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Title: Nonlinear dynamics from the relativistic Boltzmann equation in the Friedmann-Lemaître-Robertson-Walker spacetime

Abstract

The dissipative dynamics of an expanding massless gas with constant cross section in a spatially flat Friedmann-Lemaître-Robertson-Walker (FLRW) universe is researched. The mathematical problem of solving the full nonlinear relativistic Boltzmann equation is recast into an infinite set of nonlinear ordinary differential equations for the moments of the one-particle distribution function. Momentum-space resolution is determined by the number of nonhydrodynamic modes included in the moment hierarchy, i.e., by the truncation order. We show that in the FLRW spacetime the nonhydrodynamic modes decouple completely from the hydrodynamic degrees of freedom. This results in the system flowing as an ideal fluid while at the same time producing entropy. The solutions to the nonlinear Boltzmann equation exhibit transient tails of the distribution function with nontrivial momentum dependence. The evolution of this tail is not correctly captured by the relaxation time approximation nor by the linearized Boltzmann equation. Yet, the latter probes additional high-momentum details unresolved by the relaxation time approximation. While the expansion of the FLRW spacetime is slow enough for the system to move towards (and not away from) local thermal equilibrium, it is not sufficiently slow for the system to actually ever reach complete local equilibrium. Equilibration is fastest in themore » relaxation time approximation, followed, in turn, by kinetic evolution with a linearized and a fully nonlinear Boltzmann collision term.« less

Authors:
 [1];  [2]; ORCiD logo [1];  [1];  [3]
  1. The Ohio State Univ., Columbus, OH (United States)
  2. Fluminense Federal Univ., Niterói, RJ (Brazil); Brookhaven National Lab. (BNL), Upton, NY (United States)
  3. Univ. of São Paulo (Brazil)
Publication Date:
Research Org.:
The Ohio State Univ., Columbus, OH (United States); Brookhaven National Laboratory (BNL), Upton, NY (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Nuclear Physics (NP)
OSTI Identifier:
1604346
Alternate Identifier(s):
OSTI ID: 1334854
Grant/Contract Number:  
SC0004286; SC0012704
Resource Type:
Journal Article: Accepted Manuscript
Journal Name:
Physical Review D
Additional Journal Information:
Journal Volume: 94; Journal Issue: 12; Journal ID: ISSN 2470-0010
Publisher:
American Physical Society (APS)
Country of Publication:
United States
Language:
English
Subject:
73 NUCLEAR PHYSICS AND RADIATION PHYSICS; 79 ASTRONOMY AND ASTROPHYSICS

Citation Formats

Bazow, D., Denicol, G. S., Heinz, Ulrich, Martinez, M., and Noronha, J. Nonlinear dynamics from the relativistic Boltzmann equation in the Friedmann-Lemaître-Robertson-Walker spacetime. United States: N. p., 2016. Web. doi:10.1103/PhysRevD.94.125006.
Bazow, D., Denicol, G. S., Heinz, Ulrich, Martinez, M., & Noronha, J. Nonlinear dynamics from the relativistic Boltzmann equation in the Friedmann-Lemaître-Robertson-Walker spacetime. United States. https://doi.org/10.1103/PhysRevD.94.125006
Bazow, D., Denicol, G. S., Heinz, Ulrich, Martinez, M., and Noronha, J. 2016. "Nonlinear dynamics from the relativistic Boltzmann equation in the Friedmann-Lemaître-Robertson-Walker spacetime". United States. https://doi.org/10.1103/PhysRevD.94.125006. https://www.osti.gov/servlets/purl/1604346.
@article{osti_1604346,
title = {Nonlinear dynamics from the relativistic Boltzmann equation in the Friedmann-Lemaître-Robertson-Walker spacetime},
author = {Bazow, D. and Denicol, G. S. and Heinz, Ulrich and Martinez, M. and Noronha, J.},
abstractNote = {The dissipative dynamics of an expanding massless gas with constant cross section in a spatially flat Friedmann-Lemaître-Robertson-Walker (FLRW) universe is researched. The mathematical problem of solving the full nonlinear relativistic Boltzmann equation is recast into an infinite set of nonlinear ordinary differential equations for the moments of the one-particle distribution function. Momentum-space resolution is determined by the number of nonhydrodynamic modes included in the moment hierarchy, i.e., by the truncation order. We show that in the FLRW spacetime the nonhydrodynamic modes decouple completely from the hydrodynamic degrees of freedom. This results in the system flowing as an ideal fluid while at the same time producing entropy. The solutions to the nonlinear Boltzmann equation exhibit transient tails of the distribution function with nontrivial momentum dependence. The evolution of this tail is not correctly captured by the relaxation time approximation nor by the linearized Boltzmann equation. Yet, the latter probes additional high-momentum details unresolved by the relaxation time approximation. While the expansion of the FLRW spacetime is slow enough for the system to move towards (and not away from) local thermal equilibrium, it is not sufficiently slow for the system to actually ever reach complete local equilibrium. Equilibration is fastest in the relaxation time approximation, followed, in turn, by kinetic evolution with a linearized and a fully nonlinear Boltzmann collision term.},
doi = {10.1103/PhysRevD.94.125006},
url = {https://www.osti.gov/biblio/1604346}, journal = {Physical Review D},
issn = {2470-0010},
number = 12,
volume = 94,
place = {United States},
year = {Thu Dec 08 00:00:00 EST 2016},
month = {Thu Dec 08 00:00:00 EST 2016}
}

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Cited by: 32 works
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Works referencing / citing this record:

Interacting neutrinos in cosmology: exact description and constraints
journal, November 2017