Renormalized Cosmological Perturbation Theory

Abstract

We develop a new formalism to study nonlinear evolution in the growth of large-scale structure, by following the dynamics of gravitational clustering as it builds up in time. This approach is conveniently represented by Feynman diagrams constructed in terms of three objects: the initial conditions (e.g. perturbation spectrum), the vertex (describing non-linearities) and the propagator (describing linear evolution). We show that loop corrections to the linear power spectrum organize themselves into two classes of diagrams: one corresponding to mode-coupling effects, the other to a renormalization of the propagator. Resummation of the latter gives rise to a quantity that measures the memory of perturbations to initial conditions as a function of scale. As a result of this, we show that a well-defined (renormalized) perturbation theory follows, in the sense that each term in the remaining mode-coupling series dominates at some characteristic scale and is subdominant otherwise. This is unlike standard perturbation theory, where different loop corrections can become of the same magnitude in the nonlinear regime. In companion papers we compare the resummation of the propagator with numerical simulations, and apply these results to the calculation of the nonlinear power spectrum. Remarkably, the expressions in renormalized perturbation theory can be written in a way that closely resembles the halo model.

22 pages, 13 figures. Final (published) version

References in corpus (11)

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Cited by in corpus (421)

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• On the origin of transient features in cosmological N-Body Simulations
• Towards a Gravity Dual for the Large Scale Structure of the Universe
• Perturbation theory challenge for cosmological parameters estimation II.: Matter power spectrum in redshift space
• The Effective Field Theory of Large Scale Structures of a Fuzzy Dark Matter Universe
• Linear and non-linear Modified Gravity forecasts with future surveys
• Large-k Limit of Multi-Point Propagators in the RG Formalism
• The reach of next-to-leading-order perturbation theory for the matter bispectrum
• Self-similarity and stable clustering in a family of scale-free cosmologies
• Perturbation Theory Remixed II: Improved Modeling of Nonlinear Bispectrum
• Implementing spectra response function approaches for fast calculation of power spectra and bispectra
• Stability analysis of fluid flows using Lagrangian Perturbation Theory (LPT): application to the plane Couette flow
• Modeling and measuring the anisotropic halo 3-point correlation function: a coordinated study
• The Large Scale Structure Bootstrap: perturbation theory and bias expansion from symmetries
• Kinetic field theory: generic effects of alternative gravity theories on non-linear cosmic density-fluctuations
• New tests of dark sector interactions from the full-shape galaxy power spectrum
• The effect of massive neutrinos on the BAO peak
• On the symmetry properties of the PT kernels and recurrence relations
• Cosmic structure from the path integral of classical mechanics and its comparison to standard perturbation theory
• Lagrangian-space Gaussian ansatz for the matter redshift-space power spectrum and correlation function
• Testing growth rate dependence in cosmological perturbation theory using scale-free models
• Baryon-photon interactions in Resummed Kinetic Field Theory
• Stable Clustering Ansatz, Consistency Relations and Gravity Dual of Large-Scale Structure
• Systematic treatment of non-linear effects in Baryon Acoustic Oscillations
• Kinematic effects of the velocity fluctuations for dark halos population in LCDM model
• Addressing Dipole Tension via Clustering in $\Lambda$CDM and beyond
• On the Statistical Evolution of the Large-scale Structure and the Effective Dynamics
• Sensitivity of Cosmological Parameter Estimation to Nonlinear Prescription from Cosmic Shear
• Lagrangian Perturbation Theory for Biased Tracers: Significance of the Number Conservation
• The impact of projection effects on cluster observables: stacked lensing and projected clustering
• Testing Large-Scale Structure Measurements Against Fisher Matrix Predictions