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The non-linear dynamics of gravitational wave propagation in spacetime can contain drastic new phenomenology that is absent from the linearised theory. In this talk, I will probe the non-linear radiative regime of Horndeski gravity by making use of disformal field redefinition. I will discuss how disformal transformations alter the properties of congruences of geodesics and in particular how they can generate disformal gravitational waves at the fully non-linear level. I will illustrate this effect by presenting a new exact radiative solution in Horndeski gravity describing a scalar pulse. Analysing the non-linear dynamics of this new radiative solution will show that it contains tensorial gravitational waves generated by a purely time-dependent scalar monopole. This intriguing result is made possible by the higher-order nature of Horndeski gravity.

Gravitational waves from black hole binary mergers can tell us a lot about the physics of the system. At the late part of the graviational wave signal, GR predicts the presence of characteristic frequencies (called quasinormal modes) in the signal. Measuring multiple quasinormal modes is a strong consistency test for GR. Here we probe the regime where a signal can be described entirely by quasinormal modes. We consider a higher order effect, where the remnant black hole is absorbing some radiation and so has a changing mass and spin. We test the contribution of this effect to the signal in a physically relevant scenario. We find evidence that this effect causes other mode excitations as well as a changing frequency contribution.

Observational constraints on time-varying dark energy are commonly presented in terms of the two CPL parameters $w_0$ and $w_a$. Recent observations favor a sector of this parameter space in which $w_0 > -1$ and $w_0 + w_a < -1$, suggesting that the equation of state underwent a transition from violating the null energy condition (NEC) at early times to obeying it at late times. In this talk, I will demonstrate that this initial impression is misleading, by showing that simple quintessence models satisfying the NEC at all times predict an observational preference for the same sector. The upshot is that the CPL parameterization is simultaneously useful for detecting deviations from cosmological-constant dynamics ($w = -1$) but unreliable for predicting the true behavior of $w(z)$.

Exploring the structure of compact objects in modified theories of gravity is mandatory to parametrize the possible deviations w.r.t general relativity and confront these theories to the current and future observations. While important efforts have been devoted to understand the phenomenology of stars and black holes, it is still a challenging task to provide new exact analytical solutions describing rotating black hole in such theories. In this talk, I propose to recent efforts to construct such solutions. Concretely, I will review how one can mix the disformal field redefinitions affect the Petrov type of a given gravitational field and how this can be used to constrain the derivation of rotating black hole. Then, I will review the main properties of a new solution of a subset of Horndeski theories called the disformal Kerr black hole and comment on the most promising directions to derive exact rotating black hole solutions in scalar-tensor theories. This talk will be based on the two articles: https://inspirehep.net/literature/1800972, https://inspirehep.net/literature/1877661

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.

In my talk I will discuss the black hole spontaneous scalarization in scalar-Gauss-Bonnet gravity. Some of the basic ideas, results and astrophysical consequences will be presented. I will also discuss a new fully non-linear dynamical mechanism for the formation of scalarized black holes which is different from the spontaneous scalarization.

Classical energy conditions are used to provide restrictions on the matter fields present in the stress-energy tensor to avoid possible unphysical spacetimes. These classical energy conditions are imperative to the singularity theorems of Hawking and Penrose. However, we know that spacetime breaks down near said singularities and a quantum theory of gravity is needed. One insight into this area is semi-classical gravity where the spacetime is kept “classical” and the stress-energy tensor is quantized. In this regime one may ask what reasonable restrictions should be imposed on the quantum expectation of the stress-energy tensor? One such possibility is the smeared null energy conditions (SNEC). We will review motivation for the SNEC and explore its consequences in cosmological spacetimes that would otherwise violate the classical null energy condition, such as bouncing cosmologies.

Invertible disformal transformations are a useful tool to investigate ghost-free scalar-tensor theories. By performing a higher-derivative generalization of the invertible disformal transformation on Horndeski theories, we construct a novel class of ghost-free scalar-tensor theories, which we dub generalized disformal Horndeski theories. In the talk, I will clarify the basic idea for constructing the invertible disformal transformation with higher derivatives. I will also discuss some aspects of the generalized disformal Horndeski theories, including the consistency of matter coupling and cosmological perturbations.

Gravitational collapse shaped the cosmic large-scale structure and created a plethora of different density environments. For optimally probing gravity with galaxy surveys like Euclid and Rubin LSST, we need to dissect different density environments that are lumped together in traditional two-point statistics. I will explain how the one-point probability distribution of dark matter densities can be predicted analytically including signatures of modified gravity that match with cosmological simulations for nDGP and f(R) gravity. I will provide an outlook on how those predictions can be translated to galaxy clustering and weak lensing and observables.