Numerical simulations have become a powerful tool to study cosmological structure formation.

In this talk, I will first show how the initial conditions can affect the results at low redshift, and introduce  

the Horizon Run 4 (HR4), a massive cosmological N-body simulation.  I will  then discuss the rate of halo interactions and the alignment of halo pairs as a function of the environment using the HR4.  

I will then move on to cosmology beyond LCDM, and study the alignment of dark matter haloes in  

modified gravity and dark energy models. I will also assess the potential of the large-scale structure of the Universe to constrain early-Universe models that are undistinguishable from the CMB. 

Finally, I will discuss how to  reconstruct model-independently the luminosity distance from supernovae, 

and combine them with BAO measurement from BOSS DR12, to test the FLRW metric and the flatness  

of the Universe.