Mathematical Physics

The Horndeski program is motivated by arguing that scalar-tensor modifications to gravity should have two properties: effective interactions that are at most second-order in time derivatives and only a single scalar. I will argue against both of these criteria. First I argue why the low-energy limit of known well-behaved theories can have more than two-derivative field equations. Second I argue why the scalar-tensor interactions most likely to be found competing with gravity at very low energies typically are those with two derivatives, at least when semiclassical methods are justified, and this suggests exploring multiple-scalar models.

I extend EFT of inflation/dark energy to arbitrary background with timelike scalar profile. In this framework a set of consistency relations among EFT coefficients ensures the spatial diffeo invariance. Some applications to will also be discussed.

We study the weak-gravity regime of higher-order scalar-tensor theories that are degenerate in the unitary gauge. In a certain subset of theories analogous to Lorentz-violating scalar-tensor theories, we show that the Vainshtein mechanism due to nonlinear derivative interactions does not work. For this family of theories we determine all the PPN parameters in terms of the EFT of dark energy parameters and discuss the experimental bounds.

Since the discovery of the accelerated expansion of the universe, significant progress has been made to develop modified gravity theories as alternatives to dark energy and these have been developed into tests of General Relativity itself via cosmological observations. These models share common properties such as screening mechanisms they use to evade the stringent Solar System tests. In this talk, I will review recent status of observational tests of screened modified gravity models and discuss the prospect of cosmological tests of gravity from ongoing surveys such as Euclid.

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.