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Register a new userIncreasing the Fisher Information Content in the Matter Power Spectrum by Non-linear Wavelet Weiner Filtering
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We develop a purely mathematical tool to recover some of the information lost in the non-linear collapse of large-scale structure. From a set of 141 simulations of dark matter density fields, we construct a non-linear Weiner filter in order to separate Gaussian and non-Gaussian structure in wavelet space. We find that the non-Gaussian power is dominant at smaller scales, as expected from the theory of structure formation, while the Gaussian counterpart is damped by an order of magnitude on small scales. We find that it is possible to increase the Fisher information by a factor of three before reaching the translinear plateau, an effect comparable to other techniques like the linear reconstruction of the density field.
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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.
Reconstruction techniques are commonly used in cosmology to reduce complicated nonlinear behaviours to a more tractable linearized system. We study a new reconstruction technique that uses the Moving-Mesh algorithm to estimate the displacement field from nonlinear matter distribution. We show the performance of this new technique by quantifying its ability to reconstruct linear modes. We study the cumulative Fisher information $I(<k_n)$ about the initial matter power spectrum in the matter power spectra in 130 $N$-body simulations before and after reconstruction, and find that the nonlinear plateau of $I(<k_n)$ is increased by a factor of $sim 50$ after reconstruction, from $I simeq 2.5 times 10^{-5} /({rm Mpc}/h)^3$ to $I simeq 1.3 times 10^{-3}/({rm Mpc}/h)^3$ at large $k$. This result includes the decorrelation between initial and final fields, which has been neglected in some previous studies. We expect this technique to be beneficial to problems such as baryonic acoustic oscillations, redshift space distortions and cosmic neutrinos that rely on accurately disentangling nonlinear evolution from underlying linear effects.
Numerical simulations of massive neutrino cosmologies consistently find a spoon-like feature in the non-linear matter power spectrum ratios of cosmological models that differ only in the neutrino mass fraction f_N. Typically, the ratio approaches unity at low wave numbers k, decreases by ~ 10 f_N at k ~ 1 h/Mpc, and turns up again at large k. Using the halo model of large-scale structure, we show that this spoon feature originates in the transition from the two-halo power spectrum to the one-halo power spectrum. The formers sensitivity to f_N rises with k, while that of the latter decreases with k. The presence of this spoon feature is robust with respect to different choices of the halo mass function and the halo density profile, and does not require any parameter tuning within the halo model. We demonstrate that a standard halo model calculation is already able to predict the depth, width, and position of this spoon as well as its evolution with redshift z with remarkable accuracy. Predictions at z >= 1 can be further improved using non-linear perturbative inputs.
We measure the covariance of the non-linear matter power spectrum from N-body simulations using two methods. In the first case, the covariance of power is estimated from the scatter over many random realizations of the density field. In the second, we use a novel technique to measure the covariance matrix from each simulation individually by re-weighting the density field with a carefully chosen set of functions. The two methods agree at linear scales, but unexpectedly they disagree substantially at increasingly non-linear scales. Moreover, the covariance of non-linear power measured using the re-weightings method changes with box size. The numerical results are consistent with an explanation given in a companion paper, which argues that the cause of the discrepancy is beat-coupling, in which products of Fourier modes separated by a small wavevector couple by gravitational growth to the large-scale beat mode between them. We calculate the information content of the non-linear power spectrum (about the amplitude of the initial, linear power spectrum) using both methods and confirm the result of a previous paper, that at translinear scales the power spectrum contains little information over and above that in the linear power spectrum, but that there is a marked increase in information at non-linear scales. We suggest that, in real galaxy surveys, the covariance of power at non-linear scales is likely to be dominated by beat-coupling to the largest scales of the survey and that, as a result, only part of the information potentially available at non-linear scales is actually measurable from real galaxy surveys.
Constraints on gravity and cosmology will greatly benefit from performing joint clustering and weak lensing analyses on large-scale structure data sets. Utilising non-linear information coming from small physical scales can greatly enhance these constraints. At the heart of these analyses is the matter power spectrum. Here we employ a simple method, dubbed Hybrid $P_ell(k)$, based on the Gaussian Streaming Model (GSM), to calculate the quasi non-linear redshift space matter power spectrum multipoles. This employs a fully non-linear and theoretically general prescription for the matter power spectrum. We test this approach against comoving Lagrangian acceleration simulation measurements performed in GR, DGP and $f(R)$ gravity and find that our method performs comparably or better to the dark matter TNS redshift space power spectrum model for dark matter. When comparing the redshift space multipoles for halos, we find that the Gaussian approximation of the GSM with a linear bias and a free stochastic term, $N$, is competitive to the TNS model. Our approach offers many avenues for improvement in accuracy as well as further unification under the halo model.
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