Claudia de Rham

Mimicking Λ 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 a 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 and 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.

Cascading Gravity and Degravitation

We construct a cascading brane model of gravity in which the behavior of the gravitational force law interpolates from (n+4)-dimensional to (n+3)-dimensional all the way down to 4-dimensional from longer to shorter length scales. We show that, at the linearized level, this model exhibits the features necessary for degravitation of the cosmological constant. The model is shown to be ghost free with the addition of suitable brane kinetic operators, and we demonstrate this using a number of independent procedures. Consequently this is a consistent infrared (IR) modification of gravity, providing a promising framework for a dynamical, degravitating solution of the cosmological constant problem.

The effective field theory of codimension-two branes

Distributional sources of matter on codimension-two and higher branes are only well-defined as regularized objects. Nevertheless, intuition from effective field theory suggests that the low-energy physics on such branes should be independent of any high-energy regularization scheme. In this paper, we address this issue in the context of a scalar field model where matter fields (the standard model) living on such a brane interact with bulk fields (gravity). The low-energy effective theory is shown to be consistent and independent of the regularization scheme, provided the brane couplings are renormalized appropriately at the classical level. We perform explicit computations of the classical renormalization group flows at tree and one-loop level, demonstrate that the theory is renormalizable against codimension-two divergences, and extend the analysis to several physical applications such as electrodynamics and brane localized kinetic terms.

Gravitational waves in a codimension two braneworld

We consider the propagation of gravitational waves in six dimensions induced by sources living on 3-branes in the context of a recent exact solution (Mukohyama et al 2005 J. Cosmol. Astropart. Phys. JCAP07(2005)013). The brane geometries are de Sitter and the bulk is a warped geometry supported by a positive cosmological constant as well as a 2-form flux. We show that at low energies ordinary gravity is reproduced, and explicitly compute the leading corrections from six-dimensional effects. After regulating the brane we find a logarithmic dependence on the cut-off scale of brane physics even for modes whose frequency is much less than this energy scale. We discuss the possibility that this dependence can be renormalized into bulk or brane counterterms in line with effective field theory expectations. We discuss the inclusion of Gauss–Bonnet terms that have been used elsewhere to regulate codimension two branes. We find that such terms do not regulate codimension two branes for compact extra dimensions.

Flat 3-brane with tension in cascading gravity.

In the cascading gravity brane-world scenario, our 3-brane lies within a succession of lower-codimension branes, each with their own induced gravity term, embedded into each other in a higher-dimensional space-time. In the (6+1)-dimensional version of this scenario, we show that a 3-brane with tension remains flat, at least for sufficiently small tension that the weak-field approximation is valid. The bulk solution is singular nowhere and remains in the perturbative regime everywhere.

The hierarchy problem and the self-localized Higgs

We examine brane-world scenarios in which all the observed Standard Model particles reside on a brane but the Higgs is an elementary extra-dimensional scalar in the bulk. We show that, for codimension 2 branes, often-neglected interactions between the bulk Higgs and the branes cause two novel effects. First, they cause H to depend only logarithmically on the UV-sensitive coefficient, mB2, of the mass term, mB2?H*H, of the bulk potential, thus providing a new mechanism for tackling the hierarchy problem. Second, the Higgs brane couplings cause the lowest mass KK mode to localize near the brane without any need for geometrical effects like warping. We explore some preliminary implications such models have for the Higgs signature at the LHC, both in the case where the extra dimensions arise at the TeV scale, and in ADD models having Large Extra Dimensions. Novel Higgs features include couplings to fermions which can be different from Standard Model values, mf/v, despite the fermions acquiring their mass completely from the Higgs expectation value.

Exact wave solutions to 6D gauged chiral supergravity

We describe a broad class of time-dependent exact wave solutions to 6D gauged chiral supergravity with two compact dimensions. These 6D solutions are nontrivial warped generalizations of 4D pp-waves and Kundt class solutions and describe how a broad class of previously-static compactifications from 6D to 4D (sourced by two 3-branes) respond to waves moving along one of the uncompactified directions. Because our methods are generally applicable to any higher dimensional supergravity they are likely to be of use for finding the supergravity limit of time-dependent solutions in string theory. The 6D solutions are interesting in their own right, describing 6D shock waves induced by high energy particles on the branes, and as descriptions of the near-brane limit of the transient wavefront arising from a local bubble-nucleation event on one of the branes, such as might occur if a tension-changing phase transition were to occur.

Classical Renormalization of Codimension‐two Brane Couplings

The curvature on codimension‐two and higher branes is not regular for arbitrary matter sources. Nevertheless, the low‐energy theory for an observer on such a brane should be well‐defined and independent to any regularization procedure. This is achieved via appropriate classical renormalization of the brane couplings, and leads to a natural hierarchy between standard model couplings and couplings to gravity.

Cascading gravity and degravitationThis paper was presented at the Theory CANADA 4 conference, held at the Centre de Recherches Mathématiques at the Université de Montréal, Québec, Canada on 4–7 June 2008.

Cascading gravity is an explicit realization of the idea of degravitation, where gravity behaves as a high-pass filter. This could explain why a large cosmological constant does not backreact as much as anticipated from standard General Relativity. The model relies on the presence of at least two infinite extra dimensions while our world is confined on a four-dimensional brane. Gravity is then four-dimensional at short distances and becomes weaker and weaker at larger distances.Cascading gravity is an explicit realization of the idea of d egravitation, where gravity behaves as a high-pass filter. This could explain why a large c osmological constant does not backreact as much as anticipated from standard General Rela tivity. The model relies on the presence of at least two infinite extra dimensions while our world is co nfined on a four-dimensional brane. Gravity is then four-dimensional at short distances and bec omes weaker and weaker at larger distances.

Curvature corrections to the low energy effective theory in 6D regularized braneworlds

We study the effective gravitational theory on a brane in a six-dimensional Einstein-Maxwell model of flux compactification, regularizing a conical defect as a codimension-one brane. We employ the gradient expansion technique valid at low energies. A lowest order analysis showed that standard four-dimensional Einstein gravity is reproduced on the brane. We extend this study to include second order corrections in the effective equations, and show that the correction term is given by a quadratic energy-momentum tensor. Taking the thin-brane limit where the regularized brane shrinks to the pole, we find that the second order metric diverges logarithmically on the brane, giving rise to divergences in the brane effective action. Away from the branes, the effective action is, however, well defined.