We use the cosmic shear data from the Canada-France-Hawaii Telescope Lensing Survey to place constraints on $f(R)$ and {it Generalized Dilaton} models of modified gravity. This is highly complimentary to other probes since the constraints mainly come
from the non-linear scales: maximal deviations with respects to the General-Relativity + $Lambda$CDM scenario occurs at $ksim1 h mbox{Mpc}^{-1}$. At these scales, it becomes necessary to account for known degeneracies with baryon feedback and massive neutrinos, hence we place constraints jointly on these three physical effects. To achieve this, we formulate these modified gravity theories within a common tomographic parameterization, we compute their impact on the clustering properties relative to a GR universe, and propagate the observed modifications into the weak lensing $xi_{pm}$ quantity. Confronted against the cosmic shear data, we reject the $f(R)$ ${ |f_{R_0}|=10^{-4}, n=1}$ model with more than 99.9% confidence interval (CI) when assuming a $Lambda$CDM dark matter only model. In the presence of baryonic feedback processes and massive neutrinos with total mass up to 0.2eV, the model is disfavoured with at least 94% CI in all different combinations studied. Constraints on the ${ |f_{R_0}|=10^{-4}, n=2}$ model are weaker, but nevertheless disfavoured with at least 89% CI. We identify several specific combinations of neutrino mass, baryon feedback and $f(R)$ or Dilaton gravity models that are excluded by the current cosmic shear data. Notably, universes with three massless neutrinos and no baryon feedback are strongly disfavoured in all modified gravity scenarios studied. These results indicate that competitive constraints may be achieved with future cosmic shear data.
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.
At high angular frequencies, beyond the damping tail of the primary power spectrum, the dominant contribution to the power spectrum of cosmic microwave background (CMB) temperature fluctuations is the thermal Sunyaev-Zeldovich (tSZ) effect. We invest
igate various important statistical properties of the Sunyaev-Zeldovich maps, using well-motivated models for dark matter clustering to construct statistical descriptions of the tSZ effect to all orders enabling us to determine the entire probability distribution function (PDF). Any generic deterministic biasing scheme can be incorporated in our analysis and the effects of projection, biasing and the underlying density distribution can be analysed separately and transparently in this approach. We introduce the cumulant correlators as tools to analyse tSZ catalogs and relate them to corresponding statistical descriptors of the underlying density distribution. The statistics of hot spots in frequency-cleaned tSZ maps are also developed in a self-consistent way to an arbitrary order, to obtain results complementary to those found using the halo model. We also consider different beam sizes, to check the extent to which the PDF can be extracted from various observational configurations. The formalism is presented with two specific models for underlying matter clustering: (1) the hierarchical ansatz; and (2) the lognormal distribution. We find both models to be in very good agreement with the simulation results, though the lognormal model has an edge over the hierarchical model.
At high angular frequencies the thermal Sunyaev-Zeldovich (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 prope
rties provide estimates of corresponding properties of the projected 3D pressure fluctuations. Its 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.
We present a new harmonic-domain approach for extracting morphological information, in the form of Minkowski Functionals (MFs), from weak lensing (WL) convergence maps. Using a perturbative expansion of the MFs, which is expected to be valid for the
range of angular scales probed by most current weak-lensing surveys, we show that the study of three generalized skewness parameters is equivalent to the study of the three MFs defined in two dimensions. We then extend these skewness parameters to three associated skew-spectra which carry more information about the convergence bispectrum than their one-point counterparts. We discuss various issues such as noise and incomplete sky coverage in the context of estimation of these skew-spectra from realistic data. Our technique provides an alternative to the pixel-space approaches typically used in the estimation of MFs, and it can be particularly useful in the presence of masks with non-trivial topology. Analytical modeling of weak lensing statistics relies on an accurate modeling of the statistics of underlying density distribution. We apply three different formalisms to model the underlying dark-matter bispectrum: the hierarchical ansatz, halo model and a fitting function based on numerical simulations; MFs resulting from each of these formalisms are computed and compared. We investigate the extent to witch late-time gravity-induced non-Gaussianity (to which weak lensing is primarily sensitive) can be separated from primordial non-Gaussianity and how this separation depends on source redshift and angular scale.
We generalize the concept of the ordinary skew-spectrum to probe the effect of non-Gaussianity on the morphology of Cosmic Microwave Background (CMB) maps in several domains: in real-space (where they are commonly known as cumulant-correlators), and
in harmonic and needlet bases. The essential aim is to retain more information than normally contained in these statistics, in order to assist in determining the source of any measured non-Gaussianity, in the same spirit as Munshi & Heavens (2010) skew-spectra were used to identify foreground contaminants to the CMB bispectrum in Planck data. Using a perturbative series to construct the Minkowski Functionals (MFs), we provide a pseudo-Cl based approach in both harmonic and needlet representations to estimate these spectra in the presence of a mask and inhomogeneous noise. Assuming homogeneous noise we present approx- imate expressions for error covariance for the purpose of joint estimation of these spectra. We present specific results for four different models of primordial non-Gaussianity local, equilateral, orthogonal and enfolded models, as well as non-Gaussianity caused by unsubtracted point sources. Closed form results of next-order corrections to MFs too are obtained in terms of a quadruplet of kurt-spectra. We also use the method of modal decomposition of the bispectrum and trispectrum to reconstruct the MFs as an alternative method of reconstruction of morphological properties of CMB maps. Finally, we introduce the odd-parity skew-spectra to probe the odd-parity bispectrum and its impact on the morphology of the CMB sky. Although developed for the CMB, the generic results obtained here can be useful in other areas of cosmology.
