Abstract
We study the one-point probability distribution functions (PDFs) of the peculiar velocityand the density fluctuation in a cosmological fluid. Within the perturbative approach to thestructure formation scenario, the effect of ‘pressure’ has recently been an area of researchinterest. The velocity dispersion of the cosmological fluid creates effective ‘pressure’ orviscosity terms. From this viewpoint, because the pressure reflects a nonlinear effect of themotion of the fluid, the pressure model would include nonlinear effects. Herewe analyse the Lagrangian linear perturbation PDFs for both the Zel’dovichapproximation and the pressure model. We find that the PDFs of the peculiar velocityremain Gaussian, even if we consider the pressure. For the PDFs of the densityfluctuation, the occurrence of non-Gaussianity depends on the ‘equation of state’for the fluid. Therefore we distinguish the ‘equation of state’ using the PDFs.
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