Cosmological Density Distribution Function from the Ellipsoidal Collapse Model in Real Space

We calculate the one-point probability distribution function (PDF) for cosmicdensity in non-linear regime of the gravitational evolution. Under the localapproximation that the evolution of cosmic fluid fields can be characterized bythe Lagrangian local dynamics with finite degrees of freedom, the analyticexpressions of PDF are derived taking account of the smoothing effect. Thevalidity and the usefulness of the local approximation are then discussedcomparing those results with N-body simulations in a Gaussian initialcondition. Adopting the ellipsoidal collapse model (ECM) and the sphericalcollapse model (SCM) as Lagrangian local dynamics, we found that the PDFs fromthe local approximation excellently match the simulation results in the case ofthe cold dark matter initial spectrum. As for the scale-free initial spectra given by $P(k)\propto k^n$, N-body result suffers from spurious numerical effects, which prevent us togive a detailed comparison. Nevertheless, at the quality of N-body data, the model predictions based onthe ECM and the SCM quantitatively agree with N-body results in cases withspectral index n<0. For the index n>=0, choice of the Lagrangian local dynamics becomes crucialfor an accurate prediction and a more delicate modeling is required, however,we find that the model prediction based on the ECM provides a betterapproximation to the N-body results of cumulants and PDFs.Comment: 35 pages, 7 figure