Renormalizing a Viscous Fluid Model for Large Scale Structure Formation

Abstract

Using the Stochastic Adhesion Model (SAM) as a simple toy model for cosmic structure formation, we study renormalization and the removal of the cutoff dependence from loop integrals in perturbative calculations. SAM shares the same symmetry with the full system of continuity+Euler equations and includes a viscosity term and a stochastic noise term, similar to the effective theories recently put forward to model CDM clustering. We show in this context that if the viscosity and noise terms are treated as perturbative corrections to the standard eulerian perturbation theory, they are necessarily non-local in time. To ensure Galilean Invariance higher order vertices related to the viscosity and the noise must then be added and we explicitly show at one-loop that these terms act as counter terms for vertex diagrams. The Ward Identities ensure that the non-local-in-time theory can be renormalized consistently. Another possibility is to include the viscosity in the linear propagator, resulting in exponential damping at high wavenumber. The resulting local-in-time theory is then renormalizable to one loop, requiring less free parameters for its renormalization.

v1: 12 pages, 3 figures, v2: 14 pages, 3 figure, extended discussion on the need of non-local counter terms, version accepted by JCAP

References in corpus (12)

• The Effective Field Theory of Cosmological Large Scale Structures
• Resumming Cosmological Perturbations via the Lagrangian Picture: One-loop Results in Real Space and in Redshift Space
• The IR-resummed Effective Field Theory of Large Scale Structures
• Flowing with Time: a New Approach to Nonlinear Cosmological Perturbations
• A Lagrangian effective field theory
• The Bispectrum in the Effective Field Theory of Large Scale Structure
• Large-N expansions applied to gravitational clustering
• Large scale structure from viscous dark matter
• Soft-Pion Theorems for Large Scale Structure
• A coarse grained perturbation theory for the Large Scale Structure, with cosmology and time independence in the UV
• On Soft Limits of Large-Scale Structure Correlation Functions
• The adhesion model as a field theory for cosmological clustering

Cited by in corpus (7)

• Time-Sliced Perturbation Theory for Large Scale Structure I: General Formalism
• The matter power spectrum in redshift space using effective field theory
• Large-scale structure perturbation theory without losing stream crossing
• Renormalization-group flow of the effective action of cosmological large-scale structures
• The dark matter dispersion tensor in perturbation theory
• The dark matter bispectrum from effective viscosity and one-particle irreducible vertices
• Renormalization group computation of likelihood functions for cosmological data sets