Non-linear density-velocity evolution of large scale structure from phase space dynamics: LCDM vs. modified gravity.

Recent observations have indicated that the standard Lambda-Cold-Dark-Matter (LCDM) model, which is based on Einstein’s gravity, needs to be modified. Clues that help constrain the modifications are hidden in the large scale structure of the Universe. The fractional density and peculiar velocity are the two main variables that are used to characterize this structure. When the perturbations are small, the density and the divergence of the velocity field are proportional. The proportionality constant, called the `linear growth factor’ is a sensitive probe of the underlying cosmology and indeed, many current upcoming observational missions aim to constrain this factor with high precision. However, this linear relation breaks down when the perturbations are of order unity i.e. in the non-linear regime. In this talk we will investigate the non-linear extension of this relation. We will use the spherical top-hat model and examine how perturbations evolve in the joint density-velocity divergence `phase-space’. In particular, we will consider the f(R) model of modified gravity with the Hu-Sawicki form as a working example. In the LCDM model, the non-linear density-velocity divergence relation corresponds to a phase-space invariant, whereas, in the f(R) model, the results depend sensitively on the ratio of two length scales: the Compton wavelength of the scalar field associated with the modification and the width of the top-hat. Finally, we will demonstrate how invariants can, in principle, be used to disentangle degeneracies in parameter estimation.