Aspects of Galileons

Galileons are a class of scalar field theories which have been found to arise in a disparate variety of contexts and exhibit a host of interesting properties by themselves, both classical and quantum. They obey non-trivial shift symmetries which restrict their self-interactions to be of higher derivative form, yet their equations of motion remain second order so that they are free of ghost instabilities. Further, when used as a force mediator between massive objects, galileons provide a natural realization of the Vainshtein screening mechanism which shuts off the fifth force at distances close to massive sources. As such, they are well suited for cosmology and are naturally incorporated into theories of modified gravity such as the Dvali-Gabadadze-Porrati braneworld model and the de Rham-Gabadadze-Tolley theory of massive gravity. Treated as a quantum field theory, galileons obey a non-trivial non-renormalization theorem which proves that they are not renormalized to any numbers of loops. In this thesis, we explore the properties of galileon theories and their generalizations through a combination of geometric and algebraic means. On the geometry side, we demonstrate that generic galileon theories are naturally thought of as the description of branes moving in higher dimensional spacetimes. On the algebraic side, we show that there exists a precise interpretation in which galileons can be thought of as Goldstone modes which arise when spacetime symmetries are spontaneously broken. In particular, when viewed in this light the galileons are the analogue of the Wess-Zumino-Witten term of the chiral lagrangian and thus represent interactions which are technically special. These methods provide both new technical tools for analyzing galileon-like theories and offer conceptual changes for how these theories can be viewed

Stability and superluminality of spherical DBI galileon solutions

The DBI galileons are a generalization of the galileon terms, which extend the internal galilean symmetry to an internal relativistic symmetry, and can also be thought of as generalizations of DBI which yield second order field equations. We show that, when considered as local modifications to gravity, such as in the Solar system, there exists a region of parameter space in which spherically symmetric static solutions exist and are stable. However, these solutions always exhibit superluminality, casting doubt on the existence of a standard Lorentz invariant UV completion.Comment: 16 pages, 1 figure. Discussions added, version appearing in PR

Soft Theorems For Shift-Symmetric Cosmologies

We derive soft theorems for single-clock cosmologies that enjoy a shift symmetry. These so-called consistency conditions arise from a combination of a large diffeomorphism and the internal shift-symmetry and fix the squeezed limit of all correlators with a soft scalar mode. As an application, we show that our results reproduce the squeezed bispectrum for Ultra-slow-roll inflation, a particular shift-symmetric, non-attractor model which is known to violate Maldacena's consistency relation. Similar results have been previously obtained by Mooij and Palma using background-wave methods. Our results shed new light on the infrared structure of single-clock cosmological spacetimes.Comment: 4 pages, v2: citation added, v3: citations added and edited in accordance with published versio

Partially Massless Fields During Inflation

The representation theory of de Sitter space allows for a category of partially massless particles which have no flat space analog, but could have existed during inflation. We study the couplings of these exotic particles to inflationary perturbations and determine the resulting signatures in cosmological correlators. When inflationary perturbations interact through the exchange of these fields, their correlation functions inherit scalings that cannot be mimicked by extra massive fields. We discuss in detail the squeezed limit of the tensor-scalar-scalar bispectrum, and show that certain partially massless fields can violate the tensor consistency relation of single-field inflation. We also consider the collapsed limit of the scalar trispectrum, and find that the exchange of partially massless fields enhances its magnitude, while giving no contribution to the scalar bispectrum. These characteristic signatures provide clean detection channels for partially massless fields during inflation.Comment: 48 pages, 5 figures. v2: references added, published versio

Galileons Coupled to Massive Gravity: General Analysis and Cosmological Solutions

We further develop the framework for coupling galileons and Dirac-Born-Infeld (DBI) scalar fields to a massive graviton while retaining both the non-linear symmetries of the scalars and ghost-freedom of the theory. The general construction is recast in terms of vielbeins which simplifies calculations and allows for compact expressions. Expressions for the general form of the action are derived, with special emphasis on those models which descend from maximally symmetric spaces. We demonstrate the existence of maximally symmetric solutions to the fully non-linear theory and analyze their spectrum of quadratic fluctuations. Finally, we consider self-accelerating cosmological solutions and study their perturbations, showing that the vector and scalar modes have vanishing kinetic terms