The dependence of galaxy formation on cosmological parameters: can we distinguish between the WMAP1 and WMAP3 parameter sets?

We combine N -body simulations of structure growth with physical modelling of galaxy evolution to investigate whether the shift in cosmological parameters between the first- and third-year results from the Wilkinson Microwave Anisotropy Probe ( WMAP ) affects predictions for the galaxy population. Structure formation is significantly delayed in the WMAP3 cosmology, because the initial matter fluctuation amplitude is lower on the relevant scales. The decrease in dark matter clustering strength is, however, almost entirely offset by an increase in halo bias, so predictions for galaxy clustering are barely altered. In both cosmologies, several combinations of physical parameters can reproduce observed, low-redshift galaxy properties; the star formation, supernova feedback and active galactic nucleus feedback efficiencies can be played off against each other to give similar results. Models which fit observed luminosity functions predict projected two-point correlation functions which scatter by about 10–20 per cent on large scale and by larger factors on small scale, depending both on cosmology and on details of galaxy formation. Measurements of the pairwise velocity distribution prefer the WMAP1 cosmology, but careful treatment of the systematics is needed. Given present modelling uncertainties, it is not easy to distinguish between the WMAP1 and WMAP3 cosmologies on the basis of low-redshift galaxy properties. Model predictions diverge more dramatically at high redshift. Better observational data at   z > 2  will better constrain galaxy formation and perhaps also cosmological parameters.     

The WMAP data and results

The Wilkinson Microwave Anisotropy Probe (WMAP) science team has released results from the first year of operation at the Earth–Sun L₂ Lagrange point. The maps are consistent with previous observations but have much better sensitivity and angular resolution than the COBE DMR maps, and much better calibration accuracy and sky coverage than ground-based and balloon-borne experiments. The angular power spectra from these ground-based and balloon-borne experiments are consistent within their systematic and statistical uncertainties with the WMAP results. WMAP detected the large angular-scale correlation between the temperature and polarization anisotropies of the CMB caused by electron scattering since the Universe became reionized after the “Dark Ages”, giving a value for the electron scattering optical depth of 0.17 ± 0.04. The simplest ΛCDM model with n=1 and Ω_tot=1 fixed provides an adequate fit to the WMAP data and gives parameters which are consistent with determinations of the Hubble constant and observations of the accelerating Universe using supernovae. The time-ordered data, maps, and power spectra from WMAP can be found at http://lambda.gsfc.nasa.gov along with 13 papers by the WMAP science team describing the results in detail.     

The hot and cold spots in five-year WMAP data

We present an extensive frequentist analysis of the one-point statistics (number, mean, variance, skewness and kurtosis) and two-point correlation functions determined for the local extrema of the cosmic microwave background temperature field observed in five-years of Wilkinson Microwave Anisotropy Probe ( WMAP ) data. Application of a hypothesis test on the one-point statistics indicates a low variance of hot and cold spots in all frequency bands of the WMAP data. The consistency of the observations with Gaussian simulations of the best-fitting cosmological model is rejected at the 95 per cent confidence level outside the WMAP KQ75 mask and the Northern hemispheres in the Galactic and ecliptic coordinate frames. We demonstrate that it is unlikely that residual Galactic foreground emission contributes to the observed non-Gaussianities. However, the application of a high-pass filter that removes large angular scale power does improve the consistency with the best-fitting cosmological model.
Two-point correlation functions of the local extrema are calculated for both the temperature pair product [temperature–temperature (T–T)] and spatial pair-counting [point–point (P–P)]. The T–T observations demonstrate weak correlation on scales below  20°  and lie completely below the lower 3σ confidence region once various temperature thresholds are applied to the extrema determined for the KQ75 mask and northern sky partitions. The P–P correlation structure corresponds to the clustering properties of the temperature extrema, and provides evidence that it is the large angular-scale structures, and some unusual properties thereof, that are intimately connected to the properties of the hot and cold spots observed in the WMAP five-year data.     

Revisiting the baryon fractions of galaxy clusters: a comparison with WMAP 3-yr results

The universal baryonic mass fraction  (Ω_b/Ω_m)  can be sensitively constrained using X-ray observations of galaxy clusters. In this paper, we compare the baryonic mass fraction inferred from measurements of the cosmic microwave background with the gas mass fractions ( f _gas) of a large sample of clusters taken from the recent literature. In systems cooler than 4 keV, f _gas declines as the system temperature decreases. However, in higher temperature systems, f _gas( r ₅₀₀) converges to  ≈(0.12 ± 0.02)( h /0.72)^−1.5  , where the uncertainty reflects the systematic variations between clusters at r ₅₀₀. This is significantly lower than the maximum-likelihood value of the baryon fraction from the recently released Wilkinson Microwave Anisotropy Probe ( WMAP ) 3-yr results. We investigate possible reasons for this discrepancy, including the effects of radiative cooling and non-gravitational heating, and conclude that the most likely solution is that Ω_m is higher than the best-fitting WMAP value (we find  Ω_m= 0.36^+0.11_−0.08  ), but consistent at the 2σ level. Degeneracies within the WMAP data require that σ₈ must also be greater than the maximum likelihood value for consistency between the data sets.     

A special kind of local structure in the CMB intensity maps： duel peak structure

We study the local structure of Cosmic Microwave Background (CMB) tem-perature maps released by the Wilkinson Microwave Anisotropy Probe (WMAP) team, and find a new kind of structure, which can be described as follows: a peak (or valley) of average temperature is often followed by a peak of temperature fluctuation that is 4° away. This structure is important for the following reasons: both the well known cold spot detected by Cruz et al. and the hot spot detected by Vielva et al. with the same technology (the third spot in their article) have such structure; more spots that are similar to them can be found on CMB maps and they also tend to be significant cold/hot spots; if we change the 4° characteristic into an artificial one, such as 3° or 5°, there will be less "similar spots", and the temperature peaks or valleys will be less significant. The presented "sim-ilar spots" have passed a strict consistency test which requires them to be significant on at least three different CMB temperature maps. We hope that this article could arouse some interest in the relationship of average temperature with temperature fluctuation in local areas; meanwhile, we are also trying to find an explanation for it which might be important to CMB observation and theory.     

Cosmology from 3 years of WMAP CMB data

The combined 3 year observations from the Wilkinson Microwave Anisotropy Probe (WMAP) have yielded full-sky temperature and polarization maps in five frequency bands (K, Ka, Q, V, W) between 23 and 94 GHz. In this article we discuss the cosmological implications of these observations. The combination of temperature and polarization data leads to a significant improvement in the measurement of the reionization optical depth τ = 0.093 ± 0.029. This, in turn, breaks a number of key degeneracies present in the constraints from temperature measurements alone allowing the WMAP CMB data on its own to offer a powerful insight into the universe’s constituents and the processes that generated the initial conditions for structure formation.     

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.     

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.     

Probing dark energy with steerable wavelets through correlation of WMAP and NVSS local morphological measures

Using local morphological measures on the sphere defined through a steerable wavelet analysis, we examine the three-year Wilkinson Microwave Anisotropy Probe WMAP and the NRAO VLA Sky Survey (NVSS) data for correlation induced by the integrated Sachs–Wolfe (ISW) effect. The steerable wavelet constructed from the second derivative of a Gaussian allows one to define three local morphological measures, namely the signed-intensity, orientation and elongation of local features. Detections of correlation between the WMAP and NVSS data are made with each of these morphological measures. The most significant detection is obtained in the correlation of the signed-intensity of local features at a significance of 99.9 per cent. By inspecting signed-intensity sky maps, it is possible for the first time to see the correlation between the WMAP and NVSS data by eye. Foreground contamination and instrumental systematics in the WMAP data are ruled out as the source of all significant detections of correlation. Our results provide new insight on the ISW effect by probing the morphological nature of the correlation induced between the cosmic microwave background and large-scale structure of the Universe. Given the current constraints on the flatness of the Universe, our detection of the ISW effect again provides direct and independent evidence for dark energy. Moreover, this new morphological analysis may be used in future to help us to better understand the nature of dark energy.     

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.     

Constraints on primordial non-Gaussianity from a needlet analysis of the WMAP-5 data

We look for a non-Gaussian signal in the Wilkinson Microwave Anisotropy Probe ( WMAP ) 5-year temperature anisotropy maps by performing a needlet-based data analysis. We use the foreground-reduced maps obtained by the WMAP team through the optimal combination of the W, V and Q channels, and perform realistic non-Gaussian simulations in order to constrain the non-linear coupling parameter f _NL. We apply a third-order estimator of the needlet coefficients skewness and compute the  χ²  statistics of its distribution. We obtain  −80 < f _NL < 120  at 95 per cent confidence level, which is consistent with a Gaussian distribution and comparable to previous constraints on the non-linear coupling. We then develop an estimator of f _NL based on the same simulations and we find consistent constraints on primordial non-Gaussianity. We finally compute the three-point correlation function in needlet space: the constraints on f _NL improve to  −50 < f _NL < 110  at 95 per cent confidence level.     

Optimisation of the Population Monte Carlo algorithm: Application to constraining isocurvature models with cosmic microwave background data

We optimise the parameters of the Population Monte Carlo algorithm using numerical simulations. The optimisation is based on an efficiency statistic related to the number of samples evaluated prior to convergence, and is applied to a D ‐dimensional Gaussian distribution to derive optimal scaling laws for the algorithm parameters. More complex distributions such as the banana and bimodal distributions are also studied. We apply these results to a cosmological parameter estimation problem that uses CMB anisotropy data from the WMAP nine‐year release to constrain a six parameter adiabatic model and a fifteen parameter admixture model, consisting of correlated adiabatic and isocurvature perturbations. In the case of the adiabatic model and the admixture model we find that the number of sample points increase by factors of 3 and 20, respectively, relative to the optimal Gaussian case. This is due to degeneracies in the underlying parameter space. The WMAP nine‐year data constrain the admixture model to have an isocurvature fraction of 36.3 ± 2.8 %. (© 2016 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Non-Gaussianity detections in the Bianchi VIIh corrected WMAP one-year data made with directional spherical wavelets

Many of the current anomalies reported in the WMAP text ( WMAP ) one-year data disappear after 'correcting' for the best-fitting embedded Bianchi type VII _h component, albeit assuming no dark energy component. We investigate the effect of this Bianchi correction on the detections of non-Gaussianity in the WMAP data that we previously made using directional spherical wavelets. We confirm that the deviations from Gaussianity in the kurtosis of spherical Mexican hat wavelet coefficients are eliminated once the data are corrected for the Bianchi component, as previously discovered by Jaffe et al. This is due to the reduction of the cold spot at Galactic coordinates  ( l , b ) = (209°, −57°)  , which Cruz et al. claimed to be the sole source of non-Gaussianity introduced in the kurtosis. Our previous detections of non-Gaussianity observed in the skewness of spherical wavelet coefficients are not reduced by the Bianchi correction. Indeed, the most significant detection of non-Gaussianity made with the spherical real Morlet wavelet at a significant level of 98.4 per cent remains (using a very conservative method to estimate the significance). Furthermore, we perform preliminary tests to determine if foregrounds or systematics are the source of this non-Gaussian signal, concluding that it is unlikely that these factors are responsible. We make our code to simulate Bianchi-induced temperature fluctuations publicly available.     

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.     

Blind and non-blind source detection in WMAP 5-yr maps

We have analysed the efficiency in source detection and flux density estimation of blind and non-blind detection techniques exploiting the MHW2 filter applied to the Wilkinson Microwave Anisotropy Probe ( WMAP ) 5-yr maps. A comparison with the AT20G bright source sample, with a completeness limit of 0.5 Jy and accurate flux measurements at 20 GHz, close to the lowest frequency of WMAP maps, has allowed us to assess the completeness and the reliability of the samples detected with the two approaches, as well as the accuracy of flux and error estimates, and their variations across the sky. The uncertainties on flux estimates given by our procedure turned out to be about a factor of 2 lower than the rms differences with AT20G measurements, consistent with the smoothing of the fluctuation field yielded by map filtering. Flux estimates were found to be essentially unbiased except that, close to the detection limit, a substantial fraction of fluxes are found to be inflated by the contribution of underlying positive fluctuations. This is consistent with expectations for the Eddington bias associated to the true errors on flux density estimates. The blind and non-blind approaches are found to be complementary: each of them allows the detection of sources missed by the other. Combining results of the two methods on the WMAP 5-yr maps, we have expanded the non-blindly generated New Extragalactic WMAP Point Source (NEWPS) catalogue that was based on WMAP 3-yr maps. After having removed the probably spurious objects not identified with known radio sources, the new version of the NEWPS catalogue, NEWPS_5yr comprises 484 sources detected with a signal-to-noise ratio  SNR ≥ 5  .     

The statistical significance of the low cosmic microwave background mulitipoles

The Wilkinson Microwave Anisotropy Probe ( WMAP ) has measured lower amplitudes for the temperature quadrupole and octopole anisotropies than expected in the best fitting (concordance) Λ-dominated cold dark matter (ΛCDM) cosmology. Some authors have argued that this discrepancy may require new physics. However, the statistical significance of this result is not clear. Some authors have applied frequentist arguments and claim that the discrepancy would occur by chance about 1 time in 700, if the concordance model is correct. Other authors have used Bayesian arguments to claim that the data show marginal evidence for new physics. I investigate these confusing and apparently conflicting claims in this Letter using a frequentist analysis and a simplified Bayesian analysis. On either analysis, I conclude that the WMAP results are consistent with the concordance ΛCDM model.     

No Higher Criticism of the Bianchi-corrected Wilkinson Microwave Anisotropy Probe data

Higher Criticism (HC) has been proposed by Donoho & Jin as an effective statistic to detect deviations from Gaussianity. Motivated by the success of the Bianchi VII_h model in addressing many of the anomalies observed in the Wilkinson Microwave Anisotropy Probe ( WMAP ) data (Jaffe et al.), we present calculations in real and in wavelet space of the HC statistic of the Bianchi-corrected WMAP first-year data. At the wavelet scale of 5°, the HC of the WMAP map drops from a value above the 99 per cent confidence level (c.l.) to a value below the 68 per cent CL when corrected by the Bianchi template. An important property of the HC statistic is its ability to locate the pixels that account for the deviation from Gaussianity. The analysis of the uncorrected WMAP data pointed to a cold spot in the Southern hemisphere, centred at   l ∼ 209°, b ∼−57°  . The HC of the Bianchi-corrected map indicates that this spot remains prominent, albeit at a level completely consistent with Gaussian statistics. Consequently, it is debatable how much emphasis should be placed on this residual feature, but we consider the effect of modestly increasing the scaling of the template. A factor of only 1.2 renders the spot indistinguishable from the background level, with no noticeable impact on the results published in Jaffe et al. for the low- l anomalies, large-scale power asymmetry or wavelet kurtosis. A trivial interpretation would be that the Bianchi template may require a small enhancement of power on scales corresponding to the wavelet scale of 5°.     

Primordial magnetic fields in the post-recombination era and early reionization

We explore the ways in which primordial magnetic fields influence the thermal and ionization history of the post-recombination Universe. After recombination, the Universe becomes mostly neutral, resulting also in a sharp drop in the radiative viscosity. Primordial magnetic fields can then dissipate their energy into the intergalactic medium via ambipolar diffusion and, for small enough scales, by generating decaying magnetohydrodynamics turbulence. These processes can significantly modify the thermal and ionization history of the post-recombination Universe. We show that the dissipation effects of magnetic fields, which redshifts to a present value   B ₀= 3 × 10⁻⁹ G  smoothed on the magnetic Jeans scale and below, can give rise to Thomson scattering optical depths  τ≳ 0.1  , although not in the range of redshifts needed to explain the recent Wilkinson Microwave Anisotropy Probe ( WMAP ) polarization observations. We also study the possibility that primordial fields could induce the formation of subgalactic structures for   z ≳ 15  . We show that early structure formation induced by nanoGauss magnetic fields is potentially capable of producing the early reionization implied by the WMAP data. Future cosmic microwave background observations will be very useful to probe the modified ionization histories produced by primordial magnetic field evolution and constrain their strength.     

Cross-Correlation Detection of Point Sources in the WMAP First Year Data

We apply a Cross-Correlation (CC) method developed previously for detecting gamma-ray point sources to the WMAP first year data by using the Point-Spread Function of WMAP and obtain a full sky CC coefficient map. We find that the CC method is a pow- erful tool to examine the WMAP foreground residuals which can be further cleaned accord- ingly. Evident foreground signals are found in the WMAP foreground cleaned maps and the Tegmark cleaned map. In this process 101 point sources are detected, and 26 of them are new sources additional to the originally listed WMAP 208 sources. We estimate the ?ux of these new sources and verify them by another method. As a result, a revised mask file based on the WMAP first year data is produced by including these new sources.     

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.