TY - JOUR

T1 - Perturbation theory in Lagrangian hydrodynamics for a cosmological fluid with velocity dispersion

AU - Tatekawa, Takayuki

AU - Suda, Momoko

AU - Maeda, Kei ichi

AU - Morita, Masaaki

AU - Anzai, Hiroki

PY - 2002

Y1 - 2002

N2 - We extensively develop a perturbation theory for nonlinear cosmological dynamics, based on the Lagrangian description of hydrodynamics. We solve the hydrodynamic equations for a self-gravitating fluid with pressure, given by a polytropic equation of state, using a perturbation method up to second order. This perturbative approach is an extension of the usual Lagrangian perturbation theory for a pressureless fluid, in view of the inclusion of the pressure effect, which should be taken into account on the occurrence of velocity dispersion. We obtain the first-order solutions in generic background universes and the second-order solutions in a wider range of a polytropic index, whereas our previous work gives the first-order solutions only in the Einstein–de Sitter background and the second-order solutions for the polytropic index (Formula presented) Using the perturbation solutions, we present illustrative examples of our formulation in one- and two-dimensional systems, and discuss how the evolution of inhomogeneities changes for the variation of the polytropic index.

AB - We extensively develop a perturbation theory for nonlinear cosmological dynamics, based on the Lagrangian description of hydrodynamics. We solve the hydrodynamic equations for a self-gravitating fluid with pressure, given by a polytropic equation of state, using a perturbation method up to second order. This perturbative approach is an extension of the usual Lagrangian perturbation theory for a pressureless fluid, in view of the inclusion of the pressure effect, which should be taken into account on the occurrence of velocity dispersion. We obtain the first-order solutions in generic background universes and the second-order solutions in a wider range of a polytropic index, whereas our previous work gives the first-order solutions only in the Einstein–de Sitter background and the second-order solutions for the polytropic index (Formula presented) Using the perturbation solutions, we present illustrative examples of our formulation in one- and two-dimensional systems, and discuss how the evolution of inhomogeneities changes for the variation of the polytropic index.

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U2 - 10.1103/PhysRevD.66.064014

DO - 10.1103/PhysRevD.66.064014

M3 - Article

AN - SCOPUS:4243919079

VL - 66

JO - Physical Review D - Particles, Fields, Gravitation and Cosmology

JF - Physical Review D - Particles, Fields, Gravitation and Cosmology

SN - 1550-7998

IS - 6

ER -