The coming years will see an amazing increase in data on the large-scale structure of the Universe, ushering in a new phase for "precision cosmology". One of the major questions in fundamental physics concerns the nature of the dark energy, and the new data may help to shed light on this issue. But in order to unlock the full power of the future data to test alternative models like Horndeski Gravity, we need theoretical predictions that are as accurate as the new observations on all scales, including non-linear scales. In my presentation I will introduce our relativistic N-body code for cosmological simulations, gevolution, and how we are using it to look at non-linear effects in the Universe. In particular I will discuss our k-essence simulations, how to use them for cosmology, and what can happen when dark energy clustering becomes non-linear in models with low speed of sound.
This talk will introduce scalar-tensor theories of gravity that contain a single scalar degree of freedom in addition to the usual tensor modes. These theories constitute the very broad family of Degenerate Higher-Order Scalar-Tensor (DHOST) theories, which include and extend Horndeski theories. Cosmological aspects of these theories will then be discussed. Finally, I will also present some results concerning black hole perturbations in the context of these models of modified gravity.
I will present the class of effective field theories of dark energy, which aim to reproduce a dark energy-like phenomenology by modifying general relativity with the addition of a scalar graviton. I will review how non-linearities can "screen" local scales from scalar effects, therefore allowing these theories to pass existing solar-system experimental tests. I will then present fully relativistic simulations of gravitational wave generation in these theories in 1+1 dimensions (stellar oscillations and collapse) and 3+1 dimensions (binary neutron stars). I will show that screening tends to suppress the (subdominant) dipole scalar emission in binary neutron star systems, but it fails to quench monopole scalar emission in gravitational collapse, and quadrupole scalar emission in binaries. This opens the way to the exciting possibility of testing dark energy with gravitational wave data.