skip to main content
OSTI.GOV title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: Cosmological perturbation theory for baryons and dark matter: One-loop corrections in the renormalized perturbation theory framework

Abstract

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 to 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 gravitationalmore » 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

Authors:
 [1];  [2]
  1. Deutsches Elektronensynchrotron DESY, Platanenallee 6, D-15738 Zeuthen (Germany)
  2. Institute for Theoretical Physics, University of Zurich, CH-8037 Zurich (Switzerland)
Publication Date:
OSTI Identifier:
21409056
Resource Type:
Journal Article
Journal Name:
Physical Review. D, Particles Fields
Additional Journal Information:
Journal Volume: 81; Journal Issue: 2; Other Information: DOI: 10.1103/PhysRevD.81.023524; (c) 2010 The American Physical Society; Journal ID: ISSN 0556-2821
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; 79 ASTROPHYSICS, COSMOLOGY AND ASTRONOMY; APPROXIMATIONS; BARYONS; COMPARATIVE EVALUATIONS; CORRECTIONS; DISTRIBUTION; DISTURBANCES; FLUCTUATIONS; FLUIDS; MASS; NONLINEAR PROBLEMS; NONLUMINOUS MATTER; OSCILLATIONS; PERTURBATION THEORY; RECOMBINATION; RED SHIFT; RELAXATION; SIMULATION; SPECTRA; TRANSFER FUNCTIONS; UNIVERSE; CALCULATION METHODS; ELEMENTARY PARTICLES; EVALUATION; FERMIONS; FUNCTIONS; HADRONS; MATTER; VARIATIONS

Citation Formats

Somogyi, Gabor, Institute for Theoretical Physics, University of Zurich, CH-8037 Zurich, and Smith, Robert E. Cosmological perturbation theory for baryons and dark matter: One-loop corrections in the renormalized perturbation theory framework. United States: N. p., 2010. Web. doi:10.1103/PHYSREVD.81.023524.
Somogyi, Gabor, Institute for Theoretical Physics, University of Zurich, CH-8037 Zurich, & Smith, Robert E. Cosmological perturbation theory for baryons and dark matter: One-loop corrections in the renormalized perturbation theory framework. United States. doi:10.1103/PHYSREVD.81.023524.
Somogyi, Gabor, Institute for Theoretical Physics, University of Zurich, CH-8037 Zurich, and Smith, Robert E. Fri . "Cosmological perturbation theory for baryons and dark matter: One-loop corrections in the renormalized perturbation theory framework". United States. doi:10.1103/PHYSREVD.81.023524.
@article{osti_21409056,
title = {Cosmological perturbation theory for baryons and dark matter: One-loop corrections in the renormalized perturbation theory framework},
author = {Somogyi, Gabor and Institute for Theoretical Physics, University of Zurich, CH-8037 Zurich and Smith, Robert E},
abstractNote = {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 to 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.},
doi = {10.1103/PHYSREVD.81.023524},
journal = {Physical Review. D, Particles Fields},
issn = {0556-2821},
number = 2,
volume = 81,
place = {United States},
year = {2010},
month = {1}
}