Cosmological perturbations of brane-induced gravity and the vDVZ discontinuity on FLRW space-times

We investigate the cosmological perturbations of the brane-induced (Dvali-Gabadadze-Porrati) model which exhibits a van Dam-Veltman-Zakharov (vDVZ) discontinuity when linearized over a Minkowski background. We show that the linear brane scalar cosmological perturbations over an arbitrary Friedmann-Lemaitre-Robertson-Walker (FLRW) space-time have a well defined limit when the radius of transition between 4D and 5D gravity is sent to infinity with respect to the background Hubble radius. This radius of transition plays for the brane-induced gravity model a role equivalent to the Compton wavelength of the graviton in a Pauli-Fierz theory, as far as the vDVZ discontinuity is concerned. This well defined limit is shown to obey the linearized 4D Einstein's equations whenever the Hubble factor is non vanishing. This shows the disappearance of the vDVZ discontinuity for general FLRW background, and extends the previously know result for maximally-symmetric space-times of non vanishing curvature. Our reasoning is valid for matter with simple equation of state such as a scalar field, or a perfect fluid with adiabatic perturbations, and involves to distinguish between space-times with a vanishing scalar curvature and space-times with a non vanishing one. We also discuss the validity of the linear perturbation theory, in particular for those FLRW space-times where the Ricci scalar is vanishing only on a set of zero measure. In those cases, we argue that the linear perturbation theory breaks down when the Ricci scalar vanishes (and the radius of transition is sent to infinity), in a way similar to what has been found to occur around sources on a Minkowski background.Comment: 36 pages, v.2, typos correcte

Probing Gravity with Spacetime Sirens

A gravitational observatory such as LISA will detect coalescing pairs of massive black holes, accurately measure their luminosity distance and help identify a host galaxy or an electromagnetic counterpart. If dark energy is a manifestation of modified gravity on large scales, gravitational waves from cosmologically-distant spacetime sirens are direct probes of this new physics. For example, a gravitational Hubble diagram based on black hole pair luminosity distances and host galaxy redshifts could reveal a large distance extra-dimensional leakage of gravity. Various additional signatures may be expected in a gravitational signal propagated over cosmological scales.Comment: 11 pages, 1 figure, accepted for publication in ApJ Letter

Self-accelerating solutions in the cascading DGP braneworld

The self-accelerating branch of the Dvali-Gabadadze-Porrati (DGP) five-dimensional braneworld has provided a compelling model for the current cosmic acceleration. Recent observations, however, have not favored it so much. We discuss the solutions which contain a de Sitter 3-brane in the cascading DGP braneworld model, which is a kind of higher-dimensional generalizations of the DGP model,where a $p$-dimensional brane is placed on a $(p+1)$-dimensional one and the $p$-brane action contains the $(p+1)$-dimensional induced scalar curvature term. In the simplest six-dimensional model, we derive the solutions. Our solutions can be classified into two branches, which reduce to the self-accelerating and normal solutions in the limit of the original five-dimensional DGP model. In the presence of the six-dimensional bulk gravity, the `normal' branch provides a new self-accelerating solution. The expansion rate of this new branch is generically lower than that of the original one, which may alleviate the fine-tuning problem.Comment: 4 pages, critical change

Reconstructing the Distortion Function for Nonlocal Cosmology

We consider the cosmology of modified gravity models in which Newton's constant is distorted by a function of the inverse d'Alembertian acting on the Ricci scalar. We derive a technique for choosing the distortion function so as to fit an arbitrary expansion history. This technique is applied numerically to the case of LambdaCDM cosmology, and the result agrees well with a simple hyperbolic tangent.Comment: 17 pages, 1 figure, dedicated to Stanley Deser on the occasion of his 78th birthday, revised version for publication in JCA

Gauged Galileons From Branes

We show how the coupling of SO(N) gauge fields to galileons arises from a probe brane construction. The galileons arise from the brane bending modes of a brane probing a co-dimension N bulk, and the gauge fields arise by turning on certain off-diagonal components in the zero mode of the bulk metric. By construction, the equations of motion for both the galileons and gauge fields remain second order. Covariant gauged galileons are derived as well.Comment: 6 pages. v2: minor changes, version appearing in PL

General Relativity With An Auxiliary Dimension

I consider an extension of General Relativity by an auxiliary non-dynamical dimension that enables our space-time to acquire an extrinsic curvature. Obtained gravitational equations, without or with a cosmological constant, have a selfaccelerated solution that is independent of the value of the cosmological constant, and can describe the cosmic speedup of the Universe as a geometric effect. Background evolution of the selfaccelerated solution is identical to that of ordinary de Sitter space. I show that linear perturbations on this solution describe either a massless graviton, or a massive graviton and a scalar, which are free of ghosts and tachyons for certain choices of boundary conditions. The obtained linearized expressions suggest that nonlinear interactions should, for certain boundary conditions, be strongly coupled, although this issue is not studied here. The full nonlinear Hamiltonian of the theory is shown to be positive for the selfaccelerated solution, while in general, it reduces to surface terms in our and auxiliary dimensions.Comment: 1+14 pages; v2: comments and 2 refs added; minor corrections and improvements mad

On p-form theories with gauge invariant second order field equations

We explore field theories of a single p-form with equations of motions of order strictly equal to two and gauge invariance. We give a general method for the classification of such theories which are extensions to the p-forms of the Galileon models for scalars. Our classification scheme allows to compute an upper bound on the number of different such theories depending on p and on the space-time dimension. We are also able to build a non trivial Galileon like theory for a 3-form with gauge invariance and an action which is polynomial into the derivatives of the form. This theory has gauge invariant field equations but an action which is not, like a Chern-Simons theory. Hence the recently discovered no-go theorem stating that there are no non trivial gauge invariant vector Galileons (which we are also able here to confirm with our method) does not extend to other odd p cases.Comment: 29 page

Gravitational Leakage into Extra Dimensions: Probing Dark Energy Using Local Gravity

The braneworld model of Dvali-Gabadadze-Porrati (DGP) is a theory where gravity is modified at large distances by the arrested leakage of gravitons off our four-dimensional universe. Cosmology in this model has been shown to support both "conventional" and exotic explanations of the dark energy responsible for today's cosmic acceleration. We present new results for the gravitational field of a clustered matter source on the background of an accelerating universe in DGP braneworld gravity, and articulate how these results differ from those of general relativity. In particular, we show that orbits nearby a mass source suffer a universal anomalous precession as large as 5 microarcseconds/year, dependent only on the graviton's effective linewidth and the global geometry of the full, five-dimensional universe. Thus, this theory offers a local gravity correction sensitive to factors that dictate cosmological history.Comment: 18 pages, 1 figure, revtex. Reference updated. Footnote change

Short distance non-perturbative effects of large distance modified gravity

In a model of large distance modified gravity we compare the nonperturbative Schwarzschild solution of hep-th/0407049 to approximate solutions obtained previously. In the regions where there is a good qualitative agreement between the two, the nonperturbative solution yields effects that could have observational significance. These effects reduce, by a factor of a few, the predictions for the additional precession of the orbits in the Solar system, still rendering them in an observationally interesting range. The very same effects lead to a mild anomalous scaling of the additional scale-invariant precession rate found by Lue and Starkman.Comment: 13 pages, paragraph with comment added, PLB versio