Exact Solution to the "Auxiliary Extra Dimension" Model of Massive Gravity

The "Auxiliary Extra Dimension" model was proposed in order to provide a geometrical interpretation to modifications of general relativity, in particular to non-linear massive gravity. In this context, the theory was shown to be ghost free to third order in perturbations, in the decoupling limit. In this work, we exactly solve the equation of motion in the extra dimension, to obtain a purely 4-dimensional theory. Using this solution, it is shown that the ghost appears at the fourth order and beyond. We explore potential modifications to address the ghost issue and find that their consistent implementation requires going beyond the present framework.Comment: v3:8 pages, LaTex, a comment and a reference added, version to appear in PL

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.Comment: 30 pages + appendices, matches journal versio

Unitary null energy condition violation in P(X)P(X) cosmologies

A non-singular cosmological bounce in the Einstein frame can only take place if the Null Energy Condition (NEC) is violated. We explore situations where a single scalar field drives the NEC violation and derive the constraints imposed by demanding tree level unitarity on a cosmological background. We then focus on the explicit constraints that arise in P(X) theories and show that constraints from perturbative unitarity make it impossible for the NEC violation to occur within the region of validity of the effective field theory without also involving irrelevant operators that arise at a higher scale that would enter from integrating out more massive degrees of freedom. Within the context of P(X) theories we show that including such operators allows for a bounce that does not manifestly violate tree level unitarity, but at the price of either imposing a shift symmetry or involving technically unnatural small operator coefficients within the low-energy effective field theory.Comment: 35 pages, 1 figur

Proof of Consistency of Nonlinear Massive Gravity in the Stuckelberg Formulation

We address some recent concerns about the absence of the Boulware-Deser ghost in the Stuckelberg formulation of nonlinear massive gravity. First we provide general arguments for why any ghost analysis in the Stuckelberg formulation has to agree with existing consistency proofs that have been carried out without using Stuckelberg fields. We then demonstrate the absence of the ghost at the completely nonlinear level in the Stuckelberg formulation of the minimal massive gravity action. The constraint that removes the ghost field and the associated secondary constraint that eliminates its conjugate momentum are computed explicitly, confirming the consistency of the theory in the Stuckelberg formulation.Comment: v1: Latex, 11 pages, v2: a comment adde

de Sitter Galileon

We generalize the Galileon symmetry and its relativistic extension to a de Sitter background. This is made possible by studying a probe-brane in a flat five-dimensional bulk using a de Sitter slicing. The generalized Lovelock invariants induced on the probe brane enjoy the induced Poincar\'e symmetry inherited from the bulk, while living on a de Sitter geometry. The non-relativistic limit of these invariants naturally maintain a generalized Galileon symmetry around de Sitter while being free of ghost-like pathologies. We comment briefly on the cosmology of these models and the extension to the AdS symmetry as well as generic FRW backgrounds