Removable Matter-Power-Spectrum Covariance from Bias Fluctuations

We find a simple, accurate model for the covariance matrix of the real-space cosmological matter power spectrum on slightly nonlinear scales (k~0.1-0.8 h/Mpc at z=0), where off-diagonal matrix elements become substantial. The model includes a multiplicative, scale-independent modulation of the power spectrum. It has only one parameter, the variance (among realizations) of the variance of the nonlinear density field in cells, with little dependence on the cell size between 2-8 Mpc/h. Furthermore, we find that this extra covariance can be modeled out by instead measuring the power spectrum of (delta/sigma_cell), i.e. the ratio of the overdensity to its dispersion in cells a few Mpc in size. Dividing delta by sigma_cell essentially removes the non-Gaussian part of the covariance matrix, nearly diagonalizing it.Comment: Accepted to ApJ. 5 pages, 5 figures; slight clarifications to match accepted versio

Ringing the initial Universe: the response of overdensity and transformed-density power spectra to initial spikes

We present an experiment in which we 'ring' a set of cosmological N-body-simulation initial conditions, placing spikes in the initial power spectrum at different wavenumber bins. We then measure where these spikes end up in the final conditions. In the usual overdensity power spectrum, most sensitive to contracting and collapsing dense regions, initial power on slightly non-linear scales (k ~ 0.3 h/Mpc) smears to smaller scales, coming to dominate the initial power once there. Log-density and Gaussianized-density power spectra, sensitive to low-density (expanding) and high-density regions, respond differently: initial spikes spread symmetrically in scale, both upward and downward. In fact, in the power spectrum of 1/(1 + {\delta}), spikes migrate to larger scales, showing the magnifying effect of voids on small-scale modes. These power spectra show much greater sensitivity to small-scale initial features. We also test the difference between an approximation of the Ly-{\alpha} flux field, and its Gaussianized form, and give a toy model that qualitatively explains the symmetric power spreading in Gaussianized-density power spectra. Also, we discuss how to use this framework to estimate power-spectrum covariance matrices. This can be used to track the fate of information in the Universe, that takes the form of initial degrees of freedom, one random spike per initial mode.Comment: Accepted to MNRAS Letters. 6 pages, 5 figure

On the inadequacy of N-point correlation functions to describe nonlinear cosmological fields: explicit examples and connection to simulations

Motivated by recent results on lognormal statistics showing that the moment hierarchy of a lognormal variable completely fails at capturing its information content in the large variance regime, we discuss in this work the inadequacy of the hierarchy of correlation functions to describe a correlated lognormal field, which provides a roughly accurate description of the non-linear cosmological matter density field. We present families of fields having the same hierarchy of correlation functions than the lognormal field at all orders. This explicitly demonstrates the little studied though known fact that the correlation function hierarchy never provides a complete description of a lognormal field, and that it fails to capture information in the non-linear regime, where other simple observables are left totally unconstrained. We discuss why perturbative, Edgeworth-like approaches to statistics in the non-linear regime, common in cosmology, can never reproduce or predict that effect, and why it is however generic for tailed fields, hinting at a breakdown of the perturbation theory based on the field fluctuations. We make a rough but successful quantitative connection to N-body simulations results, that showed that the spectrum of the log-density field carries more information than the spectrum of the field entering the non-linear regime.Comment: 10 pages, 3 figures, matches version accepted for publication by ApJ. Some editing in the conclusion and minor changes w.r.t. v