Responses in Large-Scale Structure

Abstract

We introduce a rigorous definition of general power-spectrum responses as resummed vertices with two hard and $n$ soft momenta in cosmological perturbation theory. These responses measure the impact of long-wavelength perturbations on the local small-scale power spectrum. The kinematic structure of the responses (i.e., their angular dependence) can be decomposed unambiguously through a "bias" expansion of the local power spectrum, with a fixed number of physical response coefficients, which are only a function of the hard wavenumber $k$. Further, the responses up to $n$-th order completely describe the $(n+2)$-point function in the squeezed limit, i.e. with two hard and $n$ soft modes, which one can use to derive the response coefficients. This generalizes previous results, which relate the angle-averaged squeezed limit to isotropic response coefficients. We derive the complete expression of first- and second-order responses at leading order in perturbation theory, and present extrapolations to nonlinear scales based on simulation measurements of the isotropic response coefficients. As an application, we use these results to predict the non-Gaussian part of the angle-averaged matter power spectrum covariance ${\mathrm{Cov}}_{\ell =0}^{\mathrm{NG}}(k_1,k_2)$, in the limit where one of the modes, say $k_2$, is much smaller than the other. Without any free parameters, our model results are in very good agreement with simulations for $k_2\lesssim 0.06h/\mathrm{Mpc}$, and for any $k_1\gtrsim 2k_2$. The well-defined kinematic structure of the power spectrum response also permits a quick evaluation of the angular dependence of the covariance matrix. While we focus on the matter density field, the formalism presented here can be generalized to generic tracers such as galaxies.

28 pages + appendices and references. 5 figures. Comments welcomed

References in corpus (14)

• The Effective Field Theory of Cosmological Large Scale Structures
• Multi-Point Propagators in Cosmological Gravitational Instability
• Separate Universe Simulations
• Simulations of Baryon Acoustic Oscillations II: Covariance matrix of the matter power spectrum
• Probing dark energy with cluster counts and cosmic shear power spectra: including the full covariance
• Analytic model for the matter power spectrum, its covariance matrix, and baryonic effects
• Super-Sample Signal
• Near optimal bispectrum estimators for large-scale structure
• Large-scale assembly bias of dark matter halos
• Perturbative approach to covariance matrix of the matter power spectrum
• Matter Power Spectrum Covariance Matrix from the DEUS-PUR ΛCDM simulations: Mass Resolution and non-Gaussian Errors
• Principal Shapes and Squeezed Limits in the Effective Field Theory of Large Scale Structure
• Response approach to the squeezed-limit bispectrum: application to the correlation of quasar and Lyman-$\alpha$ forest power spectrum
• On Soft Limits of Large-Scale Structure Correlation Functions

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