We present novel statistical tools to cross-correlate frequency cleaned thermal Sunyaev-Zeldovich (tSZ) maps and tomographic weak lensing (wl) convergence maps. Moving beyond the lowest order cross-correlation, we introduce a hierarchy of mixed highe
r-order statistics, the cumulants and cumulant correlators, to analyze non-Gaussianity in real space, as well as corresponding polyspectra in the harmonic domain. Using these moments, we derive analytical expressions for the joint two-point probability distribution function (2PDF) for smoothed tSZ (y_s) and convergence (kappa_s) maps. The presence of tomographic information allows us to study the evolution of higher order {em mixed} tSZ-weak lensing statistics with redshift. We express the joint PDFs p_{kappa y}(kappa_s,y_s) in terms of individual one-point PDFs (p_{kappa}(kappa_s), p_y(y_s)) and the relevant bias functions (b_{kappa}(kappa_s), b_y(y_s)). Analytical results for two different regimes are presented that correspond to the small and large angular smoothing scales. Results are also obtained for corresponding {em hot spots} in the tSZ and convergence maps. In addition to results based on hierarchical techniques and perturbative methods, we present results of calculations based on the lognormal approximation. The analytical expressions derived here are generic and applicable to cross-correlation studies of arbitrary tracers of large scale structure including e.g. that of tSZ and soft X-ray background.
Motivated by recent suggestions that a number of observed galaxy clusters have masses which are too high for their given redshift to occur naturally in a standard model cosmology, we use Extreme Value Statistics to construct confidence regions in the
mass-redshift plane for the most extreme objects expected in the universe. We show how such a diagram not only provides a way of potentially ruling out the concordance cosmology, but also allows us to differentiate between alternative models of enhanced structure formation. We compare our theoretical prediction with observations, placing currently observed high and low redshift clusters on a mass-redshift diagram and find -- provided we consider the full sky to avoid a posteriori selection effects -- that none are in significant tension with concordance cosmology.
The first and third year data releases from the WMAP provide evidence of an anomalous Cold Spot (CS) at galactic latitude b=-57deg and longitude l=209deg. We have examined the properties of the CS in some detail in order to assess its cosmological si
gnificance. We have performed a cluster analysis of the local extrema in the CMB signal to show that the CS is actually associated with a large group of extrema rather than just one. In the light of this we have re-examined the properties of the WMAP ILC and co-added cleaned WCM maps, which have previously been used for the analysis of the properties of the signal in the vicinity of the CS. These two maps have remarkably similar properties on equal latitude rings for |b|>30deg, as well as in the vicinity of the CS. We have also checked the idea that the CMB signal has a non-Gaussian tail, localized in the low multipole components of the signal. For each ring we apply a linear filter with characteristic scale R, dividing the CMB signal in two parts: the filtered part, with characteristic scale above that of the filter R, and the difference between the initial and filtered signal. Using the filter scale as a variable, we can maximize the skewness and kurtosis of the smoothed signal and minimize these statistics for the difference between initial and filtered signal. We have discovered that the shape of the CS is formed primarily by the components of the CMB signal represented by multipoles between 10<=L<=20, with a corresponding angular scale about 5-10 degs. This signal leads to modulation of the whole CMB sky, clearly seen at |b|>30deg in both the ILC and WCM maps, rather than 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 study the coherent temperature and polarization patterns produced in homogeneous but anisotropic cosmological models. We show results for all Bianchi types with a Friedman-Robertson-Walker limit (i.e. Types I, V, VII$_{0}$, VII$_{h}$ and IX) to il
lustrate the range of possible behaviour. We discuss the role of spatial curvature, shear and rotation in the geodesic equations for each model and establish some basic results concerning the symmetries of the patterns produced. We also give examples of the time-evolution of these patterns in terms of the Stokes parameters $I$, $Q$ and $U$.
We calculate the temperature and polarization patterns generated in anisotropic cosmological models drawn from the Bianchi classification. We show that localized features in the temperature pattern, perhaps similar to the cold spot observed in the Wi
lkinson Microwave Anisotropy Probe (WMAP) data, can be generated in models with negative spatial curvature, i.e. Bianchi types V and VII$_{h}$. Both these models also generate coherent polarization patterns. In Bianchi VII$_h$, however, rotation of the polarization angle as light propagates along geodesics can convert E modes into B modes but in Bianchi V this is not necessarily the case. It is in principle possible, therefore, to generate localized temperature features without violating existing observational constraints on the odd-parity component of the polarization of the cosmic microwave background.
We present a simple heuristic model to demonstrate how feedback related to the galaxy formation process can result in a scale-dependent bias of mass versus light, even on very large scales. The model invokes the idea that galaxies form initially in l
ocations determined by the local density field, but the subsequent formation of galaxies is also influenced by the presence of nearby galaxies that have already formed. The form of bias that results possesses some features that are usually described in terms of stochastic effects, but our model is entirely deterministic once the density field is specified. Features in the large-scale galaxy power spectrum (such as wiggles that might in an extreme case mimic the effect of baryons on the primordial transfer function) could, at least in principle, arise from spatial modulations of the galaxy formation process that arise naturally in our model. We also show how this fully deterministic model gives rise to apparently stochasticity in the galaxy distribution.
Scale transformations have played an extremely successful role in studies of cosmological large-scale structure by relating the non-linear spectrum of cosmological density fluctuations to the linear primordial power at longer wavelengths. Here we gen
eralize this approach to investigate the usefulness of scale transformations for nonlinear higher-order statistics, specifically the bispectrum. We find that the bispectrum predicted by perturbation theory at tree-level can be rescaled to match the results of full numerical simulations in the weakly and intermediately nonlinear regimes, especially at high redshifts, with an accuracy that is surprising given the simplicity of the procedure used. This discovery not only offers a simple practical way of calculating the matter bispectrum, but also suggests that scale transformations may yet yield even deeper insights into the physics of hierarchical clustering.
