DR. SHARVARI NADKARNI-GHOSH

The fractional overdensity and peculiar velocity are the two main variables that characterize the observed large scale structure in the universe. In the linear regime, the density is proportional to the velocity divergence; the proportionality constant is the linear growth rate f, which depends on cosmological parameters and many recent cosmological surveys aim to constrain it. However, this relation breaks down in the non-linear regime. In this talk we will discuss extensions of the velocity-gravity relation using spherical and ellipsoidal collapse as a proxy for the non-linear regime. The relevant variables for the sphere are density and velocity divergence whereas for the ellipsoid they are the eigenvalues of the deformation tensor, the tensor of velocity derivatives and the Hessian of the gravity field. We extend the essence of the Zeldovich approximation to the non-linear regime to get implicit relations between these variables and by examining the dynamical flow of the perturbation variables in phase space, we show that the relations are universal. Initial conditions no matter where they start in phase space always lie close to these structures at late times. In principle, this attracting behavior can be exploited to remove parameter degeneracies. In addition, the phase space analysis also can give estimates of the probability density functions of the density and velocity divergence fields as well as insights into evolution of axial ratios of galaxies.