This is the first of two papers studying localization of massive bulk fields on a bane in 5D anti-de Sitter spacetime, and some of their cosmological consequences. Here we focus on a massive 5D scalar, which is known to lack a localized mode, and discuss how a seeming discontinuity between this theory and the massless theory - known to support a localized zero mode - is resolved thanks to peculiar analytic properties of the massive two-point amplitude. Furthermore, we propose a boundary term that leads to the emergence of a massless localized mode in the massive theory. Last but not least, we consider the case when the brane world-volume is de Sitter spacetime, and prove the existence of a localized massive mode. We discuss how these results, taken collectively, can be used to describe the accelerated expansion due to the massive 5D scalar field in an early, or in a late-time universe.

As is well known, both massive gravity and bigravity exhibit the linear van Dam-Veltman-Zakharov (vDVZ) discontinuity that is cured classically by the nonlinear Vainshtein mechanism due to certain low scale strongly coupled interactions. Here we show how both the vDVZ and strong coupling problems can be removed by embedding 4D covariant massive gravity into a certain 5D warped geometry. The 4D theory is a nonlinear strongly coupled massive gravity, that is being coupled to a 5D bulk theory that generates a bulk graviton mass via a one loop diagram. This induced mass leads to an additional 4D kinetic term for the 4D longitudinal mode, even on flat space. Due to this kinetic term the 4D massive theory becomes weakly coupled all the way up to a high energy scale set by the bulk cosmological constant. The same effect leads to a suppression of the interactions of the 4D longitudinal mode with a 4D matter stress-tensor, thus removing the vDVZ discontinuity. The proposed mechanism has a pure 4D holographic interpretation: a 4D nonlinear massive gravity mixes to a non-conserved symmetric tensor of a 4D CFT that has a cutoff; the latter mixing generates a large kinetic term for the longitudinal mode, and this makes the longitudinal mode be weakly coupled to a matter stress-tensor, and weakly self-coupled, all the way up to the scale of the 4D CFT cutoff.

As is well known, both massive gravity and bigravity exhibit the linear van Dam-Veltman-Zakharov (vDVZ) discontinuity that is cured classically by the nonlinear Vainshtein mechanism due to certain low scale strongly coupled interactions. Here we show how both the vDVZ and strong coupling problems can be removed by embedding 4D covariant massive gravity into a certain 5D warped geometry. The 4D theory is a nonlinear strongly coupled massive gravity, that is being coupled to a 5D bulk theory that generates a bulk graviton mass via a one loop diagram. This induced mass leads to an additional 4D kinetic term for the 4D longitudinal mode, even on flat space. Due to this kinetic term the 4D massive theory becomes weakly coupled all the way up to a high energy scale set by the bulk cosmological constant. The same effect leads to a suppression of the interactions of the 4D longitudinal mode with a 4D matter stress-tensor, thus removing the vDVZ discontinuity. The proposed mechanism has a pure 4D holographic interpretation: a 4D nonlinear massive gravity mixes to a nonconserved symmetric tensor of a 4D CFT that has a cutoff; the latter mixing generates a large kinetic term for the longitudinal mode, and this makes the longitudinal mode be weakly coupled to a matter stress-tensor, and weakly self-coupled, all the way up to the scale of the 4D CFT cutoff.

We calculate the scaling dimensions of operators with large global charge and spin in 2+1 dimensional conformal field theories. By the state-operator correspondence, these operators correspond to superfluids with vortices and can be systematically studied using effective field theory. As the spin increases from zero to the unitarity bound, the superfluid state corresponding to the lowest dimension operator passes through three distinct regimes: (1) a single phonon, (2) two vortices, and (3) multiple vortices. We also calculate correlation functions with two such operators and the Noether current.

It is well-known that the presence of a spacetime boundary requires the conventional Einstein-Hilbert (EH) action to be supplemented by the Gibbons-Hawking (GH) boundary term in order to retain the standard variational procedure. When the EH action is amended by the diffeomorphism-invariant graviton mass and potential terms, it naively appears that no further boundary terms are needed since all the new fields of massive gravity enter the action with the first derivative. However, we show that such a formulation would be inconsistent, even when the bulk action is ghost-free. The theory is well-defined only after introducing novel boundary counterterms, which dominate over the GH term in the massless limit and cancel the problematic boundary terms induced by the bulk action. The number of boundary counterterms equals the number of total derivatives one could construct in the bulk using positive powers of two derivatives of the longitudinal mode of the massive graviton.

Hellerman et al. (arXiv:1505.01537) have shown that in a generic CFT the spectrum of operators carrying a large U(1) charge can be analyzed semiclassically in an expansion in inverse powers of the charge. The key is the operator state correspondence by which such operators are associated with a finite density superfluid phase for the theory quantized on the cylinder. The dynamics is dominated by the corresponding Goldstone hydrodynamic mode and the derivative expansion coincides with the inverse charge expansion. We illustrate and further clarify this situation by first considering simple quantum mechanical analogues. We then systematize the approach by employing the coset construction for non-linearly realized space-time symmetries. Focussing on CFT3 we illustrate the case of higher rank and non-abelian groups and the computation of higher point functions. Three point function coefficients turn out to satisfy universal scaling laws and correlations as the charge and spin are varied.

The spectrum of primordial gravitational waves is one of the most robust inflationary observables, often thought of as a direct probe of the energy scale of inflation. We present a simple model, where the dynamics controlling this observable is very different than in the standard paradigm of inflation. The model is based on a peculiar finite density phase - the magnetic gaugid - which stems from a highly non-linear effective theory of a triplet of abelian gauge fields. The gaugid extends the notion of homogeneous isotropic solid, in that its spectrum of fluctuations includes helicity-2 phonons. We show how, upon implementing the gaugid to drive inflation, the helicity-2 phonon mixes with the graviton, significantly affecting the size of the primordial tensor spectrum. The rest of the features of the theory, in particular the vector and scalar perturbations, closely resemble those of solid inflation.

We study the stability of spatially flat FRW solutions which are geodesically complete, i.e. for which one can follow null (graviton) geodesics both in the past and in the future without ever encountering singularities. This is the case of NEC-violating cosmologies such as smooth bounces or solutions which approach Minkowski in the past. We study the EFT of linear perturbations around a solution of this kind, including the possibility of multiple fields and fluids. One generally faces a gradient instability which can be avoided only if the operator (3) R δ N is present and its coefficient changes sign along the evolution. This operator (typical of beyond-Horndeski theories) does not lead to extra degrees of freedom, but cannot arise starting from any theory with second-order equations of motion. The change of sign of this operator prevents to set it to zero with a generalised disformal transformation.

Many alternatives to canonical slow-roll inflation have been proposed over the years, one of the main motivations being to have a model, capable of generating observable values of non-Gaussianity. In this work, we (re-)explore the physical implications of a great majority of such models within a single, effective field theory framework (including novel models with large non-Gaussianity discussed for the first time below). The constraints we apply—both theoretical and experimental—are found to be rather robust, determined to a great extent by just three parameters: the coefficients of the quadratic EFT operators (δN)2 and δNδE, and the slow-roll parameter ε. This allows to significantly limit the majority of single-field alternatives to canonical slow-roll inflation. While the existing data still leaves some room for most of the considered models, the situation would change dramatically if the current upper limit on the tensor-to-scalar ratio decreased down to r < 10−2. Apart from inflationary models driven by plateau-like potentials, the single-field model that would have a chance of surviving this bound is the recently proposed slow-roll inflation with weakly-broken galileon symmetry. In contrast to canonical slow-roll inflation, the latter model can support r < 10−2 even if driven by a convex potential, as well as generate observable values for the amplitude of non-Gaussianity.

Canonical models of single-field, slow-roll inflation do not lead to appreciable non-Gaussianity, unless derivative interactions of the inflaton become uncontrollably large. We propose a novel slow-roll scenario where scalar perturbations propagate at a subluminal speed, leading to sizeable equilateral non-Gaussianity, f NL equil  ∝ 1/c s 4 , largely insensitive to the ultraviolet physics. The model is based on a low-energy effective theory characterized by weakly broken invariance under internal galileon transformations, ϕ → ϕ + b μ x μ , which protects the properties of perturbations from large quantum corrections. This provides the unique alternative to models such as DBI inflation in generating strongly subluminal/non-Gaussian scalar perturbations.

We propose a technically natural scenario whereby an initially large cosmological constant (c.c.) is relaxed down to the observed value due to the dynamics of a scalar evolving on a very shallow potential. The model crucially relies on a sector that violates the null energy condition (NEC) and gets activated only when the Hubble rate becomes sufficiently small — of the order of the present one. As a result of NEC violation, this low-energy universe evolves into inflation, followed by reheating and the standard Big Bang cosmology. The symmetries of the theory force the c.c. to be the same before and after the NEC-violating phase, so that a late-time observer sees an effective c.c. of the correct magnitude. Importantly, our model allows neither for eternal inflation nor for a set of possible values of dark energy, the latter fixed by the parameters of the theory.

The Vainshtein mechanism suppresses the fifth force at astrophysical distances, while enabling it to compete with gravity at cosmological scales. Typically, Vainshtein solutions exhibit superluminal perturbations. However, a restricted class of solutions with special boundary conditions was shown to be devoid of the faster-than-light modes. Here we extend this class by finding solutions in a theory of quasidilaton, amended by derivative terms consistent with its symmetries. Solutions with Minkowski asymptotics are not stable, while the ones that exhibit the Vainshtein mechanism by transitioning to cosmological backgrounds are free of ghosts, tachyons, gradient instability, and superluminality, for all propagating modes present in the theory. These solutions require a special choice of the strength and signs of nonlinear terms, as well as a choice of asymptotic cosmological boundary conditions.

In the present thesis, using an effective field theory point of view, we explore theories of single-field inflation where higher derivative operators become relevant, affecting in a novel way the dynamics and therefore the observations. For instance, concerning the scalar spectrum, they allow for measurable equilateral non-Gaussianity, whose amplitude can differ significantly from the predictions of other existing models. Moreover, we show that the stability and the consistency of such theories are ensured by an approximate Galileon symmetry. Indeed, being generically possible to build an invariant theory under Galileon transformations in flat space-time, it is instead well known that such a symmetry is unavoidably broken by gravity. In principle, this might ruin the nice and interesting properties of the Galileons in flat backgrounds, such as the non-renormalization theorem. However, we find that this does not happen if the Galileon invariance is broken only weakly, in a well defined sense, by a suitable coupling to gravity, providing therefore an extension of the quantum non-renormalization properties in curved space-times. Hence, besides discussing the phenomenological consequences and the observational predictions for inflation, we apply such Galileon theories to the context of the late-time acceleration of the Universe. In the last part, in order to probe non-standard primordial scenarios, they are also employed in a cosmology where the Big Bang singularity is smoothed down and the Universe emerges from a Minkowski space-time, in a well defined extension at all times of the Galilean Genesis scenario.

We present a sum rule for Higgs fields in general representations under SU(2) L × U(1) Y that follows from the connection between the Higgs couplings and the mechanism that gives the electroweak bosons their masses, and at the same time restricts these couplings. Sum rules that follow from perturbative unitarity will require us to include singly and doubly charged Higgses in our analysis. We examine the consequences of these sum rules for Higgs phenomenology in both model independent and model specific ways. The relation between our sum rules and other works, based on dispersion relations, is also clarified.

We propose a class of scalar models that, once coupled to gravity, lead to cosmologies that smoothly and stably connect an inflationary quasi-de Sitter universe to a low, or even zero-curvature, maximally symmetric spacetime in the asymptotic past, strongly violating the null energy condition \( \left(\overset{\cdot }{H}\gg {H}^2\right) \) at intermediate times. The models are deformations of the conformal galileon lagrangian and are therefore based on symmetries, both exact and approximate, that ensure the quantum robustness of the whole picture. The resulting cosmological backgrounds can be viewed as regularized extensions of the galilean genesis scenario, or, equivalently, as ‘early-time-complete’ realizations of inflation. The late-time inflationary dynamics possesses phenomenologically interesting properties: it can produce a large tensor-to-scalar ratio within the regime of validity of the effective field theory and can lead to sizeable equilateral nongaussianities.

We perform an isospin analysis of $B$ decays to two pseudoscalars. The analysis extracts appropriate Cabbibo-Kobayashi-Maskawa matrix elements and short distance loop factors to allow for comparison of nonperturbative QCD effects in the reduced matrix elements of the amplitudes. In decays where penguin diagrams compete with tree-level diagrams we find that the reduced matrix elements of the penguin diagrams, which are singlets or doublets under isospin, are significantly enhanced compared with the triplet and fourplet contributions of the weak Hamiltonian. This similarity to the $\mathrm{\ensuremath{\Delta}}I=\frac{1}{2}$ rule in $K\ensuremath{\rightarrow}\ensuremath{\pi}\ensuremath{\pi}$ decays suggests that, more generally, processes mediated by Hamiltonians in lower-dimensional isospin representations see enhancement over higher-dimensional ones in QCD.

We perform an isospin analysis of B decays to two pseudoscalars. The analysis extracts appropriate Cabbibo-Kobayashi-Maskawa matrix elements and short distance loop factors to allow for comparison of nonperturbative QCD effects in the reduced matrix elements of the amplitudes. In decays where penguin diagrams compete with tree-level diagrams we find that the reduced matrix elements of the penguin diagrams, which are singlets or doublets under isospin, are significantly enhanced compared with the triplet and fourplet contributions of the weak Hamiltonian. This similarity to the Delta I = 1/2 rule in K -> pi pi decays suggests that, more generally, processes mediated by Hamiltonians in lower-dimensional isospin representations see enhancement over higher-dimensional ones in QCD.

Quasidilaton massive gravity is an extension of massive general relativity to a theory with additional scale invariance and approximate internal Galilean symmetry. The theory has a novel self-accelerated solution with the metric indistinguishable (in the decoupling limit) from the de Sitter space, its curvature set by the graviton mass. The spectra of tensor, vector, and scalar perturbations on this solution contain neither ghosts nor gradient instabilities or superluminal modes, for a range of the parameter space. This represents an example of a self-accelerated solution with viable perturbations, attainable within a low-energy effective field theory.

We show that the three-body decays of the resonance recently discovered at the LHC are potentially sensitive to effects of new physics. Even if the fully integrated partial decay widths are consistent with the minimal Standard Model there is information that is lost upon integration, which can be uncovered in the differential decay widths. Concentrating on the decay h → Zℓ\( \overline{\ell} \), we identify the regions in the three-body phase space in which these effects become especially pronounced and could be detected in future experiments.

We study the renormalization of some dimension-4, 7 and 10 operators in a class of nonlinear scalar-tensor theories. These theories are invariant under: (a) linear diffeomorphisms which represent an exact symmetry of the full non-linear action, and (b) global field-space Galilean transformations of the scalar field. The Lagrangian contains a set of non-topological interaction terms of the above-mentioned dimensionality, which we show are not renormalized at any order in perturbation theory. We also discuss the renormalization of other operators, that may be generated by loops and/or receive loop-corrections, and identify the regime in which they are sub-leading with respect to the operators that do not get renormalized. Interestingly, such scalar-tensor theories emerge in a certain high-energy limit of the ghost-free theory of massive gravity. One can use the non-renormalization properties of the high-energy limit to estimate the magnitude of quantum corrections in the full theory. We show that the quantum corrections to the three free parameters of the model, one of them being the graviton mass, are strongly suppressed. In particular, we show that having an arbitrarily small graviton mass is technically natural.