Partially Massless Spin 2 Electrodynamics

We propose that maximal depth, partially massless, higher spin excitations can mediate charged matter interactions in a de Sitter universe. The proposal is motivated by similarities between these theories and their traditional Maxwell counterpart: their propagation is lightlike and corresponds to the same Laplacian eigenmodes as the de Sitter photon; they are conformal in four dimensions; their gauge invariance has a single scalar parameter and actions can be expressed as squares of single derivative curvature tensors. We examine this proposal in detail for its simplest spin 2 example. We find that it is possible to construct a natural and consistent interaction scheme to conserved vector electromagnetic currents primarily coupled to the helicity 1 partially massless modes. The resulting current-current single ``partial-photon'' exchange amplitude is the (very unCoulombic) sum of contact and shorter-range terms, so the partial photon cannot replace the traditional one, but rather modifies short range electromagnetic interactions. We also write the gauge invariant fourth-derivative effective actions that might appear as effective corrections to the model, and their contributions to the tree amplitude are also obtained.Comment: 15 pages, LaTe

On generalized Abelian deformations

We study sun-products on $\R^n$, i.e. generalized Abelian deformations associated with star-products for general Poisson structures on $\R^n$. We show that their cochains are given by differential operators. As a consequence, the weak triviality of sun-products is established and we show that strong equivalence classes are quite small. When the Poisson structure is linear (i.e., on the dual of a Lie algebra), we show that the differentiability of sun-products implies that covariant star-products on the dual of any Lie algebra are equivalent each other.Comment: LaTeX 16 pages. To be published in Reviews in Mathematical Physic

Canonical connection on a class of Riemannian almost product manifolds

The canonical connection on a Riemannian almost product manifold is an analogue to the Hermitian connection on an almost Hermitian manifold. In this paper we consider the canonical connection on a class of Riemannian almost product manifolds with non-integrable almost product structure. We construct and characterize an example by a Lie group.Comment: 19 pages, some corrections in the example; J. Geom. (2012

Unitarity constraints on the ratio of shear viscosity to entropy density in higher derivative gravity

We discuss corrections to the ratio of shear viscosity to entropy density $\eta/s$ in higher-derivative gravity theories. Generically, these theories contain ghost modes with Planck-scale masses. Motivated by general considerations about unitarity, we propose new boundary conditions for the equations of motion of the graviton perturbations that force the amplitude of the ghosts modes to vanish. We analyze explicitly four-derivative perturbative corrections to Einstein gravity which generically lead to four-derivative equations of motion, compare our choice of boundary conditions to previous proposals and show that, with our new prescription, the ratio $\eta/s$ remains at the Einstein-gravity value of $1/4\pi$ to leading order in the corrections. It is argued that, when the new boundary conditions are imposed on six and higher-derivative equations of motion, $\eta/s$ can only increase from the Einstein-gravity value. We also recall some general arguments that support the validity of our results to all orders in the strength of the corrections to Einstein gravity. We then discuss the particular case of Gauss-Bonnet gravity, for which the equations of motion are only of two-derivative order and the value of $\eta/s$ can decrease below $1/4\pi$ when treated in a nonperturbative way. Our findings provide further evidence for the validity of the KSS bound for theories that can be viewed as perturbative corrections to Einstein Gravity.Comment: Sign error in the equations of motion corrected, leading to several numerical changes. Clarifications added, references added. Main results and cnclusions essentially unchanged. V3 published version. Clarifications added, discussion of Gauss-Bonnet moved to main tex

Two loop and all loop finite 4-metrics

In pure Einstein theory, Ricci flat Lorentzian 4-metrics of Petrov types III or N have vanishing counter terms up to and including two loops. Moreover for pp-waves and type-N spacetimes of Kundt's class which admit a non-twisting, non expanding, null congruence all possible invariants formed from the Weyl tensor and its covariant derivatives vanish. Thus these Lorentzian metrics suffer no quantum corrections to all loop orders. By contrast for complete non-singular Riemannian metrics the two loop counter term vanishes only if the metric is flat.Comment: 4 pages Latex file, no figure

A rigidity theorem for nonvacuum initial data

In this note we prove a theorem on non-vacuum initial data for general relativity. The result presents a ``rigidity phenomenon'' for the extrinsic curvature, caused by the non-positive scalar curvature. More precisely, we state that in the case of asymptotically flat non-vacuum initial data if the metric has everywhere non-positive scalar curvature then the extrinsic curvature cannot be compactly supported.Comment: This is an extended and published version: LaTex, 10 pages, no figure

Dipolar Dark Matter and Dark Energy

In previous work [L. Blanchet and A. Le Tiec, Phys. Rev. D 78, 024031 (2008)], a model of dark matter and dark energy based on the concept of gravitational polarization was investigated. This model was shown to recover the concordance cosmological scenario (Lambda-CDM) at cosmological scales, and the phenomenology of the modified Newtonian dynamics (MOND) at galactic scales. In this article we prove that the model can be formulated with a simple and physically meaningful matter action in general relativity. We also provide alternative derivations of the main results of the model, and some details on the variation of the action.Comment: 11 pages, 2 figures; minor stylistic corrections, added references, added appendix; to appear in Phys. Rev.

Conformally equivariant quantization: Existence and uniqueness

We prove the existence and the uniqueness of a conformally equivariant symbol calculus and quantization on any conformally flat pseudo-Riemannian manifold (M,\rg). In other words, we establish a canonical isomorphism between the spaces of polynomials on $T^*M$ and of differential operators on tensor densities over $M$, both viewed as modules over the Lie algebra \so(p+1,q+1) where $p+q=\dim(M)$. This quantization exists for generic values of the weights of the tensor densities and compute the critical values of the weights yielding obstructions to the existence of such an isomorphism. In the particular case of half-densities, we obtain a conformally invariant star-product.Comment: LaTeX document, 32 pages; improved versio

Symmetries of distributional domain wall geometries

Generalizing the Lie derivative of smooth tensor fields to distribution-valued tensors, we examine the Killing symmetries and the collineations of the curvature tensors of some distributional domain wall geometries. The chosen geometries are rigorously the distributional thin wall limit of self gravitating scalar field configurations representing thick domain walls and the permanence and/or the rising of symmetries in the limit process is studied. We show that, for all the thin wall spacetimes considered, the symmetries of the distributional curvature tensors turns out to be the Killing symmetries of the pullback of the metric tensor to the surface where the singular part of these tensors is supported. Remarkably enough, for the non-reflection symmetric domain wall studied, these Killing symmetries are not necessarily symmetries of the ambient spacetime on both sides of the wall

Non-local Matching Condition and Scale-invariant Spectrum in Bouncing Cosmology

In cosmological scenarios such as the pre-big bang scenario or the ekpyrotic scenario, a matching condition between the metric perturbations in the pre-big bang phase and those in the post big-bang phase is often assumed. Various matching conditions have been considered in the literature. Nevertheless obtaining a scale invariant CMB spectrum via a concrete mechanism remains impossible. In this paper, we examine this problem from the point of view of local causality. We begin with introducing the notion of local causality and explain how it constrains the form of the matching condition. We then prove a no-go theorem: independent of the details of the matching condition, a scale invariant spectrum is impossible as long as the local causality condition is satisfied. In our framework, it is easy to show that a violation of local causality around the bounce is needed in order to give a scale invariant spectrum. We study a specific scenario of this possibility by considering a nonlocal effective theory inspired by noncommutative geometry around the bounce and show that a scale invariant spectrum is possible. Moreover we demonstrate that the magnitude of the spectrum is compatible with observations if the bounce is assumed to occur at an energy scale which is a few orders of magnitude below the Planckian energy scale.Comment: 15 pages, 2 figures; v3: clarifications added, changes in references, version to appear in PR