Mathematical physics

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.

I will show how to derive libraries of semi-analytic gravitational waveforms for coalescing “hairy” black hole binaries, focusing on the example of Einstein-scalar-Gauss-Bonnet gravity (ESGB). To do so, I will start from the state-of-the-art, effective-one-body waveform model “SEOBNRv5PHM” in general relativity, and deform it with ESGB corrections to infer inspiral-merger-ringdown waveform estimates.

In recent years, gravitational wave observations of compact objects have provided new opportunities to test our understanding of gravity in the strong-field, highly dynamical regime. To perform model-dependent tests of General Relativity with these observations, one needs accurate inspiral-merger-ringdown waveforms in alternative theories of gravity. In this talk, we will discuss the nonlinear dynamics of compact object mergers in a class of modified theories of gravity, as well as the challenges in numerically obtaining those solutions. The theory we focus on is Einstein-scalar-Gauss-Bonnet gravity, which is a representative example of a Horndeski gravity theory and is interesting because it admits scalar hairy black hole solutions.

Black holes in Horndeski theories of gravity are a perfect playground for exploring possible deviations from General Relativity in a theory-specific manner and studying their astrophysical manifestation. I will review the recent advances in constructing stationary hairy black hole models in Gauss-Bonnet theories. Special attention will be paid to their nonlinear dynamics when isolated or put in a binary, and the resulting astrophysical implications. The potential loss of hyperbolicity will also be discussed.

Scalar-tensor theories with a screening mechanism can serve as a viable model of cosmic acceleration, while still passing existing local tests of gravity. The validity of different screening mechanisms, such as kinetic screening (or k-mouflage) has been studied extensively in static and weak field regimes. However, only recently have works started to focus on determining whether these would work as expected near extremely compact objects. In this talk I will discuss some recent efforts to characterise kinetic screening mechanisms in these highly dynamical and non-linear regimes using numerical relativity in the case of a single oscillating neutron star, as well as how this picture may change for a binary neutron star configuration in a quasi-equilibrium state.

Simulating non-linear scales of structure formation is essential to make use of frontier data from Stage IV galaxy surveys. Performing these simulations in modified gravity theories introduces additional challenges, and further forces us to make choices about which theories we deem ‘worth’ the computational investment. Horndeski Gravity is very helpful in this regard, as it encompasses a large swathe of models of major interest. I’ll introduce Hi-COLA, a software suite which simulates large-scale structure formation in the class of luminal Horndeski theories. Hi-COLA was designed to be: i) flexible — it avoids hard-coded models and instead receives a user-specified Lagrangian; ii) consistent — the background expansion history, linear growth and nonlinear screening are solved consistently with one another; iii) efficient — using the COLA method, large sets of simulations can be generated at low cost. I’ll explain how Hi-COLA can be used to make robust predictions for scalar-tensor theories on nonlinear scales. If time permits, we’ll also dip a toe into constraining the Horndeski framework with gravitational waves.

We will discuss black hole solutions in Horndeski and beyond Horndeski theories. Starting from the no hair paradigm in GR we will elaborate on one of the first black hole solutions with secondary hair. We will then start by introducing stealth solutions, in other words GR metrics endowed with a non trivial scalar field, their regularity properties, shortcomings etc. We will then go on to construct black holes with primary scalar hair which can be regular black holes and modify usual GR static metrics. We will discuss their properties and the status of explicit stationary metrics to conclude.