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Effective theories have applications in many areas of physics, from Newtonian mechanics through to condensed matter physics. In this thesis we discuss effective field theories in the context of constructing nucleon-nucleon interactions in a systematic and model-independent way. We start with the examination of the spin-singlet P-wave, by using distorted wave methods to remove the effects of long-range pion-exchange forces from the empirical 1P1 phase shift. The divergence appearing in this channel is renormalised using a counterterm that is provided by the relevant (Weinberg) power counting. This leaves an effective interaction strength that can be analysed, and from which one can extract an approximate scale for the underlying physics. We determine this scale to be close to the delta-resonance. We then turn to coupled (spin-triplet) waves, focussing predominantly on the 3S1-3D1 wave that contains the deuteron - an important system to understand in the context of nuclear forces. Starting with the 3S1-3D1 scattered waves, we again remove long-range pion-exchange forces from the empirical phase shifts, and extract an effective interaction matrix. The element that suffers from a divergence can be renormalised using counterterms provided by a renormalisation group analysis. Switching to negative energies we look for the deuteron boundstate, which is loosely bound and so pion physics plays an important role. Using the counterterms provided at positive energies, we extrapolate to the boundstate and treat this, two-pion-exchange and recoil one-pion-exchange as a combined perturbation to the system. We then use perturbation theory techniques to calculate the first-order correction to the energy and wave function, from which we calculate some deuteron observables.

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A recent study of the positronium atom showed that the energy levels could be determined numerically using an effective field theory just as easily as the underlying true theory. Here, we expand on this idea by modeling the three-body positronium-ion and four-body di-positronium molecule with low-energy effective field theories. We then compare the results obtained using the effective theories to those found in a similar manner with the true theory to determine if numerical calculations will converge more quickly using the effective field theory due to removal of the Coulomb divergence. Finally, with the necessary framework in place, we calculate a matrix element needed to evaluate the correction to the magnetic moment of the positronium-ion due to the interaction between the positron and the two electrons which form a spin singlet.

General relativity describes gravity in terms of an interacting massless spin-2 field - the graviton. This 100-year-old theory has been spectacularly successful in explaining observations. However, theoretical exploration and the cosmological constant problem motivate the study of alternative theories of gravity. Recently, there has been great progress in understanding theories that give the graviton a mass. This thesis considers several aspects of these massive spin-2 effective field theories and related theories. These theories are first studied from the perspective of scattering amplitudes. The most general 2 → 2 scattering amplitude is constructed for theories containing a single massive graviton or vector. These amplitudes are then used to find the highest strong coupling scales in such theories, assuming a particular scaling of fields and momenta. Generalisations to include additional fields and self-interactions for massive higher-spin fields are also discussed. Constraints that arise from the existence of an ultraviolet completion are then studied. It is shown using dispersion relation arguments that the pseudo-linear massive spin-2 theory cannot admit an analytic, Lorentz-invariant, and unitary ultraviolet completion, but that such completions are not ruled out for massive vector theories. The behaviour of massive spin-2 theories under dimensional reduction is also explored. Stability conditions and the lower-dimensional spectrum are derived for the Kaluza-Klein dimensional reduction of a partially massless graviton and a massive graviton on an Einstein product manifold. Additionally, the nonlinear dimensional reduction of the zero modes in dRGT massive gravity is shown to produce a mass-varying massive gravity theory. Lastly, attempts to construct a version of unimodular gravity containing a massive graviton are discussed. A candidate theory is proposed and is shown to have pathologies. Dimensional reduction is then used to generate massive spin-2 theories with noncanonical kinetic terms and auxiliary fields. These theories are shown to be equivalent to the Fierz-Pauli theory, which provides further evidence for the uniqueness of the kinetic term used in dRGT massive gravity.

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Open Effective Field Theories are a class of Effective Field Theories (EFTs) built using ideas from open quantum systems in which a measured sector (the system) interacts with an unmeasured sector (the environment). It is argued that Open EFTs are useful tools for any situation in which a quantum system couples to a gravitational background with an event horizon. The main reason for this is that for any EFT of gravity one generically expects perturbation theory to breakdown at late times (when interactions with the background persist indefinitely). It is shown that the tools of Open EFTs allow one to resum late-time perturbative breakdowns in order to make reliable late time predictions (without resorting to solving the dynamics exactly). To build evidence of their usefulness to these types of gravitational problems, Open EFT approximation methods are applied to two toy models relating to black hole physics. / Thesis / Doctor of Philosophy (PhD) / Open Effective Field Theories are a class of quantum theories in which a measured sector (the system) is used to make physical predictions with, while interacting with an unmeasured sector (the environment). In this thesis arguments are made that Open EFTs are useful for studying gravitating quantum systems, especially when there is an event horizon present (for example in gravitational fields like that of a black hole). Open EFTs are applied to simple toy problems in such settings to illustrate their usefulness.

Since the discovery of the cosmic microwave background (CMB), our understanding of the cosmos has been rapidly evolving. Detailed measurements of the CMB temperature fluctuations have led to a standard cosmological model, which traces the origin of the large-scale structure of the universe to quantum fluctuations during inflation. Although the basic framework of inflationary cosmology is now well-established, the microphysical mechanism responsible for the accelerated expansion remains a mystery. In this thesis, we describe how the physics underlying inflation can be probed using two cosmological observables: higher-order correlations of primordial density perturbations (non-Gaussianity) and primordial gravitational waves (tensor modes). In the first part of the thesis, we explore novel signatures of high-energy physics in higher- order correlation functions of inflationary perturbations. First, we use causality and unitarity to make connections between cosmological observations and the underlying short-distance dynamics of single-field inflation. We obtain a constraint on the size and the sign of the four-point function in terms of the amplitude of the three-point function. We then study the imprints of extra massive particles of arbitrary spin on the three-point function. We classify the couplings of these particles to inflationary scalar and tensor perturbations and derive explicit shape functions for their three- point functions that can serve as templates for future observational searches. Establishing the particle content during inflation would provide important hints for the microscopic theory of inflation. In the second part, we study ways of testing the nature of inflation using inflationary tensor modes. We consider effects of gravitational corrections to Einstein gravity in models of high-scale inflation. We show that these scenarios can lead to a violation of the tensor consistency condition (i.e. the relation between the amplitude and the scale-dependence of the tensor two-point function) that is satisfied by canonical single-field inflationary models. Finally, we consider the prospects for measuring the inflationary superhorizon signature in future observations. We define an estimator that captures superhorizon correlations and present forecasts for the detectability of the signal with future CMB polarization experiments.

In this work, we use the recently developed equilibrium generating functional and systematic derivative expansion approach to hydrodynamics to explore three new regimes of relativistic hydrodynamics. First, we derive the equations of motion and write the constitutive relations to first order in derivatives for relativistic fluids coupled to an external vector field. Next, for relativistic fluids in strong magnetic fields B ~ O(1), we derive the equations of motion and present the constitutive relations to first order in derivatives. From the resulting system of equations, we find the hydrodynamic modes for these systems. We also find the constraints on the transport coefficients due to the entropy production argument and derive the corresponding Kubo formulas. Finally, we repeat the same analysis for relativistic fluids coupled to dynamical electromagnetic fields with <B> ~ O(1). / Graduate

Effective Field Theory (EFT) provides a systematic framework to study nuclear structure at low energy. The present work uses EFT to study the Coulomb effects in protonproton scattering. The Coulomb phase shift for elastic scattering is calculated. The calculation done here are on a lattice with periodic boundary conditions, and has a hard spherical wall imposed on it. The scattering inside the sphere produces spherical standing waves, the properties of which are exploited to calculate the phase shift and then compared with known theoretical calculations.