps as those typically produced from cosmic microwave background (CMB) anisotropy data sets. The algorithm is based on the two-step, parametric, likelihood-based technique recently elaborated on by Eriksen et al., where the foreground spectral parameters are estimated prior to the actual separation of the components. In contrast with the previous approaches, we accomplish the former task with help of an analytically derived likelihood function for the spectral parameters, which, we show, yields estimates equal to the maximum likelihood values of the full multidimensional data problem. We then use these estimates to perform the second step via the standard, generalized-least-squares-like procedure. We demonstrate that the proposed approach is equivalent to a direct maximization of the full data likelihood, which is recast in a computationally tractable form. We use the corresponding curvature matrices to characterize statistical properties of the recovered parameters. We incorporate in the formalism some of the essential features of the CMB data sets, such as inhomogeneous pixel domain noise, unknown map offsets as well as calibration errors and study their consequences for the separation. We find that the calibration is likely to have a dominant effect on the precision of the spectral parameter determination for a realistic CMB experiment. We apply the algorithm to simulated data and discuss the results. Our focus is on partial sky, total intensity and polarization, CMB experiments such as planned balloon-borne and ground-based efforts, however, the techniques presented here should be also applicable to the full-sky data as for instance, those produced by the Wilkinson Microwave Anisotropy Probe ( WMAP ) satellite and anticipated from the Planck mission.     

Trans‐Planckian signatures in the cosmic microwave background?

With the increasingly precise measurement of the cosmic microwave background (CMB), cosmology has entered an era where a model's predictions become testable to percent‐level accuracy. In particular, the CMB spectrum has so far provided impressive support for the scenario of inflation, first invented to solve outstanding problems of standard cosmology. While current data (COBE, WMAP etc.) have already constrained cosmological parameters like Ω₀ to high precision, next generation instruments such as the PLANCK satellite should give access to specific characteristics of the inflationary mechanism itself. Another tantalizing idea has been discussed in this context: Given the enormous expansion of the Universe during the phase of inflation, could it be that even Planck scale physics has been stretched to observable distances and is therefore within grasp in the CMB observations? In this contribution, I discuss the possibility of carrying through the calculation of the perturbation spectrum from an ansatz for short distance physics right to its imprint in the CMB. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Radial pulsations of helium stars with masses from 10 to 50<Emphasis Type="Italic">M</Emphasis><Subscript>⊙</Subscript>

We have performed hydrodynamic calculations of the radial pulsations of helium stars with masses 10M_⊙ ≤ M ≤ 50M_⊙, luminosity-to-mass ratios 5 × 10³L_⊙/M_⊙ ≤ L/M ≤ 2.5 × 10⁴L_⊙/M_⊙, and effective temperatures 2 × 10⁴ K ≤ T_eff ≤ 10⁵ K for helium and heavy-element mass fractions of Y=0.98 and Z=0.02, respectively. We show that the high-temperature boundary of the instability region for radial pulsations at L/M ? 10⁴L_⊙/M_⊙ extends to T_eff≈10⁵ K. The amplitude of the velocity variations for outer layers is several hundred km s^?1, while the brightness variations in the B band of the UBV photometric system are within the range from several hundredths to half a magnitude. At constant luminosity-to-mass ratio, the radial pulsation period is determined only by the effective temperature of the star. In the ranges of luminosity-to-mass ratios 10⁴L_⊙/M_⊙ ≤ L/M ≤ 2 × 10⁴L_⊙/M_⊙ and effective temperatures 5 × 10⁴ K ≤ T_eff ≤ 9 × 10⁴ K, the periods of the radial modes are within 6 min ?Π?10³ min.     

Understanding the WMAP Results: Low-Order Multipoles and Dust in the Vicinity of the Solar System

Analyses of the cosmic microwave background (CMB) radiation maps produced by the Wilkinson Microwave Anisotropy Probe (WMAP) have revealed anomalies not predicted by the standard cosmological theory. It has been suggested that a dust cloud in the vicinity of the Solar system may be the cause for these anomalies. In this paper, the thermal emission by particles from two known interplanetary meteoroid complexes is tested against the CMB maps. Conclusions are drawn based on the geometry of cloud projections onto the WMAP sky whether these clouds are likely to explain the observed anomaly. The smooth background Zodiacal cloud and one of the Taurid meteor complex branches do not explain the WMAP anomaly.