Publication : t95/136

Abstract:
\def\mg{\langle} \def\md{\rangle} %\def\mg{\big <} %\def\md{\big >} \def\vr{{\vec r}} \def\vx{{\vec x}} \def\vk{{\vec k}} %The large-scale gravitational bias from the quasi-linear regime %\vskip 1 cm %F. Bernardeau %\vskip 1. cm %Abstract %\vskip 1cm It is known that in gravitational instability scenarios the nonlinear dynamics induces non-Gaussian features in cosmological density fields that can be investigated with perturbation theory. Here, I derive the expression of the joint moments of cosmological density fields taken at two different locations. The results are valid when the density fields are filtered with a top-hat filter window function, and when the distance between the two cells is large compared to the smoothing length. In particular I show that it is possible to get the generating function of the coefficients $C_{p,q}$ defined by $\mg\delta^p(\vx_1)\delta^q(\vx_2)\md_c=C_{p,q} \mg\delta^2(\vx)\md^{2(p+q)-4} \mg\delta(\vx_1)\delta(\vx_2)\md$ where $\delta(\vx)$ is the local smoothed density field. It is then possible to reconstruct the joint density probability distribution function (PDF), generalizing for two points what has been obtained previously for the one-point density PDF. I discuss the validity of the large separation approximation in an explicit numerical Monte Carlo integration of the $C_{2,1}$ parameter as a function of $\vert\vx_1-\vx_2\vert$. A straightforward application is the calculation of the large-scale ``bias'' properties of the over-dense (or under-dense) regions. The properties and the shape of the bias function are presented in details and successfully compared with numerical results obtained in an N-body simulation with CDM initial conditions.