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

From k-essence to generalised Galileons

We determine the most general scalar field theories which have an action that depends on derivatives of order two or less, and have equations of motion that stay second order and lower on flat space-time. We show that those theories can all be obtained from linear combinations of Lagrangians made by multiplying a particular form of the Galileon Lagrangian by an arbitrary scalar function of the scalar field and its first derivatives. We also obtain curved space-time extensions of those theories which have second order field equations for both the metric and the scalar field. This provide the most general extension, under the condition that field equations stay second order, of k-essence, Galileons, k-Mouflage as well as of the kinetically braided scalars. It also gives the most general action for a scalar classicalizer, which has second order field equations. We discuss the relation between our construction and the Euler hierachies of Fairlie et al, showing in particular that Euler hierachies allow one to obtain the most general theory when the latter is shift symmetric. As a simple application of our formalism, we give the covariantized version of the conformal Galileon.Comment: 25 page

The radion in brane cosmology

We consider the homogeneous cosmological radion, which we define as the interbrane distance in a two brane and $Z_2$ symmetrical configuration. In a coordinate system where one of the brane is at rest, the junction conditions for the second (moving) brane give directly the (non-linear) equations of motion for the radion. We analyse the radion fluctuations and solve the non-linear dynamics in some simple cases of interest

Bigravity and Lorentz-violating Massive Gravity

Bigravity is a natural arena where a non-linear theory of massive gravity can be formulated. If the interaction between the metrics $f$ and $g$ is non-derivative, spherically symmetric exact solutions can be found. At large distances from the origin, these are generically Lorentz-breaking bi-flat solutions (provided that the corresponding vacuum energies are adjusted appropriately). The spectrum of linearized perturbations around such backgrounds contains a massless as well as a massive graviton, with {\em two} physical polarizations each. There are no propagating vectors or scalars, and the theory is ghost free (as happens with certain massive gravities with explicit breaking of Lorentz invariance). At the linearized level, corrections to GR are proportional to the square of the graviton mass, and so there is no vDVZ discontinuity. Surprisingly, the solution of linear theory for a static spherically symmetric source does {\em not} agree with the linearization of any of the known exact solutions. The latter coincide with the standard Schwarzschild-(A)dS solutions of General Relativity, with no corrections at all. Another interesting class of solutions is obtained where $f$ and $g$ are proportional to each other. The case of bi-de Sitter solutions is analyzed in some detail.Comment: 25 pages. v3 Typos corrected, references added. v4 Introduction extende

Global Structure of Deffayet (Dvali-Gabadadze-Porrati) Cosmologies

We detail the global structure of the five-dimensional bulk for the cosmological evolution of Dvali-Gabadadze-Porrati braneworlds. The picture articulated here provides a framework and intuition for understanding how metric perturbations leave (and possibly reenter) the brane universe. A bulk observer sees the braneworld as a relativistically expanding bubble, viewed either from the interior (in the case of the Friedmann-Lemaitre-Robertson-Walker phase) or the exterior (the self-accelerating phase). Shortcuts through the bulk in the first phase can lead to an apparent brane causality violation and provide an opportunity for the evasion of the horizon problem found in conventional four-dimensional cosmologies. Features of the global geometry in the latter phase anticipate a depletion of power for linear metric perturbations on large scales.Comment: 15 pages, 4 figures, RevTeX. References adde

The Vainshtein mechanism in the Decoupling Limit of massive gravity

We investigate static spherically symmetric solutions of nonlinear massive gravities. We first identify, in an ansatz appropriate to the study of those solutions, the analog of the decoupling limit (DL) that has been used in the Goldstone picture description. We show that the system of equations left over in the DL has regular solutions featuring a Vainshtein-like recovery of solutions of General Relativity (GR). Hence, the singularities found to arise integrating the full nonlinear system of equations are not present in the DL, despite the fact those singularities are usually thought to be due to a negative energy mode also seen in this limit. Moreover, we show that the scaling conjectured by Vainshtein at small radius is only a limiting case in an infinite family of non singular solutions each showing a Vainshtein recovery of GR solutions below the Vainshtein radius but a different common scaling at small distances. This new scaling is shown to be associated with a zero mode of the nonlinearities left over in the DL. We also show that, in the DL, this scaling allows for a recovery of GR solutions even for potentials where the original Vainshtein mechanism is not working. Our results imply either that the DL misses some important features of nonlinear massive gravities or that important features of the solutions of the full nonlinear theory have been overlooked. They could also have interesting outcomes for the DGP model and related proposals.Comment: 52 pages, 7 figures; v3: minor typos corrected, discussion of the validity of the Decoupling Limit extended; accepted for publication in JHE

The Accelerated Universe and the Moon

Cosmologically motivated theories that explain small acceleration rate of the Universe via modification of gravity at very large, horizon or super-horizon distances, can be tested by precision gravitational measurements at much shorter scales, such as the Earth-Moon distance. Contrary to the naive expectation the predicted corrections to the Einsteinian metric near gravitating sources are so significant that fall within sensitivity of the proposed Lunar Ranging experiments. The key reason for such corrections is the van Dam-Veltman-Zakharov discontinuity present in linearized versions of all such theories, and its subsequent absence at the non-linear level ala Vainshtein

On Brane World Cosmological Perturbations

We discuss the scalar cosmological perturbations in a 3-brane world with a 5D bulk. We first show explicitly how the effective perturbed Einstein's equations on the brane (involving the Weyl fluid) are encoded into Mukohyama's master equation. We give the relation between Mukohyama's master variable and the perturbations of the Weyl fluid, we also discuss the relation between the former and the perturbations of matter and induced metric on the brane. We show that one can obtain a boundary condition on the brane for the master equation solely expressible in term of the master variable, in the case of a perfect fluid with adiabatic perturbations on a Randall-Sundrum (RS) or Dvali-Gabadadze-Porrati (DGP) brane. This provides an easy way to solve numerically for the evolution of the perturbations as well as should shed light on the various approximations done in the literature to deal with the Weyl degrees of freedom.Comment: 36 pages, 1 figur

Halo models in modified gravity theories with self-accelerated expansion

We investigate the structure of halos in the sDGP (self-accelerating branch of the Dvali-Gavadadze-Porrati braneworld gravity) model and the galileon modified gravity model on the basis of the static and spherically symmetric solutions of the collisionless Boltzmann equation, which reduce to the singular isothermal sphere model and the King model in the limit of Newtonian gravity. The common feature of these halos is that the density of a halo in the outer region is larger (smaller) in the sDGP (galileon) model, respectively, in comparison with Newtonian gravity. This comes from the suppression (enhancement) of the effective gravity at large distance in the sDGP (galileon) model, respectively. However, the difference between these modified gravity models and Newtonian gravity only appears outside the halo due to the Vainshtein mechanism, which makes it difficult to distinguish between them. We also discuss the case in which the halo density profile is fixed independently of the gravity model for comparison between our results and previous work.Comment: 15pages, 6 figures, maches the version to be published in Int. J. Mod. Phys. D, typos correcte

Born-Infeld-type phantom on the brane world

We study the evolution of Born-Infeld-type phantom in the second Randall-Sundrum brane scenario, and find that there exists attractor solution for the potential with a maximum, which implies a cosmological constant at the late time. Especially, we discuss the BI model of constant potential without and with dust matter. In the weak tension limit of the brane, we obtain an exact solution for the BI phantom and scale factor and show that there is no big rip during the evolution of the brane.Comment: 5 pages, 2 figures, Reference added, Phys. Rev. D in pres