The Angular Power Spectrum of the First-Year WMAP Data Reanalysed

We measure the angular power spectrum of the WMAP first-year temperature anisotropy maps. We use SpICE (Spatially Inhomogeneous Correlation Estimator) to estimate Cl's for multipoles l=2-900 from all possible cross-correlation channels. Except for the map-making stage, our measurements provide an independent analysis of that by Hinshaw etal (2003). Despite the different methods used, there is virtually no difference between the two measurements for l < 700 ; the highest l's are still compatible within 1-sigma errors. We use a novel intra-bin variance method to constrain Cl errors in a model independent way. When applied to WMAP data, the intra-bin variance estimator yields diagonal errors 10% larger than those reported by the WMAP team for 100 < l < 450. This translates into a 2.4 sigma detection of systematics since no difference is expected between the SpICE and the WMAP team estimator window functions in this multipole range. With our measurement of the Cl's and errors, we get chi^2/d.o.f. = 1.042 for a best-fit LCDM model, which has a 14% probability, whereas the WMAP team obtained chi^2/d.o.f. = 1.066, which has a 5% probability. We assess the impact of our results on cosmological parameters using Markov Chain Monte Carlo simulations. From WMAP data alone, assuming spatially flat power law LCDM models, we obtain the reionization optical depth tau = 0.145 +/- 0.067, spectral index n_s = 0.99 +/- 0.04, Hubble constant h = 0.67 +/- 0.05, baryon density Omega_b h^2 = 0.0218 +/- 0.0014, cold dark matter density Omega_{cdm} h^2 = 0.122 +/- 0.018, and sigma_8 = 0.92 +/- 0.12, consistent with a reionization redshift z_{re} = 16 +/- 5 (68% CL).Comment: Matches version accepted by ApJ Letters. Main changes: emphasizes chi2 value for best-fit model given our estimate of Cls and errors vs. WMAP team's. Potential detection of systematics in WMAP data quantified. Power spectrum and other data files available at http://www.ifa.hawaii.edu/cosmowave/wmap.htm

Holographic Quantum Statistics from Dual Thermodynamics

We propose dual thermodynamics corresponding to black hole mechanics with the identifications E' -> A/4, S' -> M, and T' -> 1/T in Planck units. Here A, M and T are the horizon area, mass and Hawking temperature of a black hole and E', S' and T' are the energy, entropy and temperature of a corresponding dual quantum system. We show that, for a Schwarzschild black hole, the dual variables formally satisfy all three laws of thermodynamics, including the Planck-Nernst form of the third law requiring that the entropy tend to zero at low temperature. This is in contrast with traditional black hole thermodynamics, where the entropy is singular. Once the third law is satisfied, it is straightforward to construct simple (dual) quantum systems representing black hole mechanics. As an example, we construct toy models from one dimensional (Fermi or Bose) quantum gases with N ~ M in a Planck scale box. In addition to recovering black hole mechanics, we obtain quantum corrections to the entropy, including the logarithmic correction obtained by previous papers. The energy-entropy duality transforms a strongly interacting gravitational system (black hole) into a weakly interacting quantum system (quantum gas) and thus provides a natural framework for the quantum statistics underlying the holographic conjecture.Comment: 10 page

Constraining Primordial Non-Gaussianities from the WMAP2 2-1 Cumulant Correlator Power Spectrum

We measure the 2-1 cumulant correlator power spectrum $C^{21}_l$, a degenerate bispectrum, from the second data release of the Wilkinson Microwave Anisotropy Probe (WMAP). Our high resolution measurements with SpICE span a large configuration space ($\simeq 168\times999$) corresponding to the possible cross-correlations of the maps recorded by the different differencing assemblies. We present a novel method to recover the eigenmodes of the correspondingly large Monte Carlo covariance matrix. We examine its eigenvalue spectrum and use random matrix theory to show that the off diagonal terms are dominated by noise. We minimize the $\chi^2$ to obtain constraints for the non-linear coupling parameter $f_{NL} = 22 \pm 52 (1\sigma)$.Comment: 4 pages,2 figures; typos corrected, references change

Optimal non-linear transformations for large scale structure statistics

Recently, several studies proposed non-linear transformations, such as a logarithmic or Gaussianization transformation, as efficient tools to recapture information about the (Gaussian) initial conditions. During non-linear evolution, part of the cosmologically relevant information leaks out from the second moment of the distribution. This information is accessible only through complex higher order moments or, in the worst case, becomes inaccessible to the hierarchy. The focus of this work is to investigate these transformations in the framework of Fisher information using cosmological perturbation theory of the matter field with Gaussian initial conditions. We show that at each order in perturbation theory, there is a polynomial of corresponding order exhausting the information on a given parameter. This polynomial can be interpreted as the Taylor expansion of the maximally efficient "sufficient" observable in the non-linear regime. We determine explicitly this maximally efficient observable for local transformations. Remarkably, this optimal transform is essentially the simple power transform with an exponent related to the slope of the power spectrum; when this is -1, it is indistinguishable from the logarithmic transform. This transform Gaussianizes the distribution, and recovers the linear density contrast. Thus a direct connection is revealed between undoing of the non-linear dynamics and the efficient capture of Fisher information. Our analytical results were compared with measurements from the Millennium Simulation density field. We found that our transforms remain very close to optimal even in the deeply non-linear regime with \sigma^2 \sim 10.Comment: 11 pages, matches version accepted for publication in MNRA

Determining Bias with Cumulant Correlators

The first non-trivial cumulant correlator of the galaxy density field $Q_{21}$ is examined from the point of view of biasing. It is shown that to leading order it depends on two biasing parameters $b$, and $b_2$, and on $q_{21}$, the underlying cumulant correlator of the mass. As the skewness $Q_3$ has analogous properties, the slope of the correlation function $-\gamma$, $Q_3$, and $Q_{21}$ uniquely determine the bias parameter on a particular scale to be $b = \gamma/6(Q_{21}-Q_3)$, when working in the context of gravitational instability with Gaussian initial conditions. Thus on large scales, easily accessible with the future Sloan Digital Sky Survey and the 2 Degree Field Survey, it will be possible to extract $b$, and $b_2$ from simple counts in cells measurements. Moreover, the higher order cumulants, $Q_N$, successively determine the higher order biasing parameters. From these it is possible to predict higher order cumulant correlators as well. Comparing the predictions with the measurements will provide internal consistency checks on the validity of the assumptions in the theory, most notably perturbation theory of the growth of fluctuations by gravity and Gaussian initial conditions. Since the method is insensitive to $\Omega$, it can be successfully combined with results from velocity fields, which determine $\Omega^{0.6}/b$, to measure the total density parameter in the universe.Comment: 4 pages, submitted to MNRAS pink page

On Recovering the Nonlinear Bias Function from Counts in Cells Measurements

We present a simple and accurate method to constrain galaxy bias based on the distribution of counts in cells. The most unique feature of our technique is that it is applicable to non-linear scales, where both dark matter statistics and the nature of galaxy bias are fairly complex. First, we estimate the underlying continuous distribution function from precise counts-in-cells measurements assuming local Poisson sampling. Then a robust, non-parametric inversion of the bias function is recovered from the comparison of the cumulative distributions in simulated dark matter and galaxy catalogs. Obtaining continuous statistics from the discrete counts is the most delicate novel part of our recipe. It corresponds to a deconvolution of a (Poisson) kernel. For this we present two alternatives: a model independent algorithm based on Richardson-Lucy iteration, and a solution using a parametric skewed lognormal model. We find that the latter is an excellent approximation for the dark matter distribution, but the model independent iterative procedure is more suitable for galaxies. Tests based on high resolution dark matter simulations and corresponding mock galaxy catalogs show that we can reconstruct the non-linear bias function down to highly non-linear scales with high precision in the range of $-1 \le \delta \le 5$. As far as the stochasticity of the bias, we have found a remarkably simple and accurate formula based on Poisson noise, which provides an excellent approximation for the scatter around the mean non-linear bias function. In addition we have found that redshift distortions have a negligible effect on our bias reconstruction, therefore our recipe can be safely applied to redshift surveys.Comment: 32 pages, 18 figures; submitted to Ap