General Relativity & Quantum Cosmology

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.

I will review various mechanisms and detection strategies of precursor emission to black holes and neutron stars mergers. I will also discuss other peculiar physical processes at the intersection of electromagnetism, classical General Relativity, and the physics of continuous media.

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Some of the most fundamental challenges in quantum gravity involve determining how to take the continuum limit of the underlying regularized theory and how to preserve the causal structure of space-time. Several approaches to quantum gravity attempt to address these questions, but the technical challenges are substantial.

In this talk, we present a novel approach to a lattice-regularized theory of quantum gravity, using techniques from standard lattice quantum field theories to overcome these challenges. Our approach is inspired by quantum geometrodynamics, the earliest attempt at quantizing gravity. While the original approach suffered from the usual shortcomings pertaining to the multiplication of distributions and consequently failed, we propose a novel lattice regularization that is especially well suited for studying the continuum limit. First, we examine the lattice corrections to the theory and quantize these lattice theories in a manner that ensures the manifest causal structure of space-time. Next, we discuss the constructions involved in obtaining a well-defined continuum limit and explain how our approach can overcome some conceptually unappealing aspects.

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Asymptotically safe quantum gravity might provide a unified description of the fundamental dynamics of quantum gravity and matter. The realization of asymptotic safety, i.e., of scale symmetry at high energies, constraints the possible interactions and dynamics of a system. In this talk, I will first introduce the scenario of asymptotic safety for gravity with matter, and explain how it can be explored using functional methods. I will then emphasize, how the constraints on the microscopic dynamics of matter arising from quantum scale symmetry can turn into constraints on the gravitational dynamics, both by exploring the asymptotically safe fixed-point structure, and by exploring resulting infrared physics.

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