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Title: 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 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 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 writtenmore » in a way that closely resembles the halo model.« less

Authors:
;  [1]
  1. 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 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 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 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.},
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 one-loop 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 post-recombination Universe right through to the present day. In current theoretical and numerical models of structure formation, it is standard practice tomore » treat baryons and CDM as an effective single matter fluid--the so-called dark matter only modeling. In this approximation, one uses a weighed sum of late-time baryon and CDM transfer functions to set initial mass fluctuations. In this paper we explore whether this approach can be employed for high precision modeling of structure formation. We show that, even if we only follow the linear evolution, there is a large-scale scale-dependent bias between baryons and CDM for the currently favored WMAP5 {Lambda}CDM model. This time evolving bias is significant (>1%) until the present day, when it is driven towards unity through gravitational relaxation processes. Using the RPT formalism we test this approximation in the nonlinear regime. We show that the nonlinear CDM power spectrum in the two-component fluid differs from that obtained from an effective mean-mass one-component fluid by {approx}3% on scales of order k{approx}0.05h Mpc{sup -1} at z=10, and by {approx}0.5% at z=0. However, for the case of the nonlinear evolution of the baryons the situation is worse and we find that the power spectrum is suppressed, relative to the total matter, by {approx}15% on scales k{approx}0.05h Mpc{sup -1} at z=10, and by {approx}3%-5% at z=0. Importantly, besides the suppression of the spectrum, the baryonic acoustic oscillation (BAO) features are amplified for baryon and slightly damped for CDM spectra. If we compare the total matter power spectra in the two- and one-component fluid approaches, then we find excellent agreement, with deviations being <0.5% throughout the evolution. Consequences: high precision modeling of the large-scale distribution of baryons in the Universe cannot be achieved through an effective mean-mass one-component fluid approximation; detection significance of BAO will be amplified in probes that study baryonic matter, relative to probes that study the CDM or total mass only. The CDM distribution can be modeled accurately at late times and the total matter at all times. This is good news for probes that are sensitive to the total mass, such as gravitational weak lensing as existing modeling techniques are good enough. Lastly, we identify an analytic approximation that greatly simplifies the evaluation of the full PT expressions, and it is better than <1% over the full range of scales and times considered.« less
  • 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, wave-function, and coupling-constant 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 » and has the correct ''classical continuum limit.'' The results that in a renormalizable field theory divergences are contained in the first few terms of the Taylor series expansion of the Green's functions about the external momenta, and that these divergences are mild, play an important role in our proof. Umklapp processes characteristic of the lattice regularization do not have any observable consequences in the continuum limit. Thus Wilson's lattice action is well suited for nonperturbative considerations of gauge theories.« less
  • We consider magnetic instabilities in the two-dimensional Hubbard model at small doping. We find that the renormalization of the effective interaction prevents an immediate instability of a commensurate antiferromagnetic state upon doping. At increased doping levels, our calculations indicate the occurrence of an instability in the channel of transverse spin fluctuations. This instability is known to lead to a spiral magnetic phase. We also consider a dynamical spin susceptibility near the instability and find that conventional spin waves play no role in the transition. Instead, the incommensurate instability is governed by collective fermionic excitations coupled to the spin background.