Evolution of Cosmological Density Distribution Function from(15)

We present a general framework to treat the evolution of one-point probability distribution function (PDF) for cosmic density $\delta$ and velocity-divergence fields $\theta$. In particular, we derive an evolution equation for the one-point PDFs and consid

imationof uidequations,sinceonecanderivethefollowingequationfromequations(1)to

(3): d2δ4dδ mδ+σijσij ωijωij,(41)dt1+δ2

withahelpoftheLagrangiantimederivative.Herethequantitiesσijandωijrespectivelydenotetheshearandtherotationgivenby

σ1

ij=j

x+ v

j3θδij,

ω1 v

ij=j

xj

√

dt2αi= 4πGρmαi

∞ 1+δ2δ+λext,idτ ,bi=α1α2α3

03,

andtherelationbetweenδandαibecomes

3

δ=a

35 ;linearexternaltide,(42)(45)(46)