Cédric Deffayet

Accelerated universe from gravity leaking to extra dimensions

We discuss the idea that the accelerated universe could be the result of gravitational leakage into extra dimensions over Hubble distances rather than the consequence of a nonzero cosmological constant.

Cosmology on a brane in Minkowski bulk

Abstract We discuss the cosmology of a 3-brane embedded in a 5D bulk space–time with a cosmological constant when an intrinsic curvature Ricci scalar is included in the brane action. After deriving the ‘brane-Friedmann’ equations for a Z 2 symmetrical metric, we focus on the case of a Minkowski bulk. We show that there exist two classes of solutions, close to the usual Friedmann–Lemaitre–Robertson–Walker cosmology for small enough Hubble radii. When the Hubble radius gets larger one either has a transition to a fully 5D regime or to a self-inflationary solution which produces a late accelerated expansion. We also compare our results with a perturbative approach and eventually discuss the embedding of the brane into the Minkowski space–time. This latter part of our discussion also applies when no intrinsic curvature term is included.

Nonperturbative continuity in graviton mass versus perturbative discontinuity

We address the question whether a graviton could have a small nonzero mass. The issue is subtle for two reasons: there is a discontinuity in the mass in the lowest tree-level approximation, and, moreover, the nonlinear four-dimensional theory of a massive graviton is not defined unambiguously. First, we reiterate the old argument that for the vanishing graviton mass the lowest tree-level approximation breaks down since the higher order corrections are singular in the graviton mass. However, there exist nonperturbative solutions which correspond to the summation of the singular terms and these solutions are continuous in the graviton mass. Furthermore, we study a completely nonlinear and generally covariant five-dimensional model which mimics the properties of the four-dimensional theory of massive gravity. We show that the exact solutions of the model are continuous in the mass, yet the perturbative expansion exhibits the discontinuity in the leading order and the singularities in higher orders as in the four-dimensional case. Based on exact cosmological solutions of the model we argue that the helicity-zero graviton state which is responsible for the perturbative discontinuity decouples from the matter in the limit of vanishing graviton mass in the full classical theory.

Arbitrary p-form Galileons

We show that scalar, 0-form, Galileon actions—models whose field equations contain only second derivatives—can be generalized to arbitrary even p-forms. More generally, they need not even depend on a single form, but may involve mixed p combinations, including equal p multiplets, where odd p fields are also permitted: We construct, for given dimension D, general actions depending on scalars, vectors, and higher p-form field strengths, whose field equations are of exactly second derivative order. We also discuss and illustrate their curved-space generalizations, especially the delicate nonminimal couplings required to maintain this order. Concrete examples of pure and mixed actions, field equations, and their curved-space extensions are presented.

Supernovae, CMB, and gravitational leakage into extra dimensions

We discuss observational constraints coming from CMB and type Ia supernovae for the model of an accelerated universe produced by gravitational leakage into extra dimensions. Our fits indicate that the model is currently in agreement with the data. We also give the equations governing the evolution of cosmological perturbations. Future observations will be able to severely constrain the model.

Ghosts, strong coupling and accidental symmetries in massive gravity

We show that the strong self-interaction of the scalar polarization of a massive graviton can be understood in terms of the propagation of an extra ghostlike degree of freedom, thus relating strong coupling to the sixth degree of freedom discussed by Boulware and Deser in their Hamiltonian analysis of massive gravity. This enables one to understand the Vainshtein recovery of solutions of massless gravity as being due to the effect of the exchange of this ghost, which gets frozen at distances larger than the Vainshtein radius. Inside this region, we can trust the two-field Lagrangian perturbatively, while at larger distances one can use the higher derivative formulation. We also compare massive gravity with other models, namely, deconstructed theories of gravity, as well as the Dvali-Gabadadze-Porrati model. In the latter case, we argue that the Vainshtein recovery process is of a different nature, not involving a ghost degree of freedom.

Recovery of general relativity in massive gravity via the Vainshtein mechanism

We study in detail static spherically symmetric solutions of nonlinear Pauli-Fierz theory. We obtain a numerical solution with a constant density source. This solution shows a recovery of the corresponding solution of general relativity via the Vainshtein mechanism. This result has already been presented by us in a recent paper, and we give here more detailed information on it as well as on the procedure used to obtain it. We give new analytic insights into this problem, in particular, for what concerns the question of the number of solutions at infinity. We also present a weak-field limit which allows one to capture all the salient features of the numerical solution, including the Vainshtein crossover and the Yukawa decay.

A note on 'symmetric' vielbeins in bimetric, massive, perturbative and non perturbative gravities

A bstractWe consider a manifold endowed with two different vielbeins

A formal introduction to Horndeski and Galileon theories and their generalizations

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Counting the degrees of freedom of generalized Galileons

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