We discuss an analytical approximation for the matter power spectrum covariance matrix and its inverse on translinear scales, $k sim 0.1h - 0.8h/textrm{Mpc}$ at $z = 0$. We proceed to give an analytical expression for the Fisher information matrix of
the nonlinear density field spectrum, and derive implications for its cosmological information content. We find that the spectrum information is characterized by a pair of upper bounds, plateaux, caused by the trispectrum, and a knee in the presence of white noise. The effective number of Fourier modes, normally growing as a power law, is bounded from above by these plateaux, explaining naturally earlier findings from $N$-body simulations. These plateaux limit best possible measurements of the nonlinear power at the percent level in a $h^{-3}textrm{Gpc}^3$ volume; the extraction of model parameters from the spectrum is limited explicitly by their degeneracy to the nonlinear amplitude. The value of the first, super-survey (SS) plateau depends on the characteristic survey volume and the large scale power; the second, intra-survey (IS) plateau is set by the small scale power. While both have simple interpretations within the hierarchical textit{Ansatz}, the SS plateau can be predicted and generalized to still smaller scales within Takada and Hus spectrum response formalism. Finally, the noise knee is naturally set by the density of tracers.
Owing to the mass-sheet degeneracy, cosmic shear maps do not probe directly the Fourier modes of the underlying mass distribution on scales comparable to the survey size and larger. To assess the corresponding effect on attainable cosmological parame
ter constraints, we quantify the information on super-survey modes in a lognormal model and, when interpreted as nuisance parameters, their degeneracies to cosmological parameters. Our analytical and numerical calculations clarify the central role of super-sample covariance (SSC) in shaping the statistical power of cosmological observables. Reconstructing the background modes from their non-Gaussian statistical dependence to small scales modes yields the renormalized convergence. This diagonalizes the spectrum covariance matrix, and the information content of the corresponding power spectrum is increased by a factor of two over standard methods. Unfortunately, careful calculation of the Cramer-Rao bound shows that the information recovery can never be made complete, any observable built from shear fields, including optimal sufficient statistics, are subject to severe information loss, typically $80%$ to $90%$ below $ell sim 3000$ for generic cosmological parameters. The lost information can only be recovered from additional, non-shear based data. Our predictions hold just as well for a tomographic analysis, and/or full sky surveys.
We use a WISE-2MASS-Pan-STARRS1 galaxy catalog to search for a supervoid in the direction of the Cosmic Microwave Background Cold Spot. We obtain photometric redshifts using our multicolor data set to create a tomographic map of the galaxy distributi
on. The radial density profile centred on the Cold Spot shows a large low density region, extending over 10s of degrees. Motivated by previous Cosmic Microwave Background results, we test for underdensities within two angular radii, $5^circ$, and $15^circ$. Our data, combined with an earlier measurement by Granett et al 2010, are consistent with a large $R_{rm void}=(192 pm 15)h^{-1} Mpc $ $(2sigma)$ supervoid with $delta simeq -0.13 pm 0.03$ centered at $z=0.22pm0.01$. Such a supervoid, constituting a $sim3.5 sigma$ fluctuation in the $Lambda CDM$ model, is a plausible cause for the Cold Spot.
The sufficient statistics of the one-point probability density function of the dark matter density field is worked out using cosmological perturbation theory and tested to the Millennium simulation density field. The logarithmic transformation is rec
overed for spectral index close to $-1$ as a special case of the family of power transformations. We then discuss how these transforms should be modified in the case of noisy tracers of the field and focus on the case of Poisson sampling. This gives us optimal local transformations to apply to galaxy survey data prior the extraction of the spectrum in order to capture most efficiently the information encoded in large scale structures.
Standard inflationary hot big bang cosmology predicts small fluctuations in the Cosmic Microwave Background (CMB) with isotropic Gaussian statistics. All measurements support the standard theory, except for a few anomalies discovered in the Wilkinson
Microwave Anisotropy Probe maps and confirmed recently by the Planck satellite. The Cold Spot is one of the most significant of such anomalies, and the leading explanation of it posits a large void that imprints this extremely cold area via the linear Integrated Sachs-Wolfe (ISW) effect due to the decay of gravitational potentials over cosmic time, or via the Rees-Sciama (RS) effect due to late-time non-linear evolution. Despite several observational campaigns targeting the Cold Spot region, to date no suitably large void was found at higher redshifts $z > 0.3$. Here we report the detection of an $R =(192 pm 15) h^{-1}Mpc$ size supervoid of depth $delta = -0.13 pm 0.03$, and centred at redshift $z = 0.22$. This supervoid, possibly the largest ever found, is large enough to significantly affect the CMB via the non-linear RS effect, as shown in our Lemaitre-Tolman-Bondi framework. This discovery presents the first plausible explanation for any of the physical CMB anomalies, and raises the possibility that local large-scale structure could be responsible for other anomalies as well.
We use the WISE-2MASS infrared galaxy catalog matched with Pan-STARRS1 (PS1) galaxies to search for a supervoid in the direction of the Cosmic Microwave Background Cold Spot. Our imaging catalog has median redshift $zsimeq 0.14$, and we obtain photom
etric redshifts from PS1 optical colours to create a tomographic map of the galaxy distribution. The radial profile centred on the Cold Spot shows a large low density region, extending over 10s of degrees. Motivated by previous Cosmic Microwave Background results, we test for underdensities within two angular radii, $5^circ$, and $15^circ$. The counts in photometric redshift bins show significantly low densities at high detection significance, $gtrsim 5 sigma$ and $gtrsim 6 sigma$, respectively, for the two fiducial radii. The line-of-sight position of the deepest region of the void is $zsimeq 0.15-0.25$. Our data, combined with an earlier measurement by Granett et al. 2010, are consistent with a large $R_{rm void}=(220 pm 50) h^{-1}Mpc $ supervoid with $delta_{m} simeq -0.14 pm 0.04$ centered at $z=0.22pm0.03$. Such a supervoid, constituting at least a $simeq 3.3sigma$ fluctuation in a Gaussian distribution of the $Lambda CDM$ model, is a plausible cause for the Cold Spot.
We measure the average temperature decrement on the cosmic microwave background (CMB) produced by voids selected in the SDSS DR7 spectroscopic redshift galaxy catalog, spanning redshifts $0<z<0.44$. We find an imprint of amplitude between 2.6 and 2.9
$mu K$ as viewed through a compensated top-hat filter scaled to the radius of each void; we assess the statistical significance of the imprint at ~2$sigma$. We make crucial use of $N$-body simulations to calibrate our analysis. As expected, we find that large voids produce cold spots on the CMB through the Integrated Sachs-Wolfe (ISW) effect. However, we also find that small voids in the halo density field produce hot spots, because they reside in contracting, larger-scale overdense regions. This is an important effect to consider when stacking CMB imprints from voids of different radius. We have found that the same filter radius that gives the largest ISW signal in simulations also yields close to the largest detected signal in the observations. However, although it is low in significance, our measured signal is much higher-amplitude than expected from ISW in the concordance $Lambda$CDM universe. The discrepancy is also at the ~2$sigma$ level. We have demonstrated that our result is robust against the varying of thresholds over a wide range.
We seek to improve estimates of the power spectrum covariance matrix from a limited number of simulations by employing a novel statistical technique known as shrinkage estimation. The shrinkage technique optimally combines an empirical estimate of th
e covariance with a model (the target) to minimize the total mean squared error compared to the true underlying covariance. We test this technique on N-body simulations and evaluate its performance by estimating cosmological parameters. Using a simple diagonal target, we show that the shrinkage estimator significantly outperforms both the empirical covariance and the target individually when using a small number of simulations. We find that reducing noise in the covariance estimate is essential for properly estimating the values of cosmological parameters as well as their confidence intervals. We extend our method to the jackknife covariance estimator and again find significant improvement, though simulations give better results. Even for thousands of simulations we still find evidence that our method improves estimation of the covariance matrix. Because our method is simple, requires negligible additional numerical effort, and produces superior results, we always advocate shrinkage estimation for the covariance of the power spectrum and other large-scale structure measurements when purely theoretical modeling of the covariance is insufficient.
