Compact objects and gravitational waves. Exploring fundamental physics with tidal effects

Abstract
In this thesis we study the role of relativistic tidal effects in binary systems of compact objects and their link to fundamental physics and gravitational waves. In particular, we develop theoretical frameworks to systematically and rigorously connect the microphysical information encoded in the compact object, with the dynamical spacetime of the binary, relevant for current and future gravitational-wave observations. We start with an overview of gravitational-wave theory and tidal effects before discussing our three lines of novel work. First, we generalise the relativistic treatment of tidal effects to gravity theories beyond general relativity which give rise to scalar hair in compact objects. We uncover a new set of tidal deformabilities and compute numerical values for neutron stars in scalar-tensor theories. We assess degeneracies between internal structure and gravity theories and extract the key parameters relevant for gravitational wave observations. Second, we calculate in detail the effects on the waveform and study the role and implications that these new parameters have for gravitational wave signals of coalescing binary systems. Furthermore, we develop a novel formalism to include the quasi-normal mode structure in a frequency-dependent dynamical tidal response function from gauge-invariant scattering amplitudes. In particular, this formalism overcomes previous difficulties with unambiguous identifications of information from strong-field regimes. As a case study, we apply our formalism to scalar perturbations of a Schwarzschild black hole and recover results from previous literature on the absorption cross section and tidal Love number. Additionally, we investigate the role played by analytic continuation to resolve degeneracies between post-Newtonian corrections, characterising relativistic effects in the binary, and multipolar expansions, encoding the finite size of the bodies.

Fingerprinting New Physics with Effective Field Theories

Abstract
Given the absence of direct evidence for new resonances beyond the Standard Model (BSM) at the Large Hadron Collider (LHC) so far, a complementary strategy to search for new physics in an indirect way is provided by the Standard Model Effective Field Theory (SMEFT). As the low-energy limit of a generic ultraviolet (UV) completion of the SM, the SMEFT provides a powerful theoretical framework to correlate deviations from the SM between different processes, offering experimental sensitivity to a plethora of SM extensions. This thesis presents a state-of-the-art SMEFT interpretation of the top, Higgs, diboson and electroweak sectors, taking into account data collected at the Large Electron-Positron Collider (LEP), the SLAC Large Detector (SLD) and the LHC. We also include the effect of the upcoming High-Luminosity LHC (HL-LHC) upgrade and demonstrate the unprecedented impact on the SMEFT parameter space of two proposed electron-positron colliders: the electron-positron Future Circular Collider (FCC-ee) and the Circular Electron Positron Collider (CEPC). We present constraints both in terms of Wilson coefficients, and couplings and masses of a wide range of UV-complete models through a newly developed automatised limit-setting procedure. We further present novel methodological advances through the development of unbinned multivariate likelihoods specialised to the SMEFT that provide maximal sensitivity to new physics using classification and regression techniques from Machine Learning. Our results provide an extensive characterisation of the SMEFT parameter space as probed both by current and future colliders, providing timely input to the upcoming European Strategy for Particle Physics Update.

Topological states in aperiodic, non Hermitian and electronically correlated systems

Abstract
This thesis explores how topological concepts, usually associated with abstract mathematics, provide insights into complex physical systems. Physicists use topology to study systems that exhibit robust properties unaffected by minor changes. For example, topological insulators are materials that conduct electricity only at their boundaries and could improve the efficiency of current electronics due to their dissipationless transport properties. Similarly, topological superconductors might enable scalable quantum computing by protecting delicate quantum states from environmental interference. This thesis focuses on multiple aspects where topology can arise. One of those is on non-Hermitian systems, which typically describe systems coupled to environmental interactions. Using graph theory and the concept of latent symmetries, we identified new topological phases within seemingly complicated systems. We also constructed a continuum approximation framework to study disorder at phase transitions in non-Hermitian systems, providing insights into topological stability. Beyond non-Hermitian systems, we also developed, along similar lines, continuum approximations to study a topological insulator in the presence of electron-electron interactions, showing that they do not alter the principal mechanism behind a topological phase. A second focus is on aperiodic structures like quasicrystals, which lack traditional periodic order but exhibit long-range correlations. Quasicrystals can be constructed by projecting higher-dimensional crystals into lower dimensions, revealing hidden fractal structures. The thesis explores how impurities disrupt quasicrystalline order and examines topological phenomena in these aperiodic systems, such as topological charge pumping and boundary states protected by inversion symmetry. To summarize, this work reveals hidden topological structures in non-traditional systems, offering a foundation for future experimental and theoretical research in topological phases and aperiodic materials.