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With the data provided by the new suite of simulations we will be able to study the imprint of the different models on the non-linear clustering of dark matter. This will be possible thanks to the improved resolution that will allow to measure the Power Spectrum with high precision on both large and small scales to quantify the non-linear signatures of the models. This will be a considerable improvement over the current knowledge that in many cases is the result of an analytical study limited by linear approximations.  Then the extension of the new halo catalogues will provide a smoother realization of the halo mass function and correlation function even at higher redshift. This will allow us to quantify the impact of the new dynamics on the Dark Matter halos by measuring properties such as concentration, velocity dispersion and mass accretion history for the first time in those scenarios.  The test simulations in particular indicate that the differences in those properties can answer the questions raised by the observed observationally measured shallow halo profiles (cusp/core problem)\cite{Duffy_2010},  low abundance of dwarf halos in voids and the observed low number of satellites in Milky Way sized halos compared to the predictions of the LCDM model. Following this analysis and with the same dataset it will be possible to run the semi-analytical model of galaxy formation created by Darren Croton. This will then allow to compare the size of differences in galactic properties induced by the underlying dark energy model. The extent of the new galaxy catalogue will provide enough statistics up to redshift $z=6$ to study the evolution of the stellar mass function, correlation function, stellar mass density and star formation rate density. This Relative differences in these observables indicate how a different Dark Energy model could contribute to the solution of some of the problems present in our current understanding of galaxy formation processes such as the overprediction of intermediate-to-low mass galaxies and the discrepancy between bright satellites their host halos sizes both in Milky-Way sized halos and in the field \cite{2014arXiv1407.4665P}.  Furthermore this  analysis will be the first step towards producing a specific dataset that willallow direct comparision with observations once they will  be publicily available trough the Theoretical Astrophysical Observatory \cite{2014arXiv1403.5270B} and this will be help in  the main focus design of future surveys as it will provide a comprehensive source  of my second paper.\\ mock observations.  Another interesting project I would like to will  pursue is one that concerns the necessity to have multiple realization of the same model simulation using different initial conditions to build many mock catalogues and quantify used to reduce  the cosmic variance using and build  covariance matrices to geta  more robust predictions. Due to the computational costs this is currently unfeasible using full blown cosmological N-body simulations. Recent developments though allow to get many realization using a tecnique called Comoving Lagrangian Acceleration (COLA) \cite{Tassev_2013} that provides an accuracy comparable to that of N-Body simulations on large scale by smoothing over the details on the smaller scales. This could be coupled with a Also  recently developed a new promising  approximation technique has been developed  that allows to simulate Modified Gravity Theories without resorting to solve the numerical solution of  the full field equations \cite{Winther:2014cia} that showed promising results. \cite{Winther:2014cia}.  I would like to will  investigate if it's possible to combine the two approaches and I think this would be eased by the fact that the COLA code was improved and completed here at CAS by Jun Koda and his team. This could will  led to the inclusion of Modified Gravity mock catalogues in the observational pipelines and allow help  to hilight possible signature and constrain each models'parameters with an unprecedented precision. devise observational strategies to measure the deviations from the LCDM model.  This could will  be the focus of a third paper and I would like to network this effort with the observational group led by Chris Blake here at Swinburne to test these results against observational surveys both past like WiggleZ \cite{Blake_2011} or BOSS \cite{Dawson_2012} and future like TAIPAN \cite{Koda:2013eya}.