Renormalized cosmological perturbation theory
Abstract
We develop a new formalism to study nonlinear evolution in the growth of largescale 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 nonlinearities) 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 modecoupling 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 welldefined (renormalized) perturbation theory follows, in the sense that each term in the remaining modecoupling 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 writtenmore »
 Authors:
 Center for Cosmology and Particle Physics, Department of Physics, New York University, New York, New York 10003 (United States)
 Publication Date:
 OSTI Identifier:
 20782623
 Resource Type:
 Journal Article
 Resource Relation:
 Journal Name: Physical Review. D, Particles Fields; Journal Volume: 73; Journal Issue: 6; Other Information: DOI: 10.1103/PhysRevD.73.063519; (c) 2006 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; COMPARATIVE EVALUATIONS; COMPUTERIZED SIMULATION; CORRECTIONS; COUPLING; DISTURBANCES; FEYNMAN DIAGRAM; NONLINEAR PROBLEMS; PERTURBATION THEORY; PROPAGATOR; QUANTUM FIELD THEORY; RENORMALIZATION
Citation Formats
Crocce, Martin, and Scoccimarro, Roman. Renormalized cosmological perturbation theory. United States: N. p., 2006.
Web. doi:10.1103/PHYSREVD.73.063519.
Crocce, Martin, & Scoccimarro, Roman. Renormalized cosmological perturbation theory. United States. doi:10.1103/PHYSREVD.73.063519.
Crocce, Martin, and Scoccimarro, Roman. Wed .
"Renormalized cosmological perturbation theory". United States.
doi:10.1103/PHYSREVD.73.063519.
@article{osti_20782623,
title = {Renormalized cosmological perturbation theory},
author = {Crocce, Martin and Scoccimarro, Roman},
abstractNote = {We develop a new formalism to study nonlinear evolution in the growth of largescale 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 nonlinearities) 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 modecoupling 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 welldefined (renormalized) perturbation theory follows, in the sense that each term in the remaining modecoupling 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.},
doi = {10.1103/PHYSREVD.73.063519},
journal = {Physical Review. D, Particles Fields},
number = 6,
volume = 73,
place = {United States},
year = {Wed Mar 15 00:00:00 EST 2006},
month = {Wed Mar 15 00:00:00 EST 2006}
}

We generalize the renormalized perturbation theory (RPT) formalism of Crocce and Scoccimarro [M. Crocce and R. Scoccimarro, Phys. Rev. D 73, 063519 (2006)] to deal with multiple fluids in the Universe and here we present the complete calculations up to the oneloop level in the RPT. We apply this approach to the problem of following the nonlinear evolution of baryon and cold dark matter (CDM) perturbations, evolving from the distinct sets of initial conditions, from the high redshift postrecombination Universe right through to the present day. In current theoretical and numerical models of structure formation, it is standard practice tomore »

Continuum limit of lattice gauge theories in the context of renormalized perturbation theory
It is shown that in spite of the modifications introduced by Wilson and Polyakov, the gauge theory on a lattice in the Abelian case in the limit of zero lattice spacing has the same renormalized S matrix as quantum electrodynamics, to all orders in the renormalized coupling constant. Apparently nonrenormalizable vertices contained in the lattice Lagrangian contribute to mass, wavefunction, and couplingconstant renormalizations, but do not contribute to the ''finite parts'' as a result of being multiplied by additional powers of lattice spacing. It is crucial for this renormalizability that the lattice theory respects local gauge symmetry and discrete symmetriesmore » 
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