Cascading Gravity: Extending the Dvali-Gabadadze-Porrati Model to Higher Dimension

Abstract

We present a generalization of the Dvali-Gabadadze-Porrati scenario to higher codimensions which, unlike previous attempts, is free of ghost instabilities. The 4D propagator is made regular by embedding our visible 3-brane within a 4-brane, each with their own induced gravity terms, in a flat 6D bulk. The model is ghost-free if the tension on the 3-brane is larger than a certain critical value, while the induced metric remains flat. The gravitational force law ''cascades'' from a 6D behavior at the largest distances followed by a 5D and finally a 4D regime at the shortest scales. Introduction.-The present acceleration of the Universe is a profound mystery. While the observational data are consistent with a cosmological constant (CC) of order 10 ÿ3 eV 4 , this value is in stark disagreement with particle physics computations. The problem is even more severe than the hierarchy problem in the Standard Model, since dynamical solutions are impossible in theories with a massless 4D graviton [1]. In the same way as the perihelion precession of Mercury was explained by a modification of Newtonian gravity, an alternative approach is to assume that the acceleration signals a breakdown of general relativity at cosmological distances.The Dvali-Gabadadze-Porrati (DGP) model [2] provides a simple mechanism to modify gravity at large distances by adding a localized graviton kinetic term on a codimension 1 brane in a flat 5D spacetime. The extension to higher dimensions is particularly important both for its possible embedding into string theory and for its relevance to the CC problem [3,4]. However, the natural generalization of the DGP model with higher codimension branes is not straightforward [5,6]. On the one hand, these models require some regularization due to the divergent behavior of the Green's functions in higher codimension. More seriously, most constructions are plagued by ghost instabilities around flat space (not to be confused with those of the selfaccelerating branch of standard 5D DGP) [5,6]-see [7] for related work. The purpose of this Letter is to show that both pathologies can be resolved by embedding the codimension 2 DGP model into a codimension 1 brane with its own kinetic term. It will be interesting to see if this setup allows for higher-codimension self-accelerated solutions. Our present focus, however, is to derive a consistent framework in which gravity is modified in the infrared.Scalar.-We shall focus on the codimension 2 case. As a warm-up, we consider a real scalar field with action,

Beyond the cosmological standard model

“…Another generalization of the DGP scenario to higher dimensions is cascading gravity [774,[779][780][781]. In this construction, our 3-brane is embedded within a succession of higher-dimensional branes, each with their own induced gravity term.…”

Observational Constraints with Recent Data on the DGP Modified Gravity

“…A solution for this problem is socalled cascading DGP model in which the unlike previous attempts, it is free of ghost instabilities. In this model the 4D propagator is regulated by embedding the 3-brane within a 4-brane with their own gravity terms induced by a flat 6D bulk [52].…”

Bi-galileon theory II: phenomenology

“…Whilst Weinberg's no-go theorem makes self tuning impossible for constant field configurations, it does not rule out more general scenarios [31]. Indeed, co-dimension two braneworld models offer some hope for developing a successful self-tuning mechanism [20][21][22][23][24][25][26][27]. The reason is that adding vacuum energy to a co-dimension two brane merely alters the bulk deficit angle and not the brane geometry.…”