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\section{Thesis Content Plan}  In the first chapter of my thesis i I  will introduce the theoretical and observational motivations behind the current cosmological concordance model, this will be followed by a review of the outstanding issues that will be the starting point for the introduction of the Dark Energy and Modified Gravity models whose additions and motivations will be explored in detail.\\ The second chapter will contain a technical exploration of the growth of structure in the LCDM and all the other models previously introduced, alongside with an explanation of the principles behind N-Body simulations and the algorithmical modifications necessary to describe the new scenarios.\\  The third chapter will focus on the first set of analysis performed on the simulations and will address the effects of the new scenarios on the dark matter density field and on the caracteristichs of halos in the new scenarios.\\  In the fourth chapter I will concentrate on the issues of galaxy formation and how the current prescriptions behave under in the new cosmological settings. Looking at the behaviour of common galaxy statistical observables I will explain how the new models alleviate some of the issues in our current understanding of galaxy formation.\\  In the fifth chapter i I  will employ the results obtained in the previous chapters to produce observational predictions and compare those with availble observational data and future surveys' forecasts to investigate the possibility of detection of the signatures of every simulated scenario.