How Is the Local-scale Gravitational Instability Influenced by the Surrounding Large-scale Structure Formation?

We develop the formalism to investigate therelation between the evolution of the large-scale(quasi) linear structure and that of the small-scalenonlinear structure in Newtonian cosmology within theLagrangian framework. In doing so, we first derive thestandard Friedmann expansion law using the averagingprocedure over the present horizon scale. Then thelarge-scale (quasi) linear flow is defined by averaging the full trajectory field over a large-scaledomain, but much smaller then the horizon scale. Therest of the full trajectory field is supposed todescribe small-scale nonlinear dynamics. We obtain the evolution equations for the large-scale andsmall-scale part of the trajectory field. These arecoupled each other in most general situations. It isshown that if the shear deformation of fluid elements is ignored in the averaged large-scaledynamics, the small-scale dynamics is described byNewtonian dynamics in an effectiveFriedmann-Robertson-Walker (FRW) background with a localscale factor. The local scale factor is defined by the sum of theglobal scale factor and the expansion deformation of theaveraged large-scale displacement field. This means thatthe evolution of small-scale fluctuations is influenced by the surrounding large-scale structurethrough the modification of FRW scale factor. The effectmight play an important role in the structure formationscenario.     

Relativistic Hydrodynamic Cosmological Perturbations

Relativistic cosmological perturbation analysescan be made based on several different fundamental gaugeconditions. In the pressureless limit the variables incertain gauge conditions show the correct Newtonian behaviors. Considering the generalcurvature (K) and the cosmological constant ()in the background medium, the perturbed density in thecomoving gauge, and the perturbed velocity and the perturbed potential in the zero-shear gaugeshow the same behavior as the Newtonian ones in generalscales. In the first part, we elaborate these Newtoniancorrespondences. In the second part, using the identified gauge-in variant variables withcorrect Newtonian correspondences, we present therelativistic results with general pressures in thebackground and perturbation. We present the generalsuper-sound-horizon scale solutions of the above mentionedvariables valid for general K, Lambda, and generallyevolving equation of state. We show that, for vanishingK, the super-sound-horizon scale evolution ischaracterised by a conserved variable which is the perturbedthree-space curvature in the comoving gauge. We alsopresent equations for the multi-component hydrodynamicsituation and for the rotation and gravitational wave.