Search

The first direct detection of gravitational waves (GWs) from a black-hole (BH) binary, GW150914, by the advanced Laser Interferometer Gravitational-wave Observatory (aLIGO) detectors in 2015 heralded a new era in GW physics. Since then, over 90 compact binary merger events have been detected by the GW detector network with many more expected in the decades to come. A significant part of the theoretical foundations that underpins this achievement is the modelling of GW sources in General Relativity (GR) using numerical relativity (NR). In this thesis, we discuss the features and capabilities of the NR code GRChombo. Although GRChombo is no longer a new code, its original development and design targeted applications beyond the conventional astrophysical paradigm that other NR codes have focussed on. Here, we describe more recent additions that have allowed GRChombo to model BH binaries and other GW sources with good accuracy. Through direct comparison, we demonstrate that this accuracy is comparable to that of a more mature NR code. One of the key capabilities of GRChombo is its adaptive mesh refinement (AMR). This allows the numerical grid to dynamically adjust itself in order to sufficiently resolve the large range of spatial and temporal scales that characteristically arise in non-trivial solutions of GR as a consequence of the theory's non-linearity. However, this flexibility requires careful control in order to achieve the desired accuracy and we discuss in detail the lessons learned in order to achieve this with GRChombo. We apply GRChombo and these techniques to the investigation of the effect of orbital eccentricity on the GW emission and the gravitational recoil imparted to the BH merger remnant from the inspiral and merger of unequal-mass non-spinning BH binaries. Finally, we explore the modelling of a more exotic type of compact object: boson stars (BSs) which are comprised of complex scalar field matter. In particular, we investigate the construction of suitable initial data describing BS binaries and its effect on the ensuing evolutions.

Weak bosons are by now a well-established and observed block of the elementary particles table, but the era of Precision Physics opens up new ways of utilising them in an attempt to uncover the mystery of physics beyond the Standard Model. Being central to what is called Electroweak Symmetry Breaking mechanism, they obtain mass by interacting with the Higgs field. Their longitudinal polarisation is induced by the Goldstone modes of the Higgs field and provides a direct handle on any massive new physics models. In this thesis, we devote a particular focus on the polarised W-boson production in the context of two processes at the LHC and explore applications of our results. We discuss in depth the current approaches to simulate and measure weak boson polarisation, and present NNLO studies of W+j and W+ W− production at the LHC. We explore the effects and significance of observed perturbative corrections, and in the context of W+j, comment on their application to experimental data. In addition to that, we discuss how polarisation quantities, in particular, angular coefficients, are instrumental in precise W-boson mass measurements which aim to reach 0.01% level of precision. Aiming to fill the gap for precise theoretical input, we provide NNLO + NLO EW predictions, and comment on their effects and theoretical uncertainty. Furthermore, we explore advancements in the area of fixed-order predictions in general and present results for Wbb̄ production at NNLO precision. This is the first study of a 2 → 3 process involving a massive particle at such accuracy, which marks a milestone following significant advancements in the field. We also discuss the novel proposition for a flavoured anti-kT algorithm, which aims to combine the experimental convenience of anti-kT prescription with a modification for flavoured particles, enabling IR-safe heavy flavour tagging with two real emissions. Results based on this prescription are compared with the well-established flavour-kT method and to available data. Lastly, we introduce the new framework named HighTEA, which as we hope, will be helpful for the researchers who use the output of fixed order predictions. We present the ideas and structure of the project, the details of its current capabilities, its limitations and aspirations, and provide with user instructions to quickly bring an interested reader up to speed.

In this thesis we study string compactifications on manifolds equipped with a G-structure, placing a special emphasis on the interplay between geometry and physics. We follow two complementary approaches. In the first part of the thesis we adopt a sigma model perspective and focus on the worldsheet superconformal field theory. We consider compactifications on 7-dimensional Extra Twisted Connected Sum (ETCS) G2 manifolds as well as 8-dimensional Generalized Connected Sum (GCS) Spin(7) manifolds. These are special holonomy manifolds obtained by gluing together two open manifolds along isomorphic asymptotic ends in a particular fashion. We find that this geometric construction is reproduced in the worldsheet algebra via a diamond of algebra inclusions. A study of the automorphisms of these algebras leads us to conjecture new mirror maps for GCS manifolds. Finally, we explore-making use of the worldsheet algebras-whether these constructions produce manifolds of generic special holonomy. In the second part of the thesis we change gears and consider string compactifications from a supergravity point of view. In particular, we focus on compactifications of the heterotic string down to three spacetime dimensions preserving minimal supersymmetry N = 1. These are described by the heterotic G2 system, which is the 7-dimensional analogue of the Hull-Strominger system. Finding solutions to this system involves the study of 7-dimensional manifolds with integrable G2-structures and the construction of G2-instantons on bundles over them. In addition, the anomaly cancellation condition mixes the different degrees of freedom of the theory in a highly non-trivial way. As a result, explicit background solutions are difficult to obtain. We construct new families of solutions to the system on homogeneous 3-Sasakian manifolds-that means either the 7-sphere or the Aloff-Wallach space N(1,1)-equipped with squashed metrics. Our solutions present constant dilaton and AdS3 spacetime. Some of these families can be regarded as finite deformations from a given solution, providing an explicit description of a particular direction in the moduli space.

Directional amplification, in which signals are selectively amplified depending on their propagation direction, has attracted much attention as a key resource for applications including quantum information processing. In this thesis, we first develop a unifying framework based on non-Hermitian topology to understand non-reciprocity and directional amplification in driven-dissipative cavity arrays. Specifically, we unveil a one-to-one correspondence between a non-zero topological invariant defined on the spectrum of the dynamic matrix and regimes of directional amplification, in which the end-to-end gain grows exponentially with the number of cavities. Furthermore, we show that non-Hermitian topological amplification is robust against disorder as long as the disorder strength does not exceed the size of the point gap-the separation of the spectrum from the origin. In another part of this thesis, we revisit the bulk-boundary correspondence for non-Hermitian topological systems. It is a fundamental phenomenon of Hermitian topological phases, however, in non-Hermitian systems, it breaks down in the conventional form due to the non-Hermitian skin effect-the localisation of a macroscopic number of eigenvectors at the boundary. Here, we show that it is possible to restore the bulk-boundary correspondence by means of the singular value decomposition: when the system is topologically non-trivial, zero singular modes emerge leading to directional amplification with their number given by the topological invariant. In the final part, we extend the notion of non-reciprocity to unidirectional bosonic transport in time-reversal symmetric systems by exploiting interference between beamsplitter and two-mode-squeezing interactions. We develop a framework to identify the phenomenon we dub quadrature non-reciprocity based on features of the particle-hole graph representing the equations of motion. In addition to unidirectionality, these networks can exhibit an even-odd pairing between collective quadratures and an exponential end-to-end gain in the case of arrays of cavities. Our work opens up new avenues for signal routing, non-Hermitian topology, and amplification in bosonic systems.

In this thesis we examine several improvements which can be made to the canonical under- standing of Galactic Chemical Evolution (GCE) models in light of modern developments in stellar physics and new modelling techniques. Not only is GCE a vital component of our understanding of the history and composition of the universe in its own right, but since it incorporates physics on the scale of the cosmological to the subatomic, it may also be used as an independent probe and constraint on physics across many different fields. We develop two brand new, state-of-the-art models for studying galactic chemical evo- lution under two differing paradigms: the Simple Analytical Chemical Evolution Model (sacem) which allows for rapid and complete scans of the high-dimensional parameter space associated with GCE, and the updated version of the Radial Migration in Chemical Evolution Simulation (RAMICES II), which emulates the underlying physics chemical evolution as faithfully, and completely, as possible. These models allow us to investigate the origin of r-process nucleosynthesis within the Milky Way, in particular, identifying the ability of 'collapsar' events to contribute meaningfully to the global r-process budget. Utilising the sacem code, we are able to evaluate in excess of 10¹² potential models of the galaxy, and evaluate them against intentionally weak constrains on the resulting chemical and temporal properties, and hence provide a strong upper bound on the ability of such events to contribute to the r-process abundance of the Milky Way at late times. We study the impact of advances in stellar evolution modelling on GCE models, utilising new rotationally-resolved stellar evolution codes and nucleosynthetic yield grids. We show that the output from these new stellar models is fundamentally irreconcilable with observed data, and hence develop a number of tools which allow future stellar modelling to be rapidly diagnosed as incompatible, providing a new constraint on the internal evolution of stellar bodies. Finally, we apply our new RAMICES II model to briefly study the phenomena of metallicity- offset, strongly peaked curves in the gas-phase abundance diagrams - so called 'caustics' - and how these imprint themselves in non-trivial ways on the stellar abundance plane, using them to inform future studies of both r-process nucleosynthesis and the assembly history of the galaxy.

The aim of this thesis is to explore new constructions in supergravity to gain insights into the AdS₄/CFT₃ and AdS₅/CFT₄ correspondences. We start by deriving a simple formula for the action of any supersymmetric solution to minimal gauged supergravity in the AdS₄/CFT₃ correspondence. We find that the holographically renormalized action localizes to the fixed points of a supersymmetric Killing vector and may then be expressed entirely in terms of topological data. In this sense, the gravitational partition function localizes in the bulk. Our general formula reproduces all known examples in the literature and makes predictions for new solutions, assuming they exist. Also in D=4, N=2 minimal gauged supergravity, we sudy a class of accelerating, rotating and dyonic black holes in AdS₄. When the acceleration is non-vanishing, These D=4 black hole metrics have conical singularities but we find a new way to desingularize them by uplifting to solutions of D=11 supergravity using a regular Sasaki-Einstein SE₇ manifold. These D=11 solutions are associated to M2-branes wrapped around a two-dimensional weighted projective space, WCP¹[ₙ₋,ₙ₊], also known as a spindle, and we find that supersymmetry is not preserved through a usual topological twist. We also discuss the supersymmetric and extremal limits of these solutions and compute the entropy of these black holes, arguing that it should be possible to derive it from certain N=2, d=3 quiver gauge theories compactified on a spinning spindle with magnetic flux. In the AdS₅/CFT₄ correspondence we continue exploring these ideas by constructing AdS₃ x WCP¹[ₙ₋,ₙ₊] solutions of different D=5 supergravity theories. Again we find that these solutions can be uplifted to find smooth solutions in D=10/11 and that supersymmetry is preserved in a different way than through the topological twist. Our construction suggests a path to the dual d=2, N=(0,2) SCFTs in the IR, associated to D3 or M5 branes wrapped on a spindle. We make a precision test of this conjecture by computing the central charge and R-symmetry of the field theories and find agreement with the gravity computations in all cases.

Shannon's theory of information laid the groundwork for the rapid developments in information and communications technologies over the last century. Yet, it assumed that information carriers were described by the laws of classical physics, whilst at the most fundamental level, nature obeys the laws of quantum physics. Quantum Shannon theory, which describes information carriers as quantum states, has led to a new era of possibilities, such as perfectly secure cryptography without pre-established keys. Yet, there is a sense in which this transition from classical to quantum is incomplete. Traditionally, quantum Shannon theory has focused on scenarios where the internal states of information carriers are quantum, whilst their trajectories in spacetime have still been assumed to be classical. This work presents a second level of quantisation where both the information itself and its propagation in spacetime are treated in a quantum fashion. The second-quantised Shannon theory describes the possibility of a single particle being simultaneously transmitted through multiple communication channels in a quantum superposition. The framework is developed using the tools of higher-order transformations and quantum resource theories, formally quantifying the resources required for communication between a sender and receiver in this setting. The advantages of the second-quantised theory are illustrated in a series of examples, showcasing various counterintuitive phenomena that occur when information is simultaneously transmitted through multiple communication channels. In particular, when a single particle travels in a quantum superposition through two alternative transmission lines, the noisy processes in the two lines can destructively interfere, leading to a cleaner communication channel overall. Various different scenarios are encompassed in the framework, including transmission through a superposition of both independent and correlated channels, as well as through large-scale communication networks. This work concludes with a study of the robustness of these protocols to errors and a discussion of recent experimental demonstrations of their associated communication advantages.

This thesis details studies into soft and collinear radiation dressing QCD hard process amplitudes. Primarily, we present a formalism which reduces the computation of arbitrary multiplicities of soft and collinear QCD radiation in the massless limit, dressing any QCD hard process, to a single Markovian evolution equation. We present the evolution equation at leading logarithmic order, with complete spin correlations, and notably without approximating the QCD colour charge; though our formalism can be systematically extended beyond this order. We investigate the formalism and find that it can be used to study the accuracy of modern day parton showers, motivate new parton showers with increased accuracy, and study the factorisation properties of QCD processes in hadron colliders. From our studies, we introduce a new form of dipole shower, constructed to inherit the accuracy of an angular-ordered shower without losing the benefits and generalised applicability of a traditional dipole shower. We also study observables which suffer from coherence violating logarithms in proton evolution at hadron colliders. We arrive at the conclusion that almost all observables at hadron colliders will violate coherence to some degree. Only observables entirely insensitive to wide-angle soft physics remain completely safe. This thesis consists of five individual publications and supplementary material providing context and greater detail. This thesis is also supplemented with an extended discussion of introductory material on quantum chromodynamics and quantum field theories more broadly.

We examine three topics in the physics of three-dimensional systems, paying particular attention to the roles of topological field theory, topological solitons, and duality. First, we consider the dynamics of nonrelativistic Chern--Simons-matter theories in $2+1$ dimensions. The theories we consider support vortex solutions and, at critical coupling, they admit an effective low-temperature description as a topological quantum mechanics on the moduli space of these vortices. Using localisation techniques, we compute the 'expected' dimension of the Hilbert space of this quantum mechanics (that is, the Euler characteristic of the relevant quantum line bundle on the moduli space) in the case of $U(N_c)$ gauge theory with $N_f$ fundamental flavours at arbitrary Chern--Simons level, $\lambda$, compactified on an arbitrary closed Riemann surface. We apply this result to the analysis of the duality between the vortices of these theories and the (composite) fermions that arise in descriptions of strongly correlated electron systems and, in particular, of (nonAbelian, fractional) quantum Hall fluids. In simple cases, where the degeneracies of the fermion fluids are well understood, the results give quantitative evidence for these dualities. For example, when $N_c = N_f = \lambda$ we find strong evidence that the vortices are dual to fermions in the lowest nonAbelian Landau level associated to a background $U(N_f)$ flux. In more complicated examples, the results lead us to quantitative insight into the conjectural dual theory. We find that quantum vortices generally admit a description as composite objects, bound states of (dual) anyons. We comment on potential links with three-dimensional mirror symmetry. We also compute the equivariant expected degeneracy of local Abelian vortices on the $\Omega$-deformed sphere, finding it to be a $q$-analog of the undeformed version. By taking the semiclassical limit, we use our result to compute the volumes of vortex moduli spaces (which are closely related to the statistical mechanical partition functions of vortex gases). The volume of the $k$-vortex moduli space is a polynomial in the volume of physical space and, in the local case of $N_c = N_f$, we find a reduction in the degree of this polynomial, from $N_f k$ to $k$, resolving a point of confusion in the literature. We also find new integrability results relating solutions of the exotic vortex equations, which generalise the Jackiw--Pi and Ambjørn--Olesen vortex equations, in theories with $N_f=1$ to pairs consisting of a flat $PSU(N_c+1)$ connection and a holomorphic section of the associated holomorphic $\mathbb{C}P^{N_c}$-bundle. As well as providing a way to generate exact exotic vortex solutions in nonAbelian gauge theories, this leads to conjectural descriptions of the moduli spaces of exotic vortices and to topology-dependent selection rules for exotic vortex solutions (generalising the fact that Jackiw--Pi vortex solutions on the infinite sphere always have even flux). Second, we turn our attention to three-dimensional sigma models with $\mathcal{N}=4$ supersymmetry. When its target space is a hyperKähler manifold carrying a (so-called) permuting $Sp(1)$ action, such a sigma model admits two topological twists: the A-twist and the B-twist. The B-twist, also known as Rozansky--Witten theory, is well-understood, while the A-twist is a little more mysterious. The two twists are expected to be related by three-dimensional mirror symmetry. We construct the A-twist on general three-manifolds and analyse its local and extended operators. We show that compactifying the theory on a circle gives the two-dimensional A-model in the presence of a certain 'defect operator'. We then outline the construction of the 2-category of boundary conditions in the three-dimensional A-twist. In particular, we find that the A-twist induces a monoidal structure on the Fukaya categories of a certain, restricted, class of Kähler manifolds. Third, we consider magnetic Skyrmions in ferromagnetic materials. We produce a continuum toy model of fractionalised electrons in three spatial dimensions describing magnetic Skyrmions and their creation and destruction via emergent magnetic monopoles. When an external magnetic field is applied, the model has a critical point where confined monopoles are dynamically stabilised and monopole-antimonopole pairs may condense. We find novel 'BPS-like' equations for these configurations. By tuning the model to critical coupling and then deforming it, we find qualitative agreement with the observed phase structure of chiral ferromagnets. We then consider the critically-coupled model for magnetic Skyrmions on thin films, generalising it to thin films with curved geometry. We find exact Skyrmion solutions on some curved films with symmetry, namely spherical, conical, and cylindrical films. We prove the existence of Skyrmion solutions in the model on general compact films and investigate the geometry of the (resolved) moduli space of solutions.

In quantum gravity and field theory, large gauge transformations lead to novel degrees of freedom living at the boundary. In the presence of a black hole they are called ‘soft hair’, and it has been suggested that they go some way towards answering the black hole information problem. More generally, they are known as ‘edge modes’, and play a key role in the structure of the quantum state. Another approach to black hole information involves entanglement, and a key theme of this thesis is to explore aspects of the relationship between edge modes and entanglement. We first establish a thermodynamical interpretation of soft hair by deriving generalisations of the laws of black hole mechanics. These laws lead to a natural definition of an entropy density on the black hole horizon, and reveal that soft hairs at neighbouring points are in thermal contact with one another. There are boundary ambiguities in the traditional construction of phase spaces in field theory, and resolving these ambiguities is a step that must be taken before one can fully understand edge modes and soft hair. We provide two possible approaches to such a resolution. The first approach applies to theories without gravity, and involves a direct evaluation of the Poisson structure from a semiclassical path integral. This is then inverted to give the symplectic structure. The second approach applies in holographic theories of quantum gravity. We show how one can recover the symplectic structure in a bulk subregion by measuring an object known as ‘Uhlmann holonomy’ on the boundary, which is a generalisation of Berry phase. The Uhlmann holonomy is actually a direct measure of the entanglement in the quantum state, and so this provides a connection between edge modes and entanglement. In the final part of the thesis we study Uhlmann phase more generally, showing that it may be computed with a holographic path integral in a generic system, so long as the state of the system involves a sufficient degree of entanglement. This suggests that there are deep connections between Uhlmann holonomy, entanglement and holography.

Cosmic strings are a fundamental feature of many physically-motivated field theories which inevitably form in the early Universe, as a result of a symmetry breaking phase transition. An important example is the Peccei-Quinn mechanism, from which strings emerge as a potential source of dark matter axions. They are also a strong source of gravitational wave (GW) emission, with the potential for detection by the Laser Interferometer Gravitational-Wave Observatory (LIGO) and other GW experiments. The nonlinear evolution of cosmic strings has been extensively studied using large-scale numerical simulations. However, the vast difference in scale between a typical string width and the string curvature poses a significant computational challenge. This is usually addressed by approximating the string to have either zero or fixed comoving width, resulting in inconsistencies in predictions between different methods. One technique that can address this issue is adaptive mesh refinement (AMR), which allows the resolution of the numerical grid to adapt to the scale of the features of interest in the simulation. This thesis uses GRChombo, a sophisticated code originally designed for numerical relativity, to perform the first AMR simulations of global cosmic strings. We also present our numerical contributions to GRChombo as a core developer, including novel diagnostic tools and performance enhancement. We perform a detailed quantitative investigation of single sinusoidally displaced string configurations, comparing oscillating string trajectories with a backreaction model accounting for radiation energy losses. We conclude that analytic radiation modelling in the thin-string (Nambu-Goto) limit provides the appropriate picture for cosmological evolution. We also investigate the resulting massless (Goldstone boson or axion) and massive (Higgs) radiation signals, using quantitative diagnostic tools to determine their eigenmode decomposition. We find that the massless quadrupole is dominant and massive radiation is strongly suppressed with increasing mass, with a complex wavepacket structure that is sensitive to numerical resolution. String network configurations are also simulated, with advanced visualisation of radiation used to reveal new qualitative phenomena as strings reconnect and small loops decay. The thesis concludes with the cosmological implications of this work, considering dark matter axions radiated by cosmic strings and the outlook for gravitational wave signatures.

Light scalar fields emerge as a generic prediction in physics beyond the Standard Model. For example, they arise as new degrees of freedom in modified gravity, as Kaluza-Klein modes from extra compactified dimensions, and as Nambu-Goldstone bosons from spontaneously broken symmetries. Far from being just objects of theoretical interest, these scalar fields could also play crucial roles in resolving some of the most important open problems, such as the nature of dark matter and dark energy. Given this ubiquity in modern theoretical physics and their potentially far-reaching implications, efforts to detect or otherwise rule out these hypothetical scalars have burgeoned into a global enterprise in recent years. This thesis contributes to this ongoing effort by updating our understanding of how light scalar fields influence the dynamics of moving bodies, focusing on two novel scenarios. We begin by reanalysing the motion of electrons in laboratory experiments designed to deliver high-precision measurements of the fine-structure constant. The vacuum chambers employed in these setups make them ideal testing grounds for a class of scalar--tensor theories that screen the effects of their scalar mode based on the ambient density. If unscreened, the scalar exerts an attractive “fifth” force on the electron and, moreover, transforms the vacuum cavity into a dielectric medium due to its interactions with electromagnetic fields. Because these effects introduce different amounts of systematic bias into each experiment, good agreement between independent measurements of the fine-structure constant can be used to establish meaningful constraints on the parameter spaces of these models. In the second part of this thesis, we turn to investigate how ambient scalar fields influence the motion of binary black holes. Even though the models we consider are subject to no-hair theorems, the interplay between absorption at the horizons and momentum transfer in the bulk of the spacetime still gives rise to interesting phenomenology. We show that this interaction causes a fraction of the ambient field to be ejected from the system as scalar radiation, while the black holes themselves are seen to feel the effects of an emergent fifth force. Moreover, if the ambient field corotates with the binary, it can extract energy from the orbital motion and grow exponentially through a process akin to superradiance. Although these effects turn out to be highly suppressed in the regime amenable to analytic methods, the novel techniques developed herein lay the groundwork for future studies of these complex gravitational systems.

The Large-Scale Structure (LSS) of the Universe, i.e. the distribution of matter and luminous tracers (such as galaxies), contains a wealth of information about the origin, composition, and evolution of the Universe. In order to extract this information, the non-linearities present in late-time observables provided by LSS surveys must be understood well. In general, there are three main sources of non-linearities: (1) non-linear matter clustering due to gravity; (2) non-linear biasing, i.e. the relation between the distribution of tracers and dark matter; and (3) primordial non-Gaussianity, which induces non-linearities in the initial conditions. The Effective Field Theory of Large-Scale Structure (EFTofLSS) provides a powerful framework to model the non-linear clustering due to gravity. In this thesis, we focus on understanding the non-linearities due to galaxy biasing using the EFTofLSS and numerical N-body simulations. This thesis is comprised of the following three projects: In the first part, we present a novel method to constrain quadratic and cubic galaxy bias parameters in dark matter simulations. The natural statistics to constrain quadratic and cubic bias parameters are tree-level bispectrum and trispectrum, respectively. Since these statistics are computationally quite expensive, we use efficient squared and cubic field estimators that contain integrated bispectrum and trispectrum information. We use the constraints to model the one-loop halo-matter power spectrum and show that the results agree with simulations up to kmax = 0.1h Mpc 1 once an additional derivative bias is implemented (Published in: Abidi & Baldauf, JCAP07(2018)029). In the second part, we develop a formalism to reconstruct the linear density field based on quadratic couplings in galaxy clustering. We employ a quadratic estimator inspired by Cosmic Microwave Background (CMB) lensing reconstruction. We incorporate non-linearities due to gravity, galaxy biasing and primordial non-Gaussianity, and verify our predictions with N-body simulations. We perform a Fisher matrix analysis on how the reconstructed field in combination with the biased tracer field can improve constraints on local type primordial non-Gaussianity. We find significant improvement on constraints due to cosmic variance cancellation resulting from the additional correlated modes of the reconstructed field, similar to multi-tracer analyses. In the third part, we develop a method to constrain non-linear galaxy bias parameters using the two- and three-point functions of projected galaxy clustering in correlation with CMB lensing convergence. The project thus aims to bring the methodology developed in project 1 above closer to data. We develop the quadratic field method for projected fields to avoid complications from non-linear redshift space distortions. We perform a Fisher forecast to show that this method can indeed be used to put constraints on bias parameters and the amplitude of matter fluctuations. Finally, using N-body simulations we ascertain that the projected statistics do indeed reduce the impact of finger-of-god corrections.

In this thesis we explore Einstein gravity coupled to matter, and more specifically, we focus on the Kerr black hole in the presence of a massive scalar field. We investigate the superradiant phenomenon present in this setting - amplified scattering of scalar waves by the black hole given the right conditions on the scalar field's frequency are satisfied. Due to the mass term the spacetime develops a trapping region where the scalar waves can get localised instead of dispersing to infinity. In this way, the energy extracted from the black hole leads to the formation of a quasi bound state of the scalar field around it, known as a scalar cloud. This parallels the situation in Kerr-AdS, where due to the timelike character of the boundary this phenomenon appears more naturally and one does not necessarily need to make the field massive. We explore some of the consequences due to the formation of the scalar clouds in the asymptotically flat context. In the case of a complex scalar field the configuration can actually settle to a stationary solution to the Einstein equation which represents a scalar hairy Kerr black hole in asymptotically flat four dimensions - the first example of such black holes that does not violate energy conditions, discovered recently. These scalar hairy black holes branch off from the Kerr solution at the onset of scalar superradiance, when the scalar cloud starts forming. Since their discovery a number of studies have been carried out, trying to relate their properties to astrophysics. However, prior to our work, no stability analysis was performed. This is particularly important if we want to argue for the astrophysical significance of such solutions. We made the initial step in answering this question by showing that such black holes are unstable towards higher excited superradiant modes than the mode from whose onset they branched off. This required the construction of the black hole backgrounds numerically, utilising the DeTurck method and solving a system of PDEs with extended precision using spectral methods. Afterwards, a clever choice of gauge allowed us to decouple the scalar field perturbations form the gravitational sector and perform the analysis by looking at the quasinormal mode spectrum of the hairy solutions. When the scalar field is real, these stationary hairy solutions do not exist, but scalar clouds still form around the black hole. Moreover, our previous work suggested that for any parameters of the Kerr black hole, an unstable scalar mode will be present. We showed this analytically using a hybrid WKB and matched asymptotic expansion technique and confirmed it with numerical data. This led us to explore an idea for a plausible counterexample to the Weak Cosmic Censorship Conjecture in flat four dimensions, based on the cascading of energies, as seen in AdS, whereby with time even higher superradiant modes become dominant and form clouds around the black hole. In support of our claim we have integrated the sourced Teukolsky equation for gravitational perturbations of Kerr numerically with extended precision in order to obtain the backreaction of the scalar field on the geometry and also analysed the system analytically, as detailed above, in order to confirm our numerics and discuss the endpoint of the evolution of the system.

Ultracold atomic gases loaded into optical cavities constitute one of the most versatile platforms for the study of out-of-equilibrium dynamics and quantum simulation of many- body systems. In this thesis, we explore these two possibilities, motivated by current state-of-the-art atom-cavity experiments, uncovering novel phenomena and opening up new theoretical and experimental avenues into the intriguing world of quantum many- body physics. First, we study a gas of ultracold atoms coupled to three optical resonators. We show that the inherent Z2 symmetries, associated with each atom-cavity coupling, can be combined into a global SO(3) rotational symmetry which can be spontaneously broken. We determine the phase diagram of the system, which shows the emergence and breaking of the continuous symmetries and displays first- and second-order phase transitions. We argue that by coupling the atoms equally to n different modes, it will in general be possible to generate a global SO(n) symmetry. Second, we investigate the dynamics of a spinor BEC inside an optical cavity. We focus on a two-component Dicke model with complex light-matter couplings, accounting for photon losses. We compute the steady-state phase diagram and find dynamical in- stabilities in the form of limit cycles, heralded by the presence of exceptional points and level attraction. We show that the instabilities are induced by dissipative processes that generate nonreciprocal couplings between the two collective spins. Lastly, we explore the dynamics of a BEC inside an optical cavity in the presence of an optical lattice. We derive an effective master equation by adiabatically eliminating the cavity field. In the bad-cavity regime, we find an infinite-temperature steady state, but with relaxation dynamics that can be highly nontrivial. For small hopping, the interplay between dissipation and strong interactions leads to an algebraic relaxation of the system, whereas for large hopping, the approach to the steady state is exponential. In the good- cavity regime, we show that the system allows for optical pumping between momentum modes, enabling cavity cooling.

Cosmological inflation is a simple, and observationally well-supported, mechanism for generating a flat, spatially homogeneous universe with the statistical correlations in the cosmic microwave background we see today. Determining precisely how inflation happened, and how many fields were involved, are some of the main challenges of modern cosmology. The first part of the thesis, consisting of Chapters 2 and 3, addresses this question by looking at what future measurements of local non-Gaussianity will tell us. Local non-Gaussianity has been proposed as a key observable for distinguishing between single- and multifield inflation, as a large value of this parameter would rule out the former. However, a small value would not necessarily rule out the latter. Using a new technique for generating random functions with Gaussian random fields, which we also prove the validity of, we generate random potentials for as many as 100 fields for inflation. We look at the observables of these models and in particular compute the local non-Gaussianity. An overwhelming majority of these models give local non-Gaussianity compatible with single-field inflation, despite significant multifield effects on superhorizon scales, indicating that this observable may not be sufficient to distinguish between these types of models. The second part of the thesis, consisting of Chapters 4 and 5, addresses another aspect of this question by looking at other types of inflationary solutions than slow-roll, slow-turn. Slow-roll, slow-turn is an easily realised solution, but requires a very flat potential over large distances in field-space. The fine-tuning needed for this remains an Achilles heel of the inflationary paradigm. However, there are inflationary solutions which can be realised in steep potentials. `Hyperinflation' is a particularly interesting one of these, and we investigate this solution in detail. Using the techniques developed to study hyperinflation, we then show that there exists a new, completely general two-field attractor solution that is characterised by rapidly turning fields. This `rapid-turn attractor' does not require any particular background geometry, and explains how several recently studied two-field inflation models are related to each other.

Lovelock and Horndeski theories are natural generalisations of Einstein’s theory of General Relativity. They find applications in Astrophysics, Cosmology and String Theory. This dissertation discusses some issues regarding the mathematical consistency of these theories. In the first part of the thesis we study the Shapiro time delay for gravitons in spherically symmetric spacetimes in Einstein–Gauss–Bonnet gravity (a Lovelock theory). In Lovelock theories, gravitons can propagate faster or slower than light. We show that, thanks to this property, it is possible for them to experience a negative time delay. It was recently argued that this feature could be employed to construct closed causal curves, implying that the theory should be discarded as causally pathological. We show that this construction is unphysical, for it cannot be realised as the evolution of sensible initial data. The second part investigates the local well-posedness of the initial value problem for Lovelock and Horndeski theories. For the initial value problem to be well-posed it is necessary that the equations of motion be strongly hyperbolic. It is known that when the background fields are large, even weak hyperbolicity may fail. Hence, we consider the weak field regime, in which these equations can be considered as small perturbations of the Einstein equations. We prove that both Lovelock and Horndeski theories are weakly hyperbolic in a generic weak field background in harmonic and generalised harmonic gauge, respectively. We show that Lovelock theories fail to be strongly hyperbolic in this setting. We also prove that the most general Horndeski theory which is strongly hyperbolic is simply a “k-essence” theory coupled to Einstein gravity and that any more general theory would necessarily fail to be so. Our results imply that the standard methods used to prove the well-posedness of the initial value problem for the Einstein equations cannot be extended to Lovelock or Horndeski theories. This raises the possibility that these theories may not admit a well-posed initial value problem even for weak fields and hence might not constitute a valid alternative to General Relativity.

The ΛCDM model for the Universe is highly successful in explaining cosmological observations to date, and its parameters tightly constrained by Cosmic Microwave Background (CMB) experiments such as Planck. Higher-order statistics, like the three-point correlation function or bispectrum in Fourier space, will be indispensable for furthering our understanding of the Universe. While these methodologies have been developed over the years and applied to CMB analyses, similar work on large-scale structure is still in its infancy. Additionally, information from future galaxy surveys such as LSST and Euclid will soon exceed that available from the CMB, demonstrating a pressing need for such tools. The theoretical modelling of non-linear gravitational interactions is difficult beyond the perturbative regime, necessitating large, expensive N-body dark matter simulations to understand the small-scale dynamics. Additionally, the direct numerical computation of the matter bispectrum is intractable due to the multiplicity of triangular configurations. In this Thesis, we make breakthroughs in both of these problems. First, we present the newly rewritten MODAL-LSS formalism that enables efficient and optimal estimation of the full bispectrum for any matter density field to unprecedented accuracy, as well as demonstrating rapid convergence which makes it ideal for the analysis of large datasets. This has allowed us to benchmark fast dark matter codes (e.g. particle-mesh or L-PICOLA) against GADGET-3 using the bispectrum, showing quantitatively how the mismatch at large k can be improved with a simple boosting technique in the power spectrum. We have also estimated the non-Gaussian contribution to the dark matter bispectrum covariance, which cannot be computed analytically in the non-linear regime. This will be vital for the extraction of cosmological parameters from data in the future. In preparation for the analysis of future galaxy datasets we have also investigated the non-trivial problem of linking the underlying dark matter density field to the observed galaxy distribution. As an important milestone we have investigated the effects of the halo profile, the Halo Occupation Distribution (HOD) model, and multivariate assembly bias models of the halo occupation and concentration on the power spectrum and full bispectrum of a subhalo catalogue derived from the ROCKSTAR halo finder. These fast, phenomenological methods allow us to pave the way for the efficient generation of mock galaxy catalogues.

In this thesis we consider the motion of a charged particle in strong electromagnetic background fields, having in mind applications to state-of-the-art high-power lasers. To find solutions of the Lorentz force equation of motion, we make use of Noether's theorem to identify conserved quantities of the charge dynamics. We will explain how, given enough symmetries, a dynamical system becomes integrable or, with a maximum number of conserved quantities, maximally superintegrable. Beginning with charged particles in vector background fields, we shall show that the relevant symmetry group is the Poincaré group. The dynamics for constant and univariate fields is classified, and their integrability properties are clarified. We then move on to the problem of a particle in a scalar background field and show that the symmetry group is extended to the conformal group. We then present examples of fields which include Poincaré, dilation and special conformal symmetries leading to varying extents of integrability.

Holographic dualities are now an established tool in the study of universal properties of strongly coupled field theories. Yet, theories without translational symmetry are still poorly understood in this context. In this dissertation, we investigate three new approaches to this challenging problem. The first part of the dissertation concerns a class of phenomenological holographic models in which momentum relaxation can be achieved without breaking translational symmetry in the dual geometry. In particular, we focus on an example in which the dual geometry is similar to anti-de Sitter (AdS) Brans-Dicke theory. We study the thermodynamic and transport properties of the model and show that for strong momentum relaxation and low temperatures the model has insulator-like behaviour. In the second part, we go beyond the effective description and consider holographic theories which explicitly break translational symmetry. From the perspective of gravity, these theories translate to geometries that vary explicitly in the boundary space-like coordinates. We refer to these geometries as 'inhomogeneous' and investigate two approaches to study them. The first is motivated by the question: "what happens to a homogeneous geometry when coupled with a field varying randomly in space?". Starting from an AdS geometry at zero or finite temperature, we show that a spatially varying random Maxwell potential drives the dual field theory to a non-trivial infra-red fixed point characterised by an emerging scale invariance. Thermodynamic and transport properties of this disordered ground state are also discussed. The second is motivated by the complementary question: "how does a random geometry affect a probe field?". In the weak disorder limit, we show that disorder induces an additional power-law decay in the dual correlation functions. For certain choices of geometry profile, this contribution becomes dominant in the infra-red, indicating the breaking of perturbation theory and the possible existence of a phase transition induced by disorder. The third and last part of this dissertation switches from the gravity to the field theoretical side of the duality. We discuss the Sachdev-Ye-Kitaev (SYK) model, a disordered many-body model with distinctive black hole-like properties. We provide analytical and numerical evidence that these holographic properties are robust against a natural one-body deformation for a finite range of parameters. Outside this interval, this system undergoes a chaotic-integrable transition.