We study the cosmological information of weak lensing (WL) peaks, focusing on two other statistics besides their abundance: the stacked tangential-shear profiles and the peak-peak correlation function. We use a large ensemble of simulated WL maps wit
h survey specifications relevant to future missions like Euclid and LSST, to explore the three peak probes. We find that the correlation function of peaks with high signal-to-noise (S/N) measured from fields of size 144 sq. deg. has a maximum of ~0.3 at an angular scale ~10 arcmin. For peaks with smaller S/N, the amplitude of the correlation function decreases, and its maximum occurs on smaller angular scales. We compare the peak observables measured with and without shape noise and find that for S/N~3 only ~5% of the peaks are due to large-scale structures, the rest being generated by shape noise. The covariance matrix of the probes is examined: the correlation function is only weakly covariant on scales < 30 arcmin, and slightly more on larger scales; the shear profiles are very correlated for theta > 2 arcmin, with a correlation coefficient as high as 0.7. Using the Fisher-matrix formalism, we compute the cosmological constraints for {Om_m, sig_8, w, n_s} considering each probe separately, as well as in combination. We find that the correlation function of peaks and shear profiles yield marginalized errors which are larger by a factor of 2-4 for {Om_m, sig_8} than the errors yielded by the peak abundance alone, while the errors for {w, n_s} are similar. By combining the three probes, the marginalized constraints are tightened by a factor of ~2 compared to the peak abundance alone, the least contributor to the error reduction being the correlation function. This work therefore recommends that future WL surveys use shear peaks beyond their abundance in order to constrain the cosmological model.
Through a large ensemble of Gaussian realisations and a suite of large-volume N-body simulations, we show that in a standard LCDM scenario, supervoids and superclusters in the redshift range $zin[0.4,0.7]$ should leave a {em small} signature on the I
SW effect of the order $sim 2 mu$K. We perform aperture photometry on WMAP data, centred on such superstructures identified from SDSS LRGs, and find amplitudes at the level of 8 -- 11$ mu$K -- thus confirming the earlier work of Granett et al 2008. If we focus on apertures of the size $sim3.6degr$, then our realisations indicate that LCDM is discrepant at the level of $sim4 sigma$. If we combine all aperture scales considered, ranging from 1degr--20degr, then the discrepancy becomes $sim2sigma$, and it further lowers to $sim 0.6 sigma$ if only 30 superstructures are considered in the analysis (being compatible with no ISW signatures at $1.3sigma$ in this case). Full-sky ISW maps generated from our N-body simulations show that this discrepancy cannot be alleviated by appealing to Rees-Sciama mechanisms, since their impact on the scales probed by our filters is negligible. We perform a series of tests on the WMAP data for systematics. We check for foreground contaminants and show that the signal does not display the correct dependence on the aperture size expected for a residual foreground tracing the density field. The signal also proves robust against rotation tests of the CMB maps, and seems to be spatially associated to the angular positions of the supervoids and superclusters. We explore whether the signal can be explained by the presence of primordial non-Gaussianities of the local type. We show that for models with $FNL=pm100$, whilst there is a change in the pattern of temperature anisotropies, all amplitude shifts are well below $<1mu$K.
