DGP specteroscopy

We systematically explore the spectrum of gravitational perturbations in codimension-1 DGP braneworlds, and find a 4D ghost on the self-accelerating branch of solutions. The ghost appears for any value of the brane tension, although depending on the sign of the tension it is either the helicity-0 component of the lightest localized massive tensor of mass

A short review of "DGP Specteroscopy"

In this paper we provide a short review of the main results developed in hep-th/0604086. We focus on linearised vacuum perturbations about the self-accelerating branch of solutions in the DGP model. These are shown to contain a ghost in the spectrum for any value of the brane tension. We also comment on hep-th/0607099, where some counter arguments have been presented.Comment: Minor typos correcte

Galileon Hairs of Dyson Spheres, Vainshtein's Coiffure and Hirsute Bubbles

We study the fields of spherically symmetric thin shell sources, a.k.a. Dyson spheres, in a {\it fully nonlinear covariant} theory of gravity with the simplest galileon field. We integrate exactly all the field equations once, reducing them to first order nonlinear equations. For the simplest galileon, static solutions come on {\it six} distinct branches. On one, a Dyson sphere surrounds itself with a galileon hair, which far away looks like a hair of any Brans-Dicke field. The hair changes below the Vainshtein scale, where the extra galileon terms dominate the minimal gradients of the field. Their hair looks more like a fuzz, because the galileon terms are suppressed by the derivative of the volume determinant. It shuts off the `hair bunching' over the `angular' 2-sphere. Hence the fuzz remains dilute even close to the source. This is really why the Vainshtein's suppression of the modifications of gravity works close to the source. On the other five branches, the static solutions are all {\it singular} far from the source, and shuttered off from asymptotic infinity. One of them, however, is really the self-accelerating branch, and the singularity is removed by turning on time dependence. We give examples of regulated solutions, where the Dyson sphere explodes outward, and its self-accelerating side is nonsingular. These constructions may open channels for nonperturbative transitions between branches, which need to be addressed further to determine phenomenological viability of multi-branch gravities.Comment: 29+1 pages, LaTeX, 2 .pdf figure

Bi-galileon theory II: phenomenology

We continue to introduce bi-galileon theory, the generalisation of the single galileon model introduced by Nicolis et al. The theory contains two coupled scalar fields and is described by a Lagrangian that is invariant under Galilean shifts in those fields. This paper is the second of two, and focuses on the phenomenology of the theory. We are particularly interesting in models that admit solutions that are asymptotically self accelerating or asymptotically self tuning. In contrast to the single galileon theories, we find examples of self accelerating models that are simultaneously free from ghosts, tachyons and tadpoles, able to pass solar system constraints through Vainshtein screening, and do not suffer from problems with superluminality, Cerenkov emission or strong coupling. We also find self tuning models and discuss how Weinberg's no go theorem is evaded by breaking Poincar\'e invariance in the scalar sector. Whereas the galileon description is valid all the way down to solar system scales for the self-accelerating models, unfortunately the same cannot be said for self tuning models owing to the scalars backreacting strongly on to the geometry

Inflaton perturbations in brane-world cosmology with induced gravity

We study cosmological perturbations in the brane models with an induced Einstein-Hilbert term on a brane. We consider an inflaton confined to a de Sitter brane in a five-dimensional Minkowski spacetime. Inflaton fluctuations excite Kaluza-Klein modes of bulk metric perturbations with mass $m^2 = -2(2\ell-1) (\ell +1) H^2$ and $m^2 = -2\ell(2\ell+3) H^2$ where $\ell$ is an integer. There are two branches ($\pm$ branches) of solutions for the background spacetime. In the $+$ branch, which includes the self-accelerating universe, a resonance appears for a mode with $m^2 = 2 H^2$ due to a spin-0 perturbation with $m^2 = 2H^2$. The self-accelerating universe has a distinct feature because there is also a helicity-0 mode of spin-2 perturbations with $m^2 = 2H^2$. In the $-$ branch, which can be thought as the Randall-Sundrum type brane-world with the high energy quantum corrections, there is no resonance. At high energies, we analytically confirm that four-dimensional Einstein gravity is recovered, which is related to the disappearance of van Dam-Veltman-Zakharov discontinuity in de Sitter spacetime. On sufficiently small scales, we confirm that the lineariaed gravity on the brane is well described by the Brans-Dicke theory with $\omega=3Hr_c$ in $-$ branch and $\omega = -3H r_c$ in $+$ branch, respectively, which confirms the existence of the ghost in $+$ branch. We also study large scale perturbations. In $+$ branch, the resonance induces a non-trivial anisotropic stress on the brane via the projection of Weyl tensor in the bulk, but no instability is shown to exist on the brane.Comment: 20 pages, 4 figure

Ghosts in the self-accelerating universe

The self-accelerating universe realizes the accelerated expansion of the universe at late times by large-distance modification of general relativity without a cosmological constant. The Dvali-Gabadadze-Porrati (DGP) braneworld model provides an explicit example of the self-accelerating universe. Recently, the DGP model becomes very popular to study the observational consequences of the modified gravity models as an alternative to dark energy models in GR. However, it has been shown that the self-accelerating universe in the DGP model contains a ghost at the linearized level. The ghost carries negative energy densities and it leads to the instability of the spacetime. In this article, we review the origin of the ghost in the self-accelerating universe and explore the physical implication of the existence of the ghost.Comment: Invited topical review for Classical and Quantum Gravity, 20 pages, 4 figure

Ghost-free braneworld bigravity

We consider a generalisation of the DGP model, by adding a second brane with localised curvature, and allowing for a bulk cosmological constant and brane tensions. We study radion and graviton fluctuations in detail, enabling us to check for ghosts and tachyons. By tuning our parameters accordingly, we find bigravity models that are free from ghosts and tachyons. These models will lead to large distance modifications of gravity that could be observable in the near future.Comment: Dedicated to the memory of Ian Kogan. Version to appear in Classical and Quantum Gravit

Mimicking Lambda with a spin-two ghost condensate

We propose a simple higher-derivative braneworld gravity model which contains a stable accelerating branch, in the absence of cosmological constant or potential, that can be used to describe the late time cosmic acceleration. This model has similar qualitative features to that of Dvali-Gabadadze-Porrati, such as the recovery of four-dimensional gravity at subhorizon scales, but unlike that case, the graviton zero mode is massless and there are no linearized instabilities. The acceleration rather is driven by bulk gravity in the form of a spin-two ghost condensate. We show that this model can be consistent with cosmological bounds and tests of gravity.Comment: references adde

Perturbations of Self-Accelerated Universe

We discuss small perturbations on the self-accelerated solution of the DGP model, and argue that claims of instability of the solution that are based on linearized calculations are unwarranted because of the following: (1) Small perturbations of an empty self-accelerated background can be quantized consistently without yielding ghosts. (2) Conformal sources, such as radiation, do not give rise to instabilities either. (3) A typical non-conformal source could introduce ghosts in the linearized approximation and become unstable, however, it also invalidates the approximation itself. Such a source creates a halo of variable curvature that locally dominates over the self-accelerated background and extends over a domain in which the linearization breaks down. Perturbations that are valid outside the halo may not continue inside, as it is suggested by some non-perturbative solutions. (4) In the Euclidean continuation of the theory, with arbitrary sources, we derive certain constraints imposed by the second order equations on first order perturbations, thus restricting the linearized solutions that could be continued into the full nonlinear theory. Naive linearized solutions fail to satisfy the above constraints. (5) Finally, we clarify in detail subtleties associated with the boundary conditions and analytic properties of the Green's functions.Comment: 39 LaTex page

Brane-World Gravity

The observable universe could be a 1+3-surface (the "brane") embedded in a 1+3+\textit{d}-dimensional spacetime (the "bulk"), with Standard Model particles and fields trapped on the brane while gravity is free to access the bulk. At least one of the \textit{d} extra spatial dimensions could be very large relative to the Planck scale, which lowers the fundamental gravity scale, possibly even down to the electroweak ($\sim$ TeV) level. This revolutionary picture arises in the framework of recent developments in M theory. The 1+10-dimensional M theory encompasses the known 1+9-dimensional superstring theories, and is widely considered to be a promising potential route to quantum gravity. At low energies, gravity is localized at the brane and general relativity is recovered, but at high energies gravity "leaks" into the bulk, behaving in a truly higher-dimensional way. This introduces significant changes to gravitational dynamics and perturbations, with interesting and potentially testable implications for high-energy astrophysics, black holes, and cosmology. Brane-world models offer a phenomenological way to test some of the novel predictions and corrections to general relativity that are implied by M theory. This review analyzes the geometry, dynamics and perturbations of simple brane-world models for cosmology and astrophysics, mainly focusing on warped 5-dimensional brane-worlds based on the Randall--Sundrum models. We also cover the simplest brane-world models in which 4-dimensional gravity on the brane is modified at \emph{low} energies -- the 5-dimensional Dvali--Gabadadze--Porrati models. Then we discuss co-dimension two branes in 6-dimensional models.Comment: A major update of Living Reviews in Relativity 7:7 (2004) "Brane-World Gravity", 119 pages, 28 figures, the update contains new material on RS perturbations, including full numerical solutions of gravitational waves and scalar perturbations, on DGP models, and also on 6D models. A published version in Living Reviews in Relativit