# B17 - Development of new analytical non-linear methods for gravitational evolution and comparison with numerical tools

#### Principal Investigators: L. Amendola, M. Bartelmann, V. Pettorino, Ch. Wetterich (Heidelberg)

## Summary

A correct understanding of the non-linear evolution of cosmic structures is one of the main challenges for current cosmology. This influences our theoretical knowledge of the Dark Universe as well as our ability to interpret the data coming from forthcoming generations of galaxy surveys. We propose a new project that will attack non-linear structure formation from three different sides. We will develop new analytical and semi-analytical tools that can describe the non-linear evolution of the gravitational potential and compare results from three different approaches.
(1) We will improve existing time renormalization group methods (TRG): TRG methods can be applied to models beyond ΛCDM (e.g. when an interaction in the dark sector is present) and integrated with available Boltzmann codes, in order to estimate non-linear corrections to the matter power spectra.
(2) We will derive spherically symmetric solutions for scalar field profiles around a halo, distinguishing between screened and unscreened density regions. One of our main goals is to see whether non-linear clustering can be understood as a function of the smoothing scale.
(3) We will make use of methods from statistical quantum field theory, applied to classical kinetic theory. In this approach, Hamiltonâ€™s equations allow a simple formulation of an effective action: this will allow us to set up appropriate generating functionals for self-gravitating systems, derive the effective actions and estimate the correlation functions for the dark-matter density.
We will compare and join the analytical methods listed above to available numerical methods, facilitating the analysis and speeding up numerical simulations, which will be an important achievement given the present need to analyze a large amount of data and models. This analysis will also impact on our understanding of Dark Energy models, allowing us to follow non-linearities in the Dark Energy scalar field. Our analysis will be of interest for the field, especially in view of satellite missions like Euclid, a joint ESA and NASA collaboration in which the Transregio cosmology community is deeply involved at all levels (Amendola, Pettorino etal 2012).