Trodden, Mark
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Publication Retarded Green’s function of a Vainshtein system and Galileon waves(2013-01-07) Chu, Yi-Zen; Trodden, MarkMotivated by the desire to test modified gravity theories exhibiting the Vainshtein mechanism, we solve in various physically relevant limits, the retarded Galileon Green’s function (for the cubic theory) about a background sourced by a massive spherically symmetric static body. The static limit of our result will aid us, in a forthcoming paper, in understanding the impact of Galileon fields on the problem of motion in the solar system. In this paper, we employ this retarded Green’s function to investigate the emission of Galileon radiation generated by the motion of matter lying deep within the Vainshtein radius rv of the central object: acoustic waves vibrating on its surface, and the motion of compact bodies gravitationally bound to it. If λ is the typical wavelength of the emitted radiation, and r0 is the typical distance of the source from the central mass, with r0≪rv, then, compared to its noninteracting massless scalar counterpart, we find that the Galileon radiation rate is suppressed by the ratio (rv/λ)-3/2 at the monopole and dipole orders at high frequencies rv/λ≫1. However, at high enough multipole order, the radiation rate is enhanced by powers of rv/r0. At low frequencies rv/λ≪1, and when the motion is nonrelativistic, Galileon waves yield a comparable rate for the monopole and dipole terms, and are amplified by powers of the ratio rv/r0 for the higher multipoles.Publication Tackling Higher Derivative Ghosts with the Euclidean Path Integral(2011-05-17) Fontanini, Michele; Trodden, MarkAn alternative to the effective field theory approach to treat ghosts in higher derivative theories is to attempt to integrate them out via the Euclidean path integral formalism. It has been suggested that this method could provide a consistent framework within which we might tolerate the ghost degrees of freedom that plague, among other theories, the higher derivative gravity models that have been proposed to explain cosmic acceleration. We consider the extension of this idea to treating a class of terms with order six derivatives, and find that for a general term the Euclidean path integral approach works in the most trivial background, Minkowski. Moreover we see that even in de Sitter background, despite some difficulties, it is possible to define a probability distribution for tensorial perturbations of the metric.Publication Instabilities of spherical solutions with multiple Galileons and SO(N) symmetry(2011-02-24) Andrews, Melinda; Hinterbichler, Kurt; Khoury, Justin; Trodden, MarkThe 4-dimensional effective theory arising from an induced gravity action for a codimension greater than one brane consists of multiple Galileon fields π1, I = 1,...,N, invariant under separate Galilean transformations for each scalar, and under an internal SO(N) symmetry. We study the viability of such models by examining spherically symmetric solutions.We find that for general, nonderivative couplings to matter invariant under the internal symmetry, such solutions exist and exhibit a Vainshtein screening effect. By studying perturbations about such solutions, we find both an inevitable gradient instability and fluctuations propagating at superluminal speeds. These findings suggest that more general, derivative couplings to matter are required for the viability of SOðNÞ Galileon theories.Publication Scalar Kinks in Warped Extra Dimensions(2010-07-15) Trodden, Mark; Toharia, Manuel; West, Eric JWe study the existence and stability of static kinklike configurations of a five-dimensional scalar field, with Dirichlet boundary conditions, along the extra dimension of a warped braneworld. In the presence of gravity such configurations fail to stabilize the size of the extra dimension, leading us to consider additional scalar fields with the role of stabilization. We numerically identify multiple nontrivial solutions for a given five-dimensional action, made possible by the nonlinear nature of the background equations, which we find is enhanced in the presence of gravity. Finally, we take a first step toward addressing the question of the stability of such configurations by deriving the full perturbative equations for the gravitationally coupled multifield system.Publication Distinguishing k-defects from their Canonical Twins(2010-11-09) Andrews, Melinda; Trodden, Mark; Lewandowski, Matt; Wesley, DanielWe study k-defects—topological defects in theories with more than two derivatives and second-order equations of motion—and describe some striking ways in which these defects both resemble and differ from their analogues in canonical scalar field theories. We show that, for some models, the homotopy structure of the vacuum manifold is insufficient to establish the existence of k-defects, in contrast to the canonical case. These results also constrain certain families of Dirac-Born-Infeld instanton solutions in the 4-dimensional effective theory. We then describe a class of k-defect solutions, which we dub ‘‘doppelgängers,’’ that precisely match the field profile and energy density of their canonical scalar field theory counterparts. We give a complete characterization of Lagrangians which admit doppelgänger domain walls. By numerically computing the fluctuation eigenmodes about domain wall solutions, we find different spectra for doppelgängers and canonical walls, allowing us to distinguish between k-defects and the canonical walls they mimic. We search for doppelgängers for cosmic strings by numerically constructing solutions of Dirac-Born-Infeld and canonical scalar field theories. Despite investigating several examples, we are unable to find doppelgänger cosmic strings, hence the existence of doppelgängers for defects with codimension >1 remains an open question.Publication Can Cosmic Parallax Distinguish Between Anisotrophic Cosmologies?(2009-12-11) Fontanini, Michele; West, Eric J.; Trodden, MarkIn an anisotropic universe, observers not positioned at a point of special symmetry should observe cosmic parallax—the relative angular motion of test galaxies over cosmic time. It was recently argued that the nonobservance of this effect in upcoming precision astrometry missions such as GAIA may be used to place strong bounds on the position of off-center observers in a void-model universe described by the Lemaitre-Tolman-Bondi metric. We consider the analogous effect in anisotropic cosmological models described by an axisymmetric homogeneous Bianchi type I metric and discuss whether any observation of cosmic parallax would distinguish between different anisotropic evolutions.Publication Vortex Scattering and Intercommuting Cosmic Strings on a Noncommutative Spacetime(2010-02-26) Joseph, Anosh; Trodden, MarkWe study the scattering of noncommutative vortices, based on the noncommutative field theory developed in [A. P. Balachandran, T. R. Govindarajan, G. Mangano, A. Pinzul, B. A. Qureshi, and S. Vaidya, Phys. Rev. D 75, 045009 (2007).], as a way to understand the interaction of cosmic strings. In the center-of-mass frame, the effects of noncommutativity vanish, and therefore the reconnection of cosmic strings occurs in an identical manner to the commutative case. However, when scattering occurs in a frame other than the center-of-mass frame, strings still reconnect but the well-known 90º scattering no longer need correspond to the head-on collision of the strings, due to the breakdown of Lorentz invariance in the underlying noncommutative field theory.Publication Dark Matter with Density-dependent Interactions(2012-12-28) Boddy, Kimberly K; Carroll, Sean M; Trodden, MarkThe decay and annihilation cross sections of dark matter particles may depend on the value of a chameleonic scalar field that both evolves cosmologically and takes different values depending on the local matter density. This possibility introduces a separation between the physics relevant for freeze-out and that responsible for dynamics and detection in the late universe. We investigate how such dark sector interactions might be implemented in a particle physics Lagrangian and consider how current and upcoming observations and experiments bound such dark matter candidates. A specific simple model allows for an increase in the annihilation cross section by a factor of 106 between freeze-out and today, while more complicated models should also allow for scattering cross sections near the astrophysical bounds.Publication Screening Bulk Curvature in the Presence of Large Brane Tension(2011-06-01) Agarwal, Nishant; Khoury, Justin; Bean, Rachel; Trodden, MarkWe study a flat brane solution in an effective 5D action for cascading gravity in six dimensions, and propose a mechanism to screen extrinsic curvature in the presence of a large tension on the brane. The screening mechanism leaves the bulk Riemann-flat, thus making it simpler to generalize large extradimension dark energy models to higher codimensions. By studying an action with cubic interactions for the brane-bending scalar mode, we find that the perturbed action suffers from ghostlike instabilities for positive tension. The solution can be made ghost-free for sufficiently small negative tension, though the connection to 6D cascading gravity is less clear in this case.Publication Multifield Galileons and Higher Codimension Branes(2010-12-07) Hinterbichler, Kurt; Trodden, Mark; Wesley, DanielIn the decoupling limit, the Dvali-Gabadadze-Porrati model reduces to the theory of a scalar field π, with interactions including a specific cubic self-interaction—the Galileon term. This term, and its quartic and quintic generalizations, can be thought of as arising from a probe 3-brane in a five-dimensional bulk with Lovelock terms on the brane and in the bulk.We study multifield generalizations of the Galileon and extend this probe-brane view to higher codimensions. We derive an extremely restrictive theory of multiple Galileon fields, interacting through a quartic term controlled by a single coupling, and trace its origin to the induced brane terms coming from Lovelock invariants in the higher codimension bulk. We explore some properties of this theory, finding de Sitter like self-accelerating solutions. These solutions have ghosts if and only if the flat space theory does not have ghosts. Finally, we prove a general nonrenormalization theorem: multifield Galileons are not renormalized quantum mechanically to any loop in perturbation theory.