TY - JOUR

T1 - How is the local-scale gravitational instability influenced by the surrounding large-scale structure formation?

AU - Takada, Masahiro

AU - Futamase, Toshifumi

N1 - Copyright:
Copyright 2020 Elsevier B.V., All rights reserved.

PY - 1999/4

Y1 - 1999/4

N2 - We develop the formalism to investigate the relation between the evolution of the large-scale (quasi) linear structure and that of the small-scale nonlinear structure in Newtonian cosmology within the Lagrangian framework. In doing so, we first derive the standard Friedmann expansion law using the averaging procedure over the present horizon scale. Then the large-scale (quasi) linear flow is defined by averaging the full trajectory field over a large-scale domain, but much smaller then the horizon scale. The rest of the full trajectory field is supposed to describe small-scale nonlinear dynamics. We obtain the evolution equations for the large-scale and small-scale part of the trajectory field. These are coupled each other in most general situations. It is shown that if the shear deformation of fluid elements is ignored in the averaged large-scale dynamics, the small-scale dynamics is described by Newtonian dynamics in an effective Friedmann-Robertson-Walker (FRW) background with a local scale factor. The local scale factor is defined by the sum of the global scale factor and the expansion deformation of the averaged large-scale displacement field. This means that the evolution of small-scale fluctuations is influenced by the surrounding large-scale structure through the modification of FRW scale factor. The effect might play an important role in the structure formation scenario.

AB - We develop the formalism to investigate the relation between the evolution of the large-scale (quasi) linear structure and that of the small-scale nonlinear structure in Newtonian cosmology within the Lagrangian framework. In doing so, we first derive the standard Friedmann expansion law using the averaging procedure over the present horizon scale. Then the large-scale (quasi) linear flow is defined by averaging the full trajectory field over a large-scale domain, but much smaller then the horizon scale. The rest of the full trajectory field is supposed to describe small-scale nonlinear dynamics. We obtain the evolution equations for the large-scale and small-scale part of the trajectory field. These are coupled each other in most general situations. It is shown that if the shear deformation of fluid elements is ignored in the averaged large-scale dynamics, the small-scale dynamics is described by Newtonian dynamics in an effective Friedmann-Robertson-Walker (FRW) background with a local scale factor. The local scale factor is defined by the sum of the global scale factor and the expansion deformation of the averaged large-scale displacement field. This means that the evolution of small-scale fluctuations is influenced by the surrounding large-scale structure through the modification of FRW scale factor. The effect might play an important role in the structure formation scenario.

KW - Averaging method

KW - Gravitational instability

KW - Large-scale structure of the universe

KW - Newtonian cosmology

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U2 - 10.1023/a:1026638021372

DO - 10.1023/a:1026638021372

M3 - Article

AN - SCOPUS:0033247471

VL - 31

SP - 461

EP - 486

JO - General Relativity and Gravitation

JF - General Relativity and Gravitation

SN - 0001-7701

IS - 4

ER -