Late acceleration andw=−1crossing in induced gravity

Abstract

We study the cosmological evolution on a brane with induced gravity within a bulk with arbitrary matter content. We consider a Friedmann-Robertson-Walker brane, invariantly characterized by a six-dimensional group of isometries. We derive the effective Friedmann and Raychaudhuri equations. We show that the Hubble expansion rate on the brane depends on the covariantly defined integrated mass in the bulk, which determines the energy density of the generalized dark radiation. The Friedmann equation has two branches, distinguished by the two possible values of the parameter ǫ = ±1. The branch with ǫ = 1 is characterized by an effective cosmological constant and accelerated expansion for low energy densities. Another remarkable feature is that the contribution from the generalized dark radiation appears with a negative sign. As a result, the presence of the bulk corresponds to an effective negative energy density on the brane, without violation of the weak energy condition. The transition from a period of domination of the matter energy density by nonrelativistic brane matter to domination by the generalized dark radiation corresponds to a crossing of the phantom divide w = −1.

Effective cosmological equations of inducedf(ℛ) gravity

“…The result is [14,15] 19) wherep = T AB n A n B is the pressure along the direction of the preferred spacelike vector field n A , and M is the "comoving mass" of the bulk fluid, satisfying .20) Only in the spherically symmetric case (k = 1) the "comoving mass" M has the usual physical interpretation as the effective gravitational mass contained within a sphere with radius ℓ. However, we shall refer to M as the "comoving mass" for all geometries of the hypersurfaces D. The integration constant M 0 in equation (2.20) can be interpreted as the mass of a black hole at ℓ 0 = 0.…”

“…The matter content of the bulk is described by the EM tensor T AB , which can be written in the usual way with respect to the bulk observers u A : 15) where…”

“…In the opposite limit kr c ≪ 1, we have α ≫ 1 and the regime of accelerated expansion is much shorter than in the conventional scenario. The branch with ǫ 2 = −1 is the generalization of the self-accelerating branch of DGP cosmology [6,7,9,15]. The acceleration is induced by an effective cosmological constant ∼ (1 + kr c )/r 2 c .…”

“…As expected, apart from the higher derivative corrections, these equations contain the generalized dark radiation term. We also show that there is conservation of energy between the brane matter and the generalized dark radiation, generalizing in this way the result of [14,15]. In section 3 we solve the field equations in a specific coordinate system by assuming a static and anisotropic fluid in the bulk.…”

“…This difficulty was overcome by employing covariant techniques in order to describe the solution of the braneworld equations. The covariant approach was used in [14,15,16], where it was found that the solution depends on the so called "comoving mass" M of the bulk fluid. This is a function of the brane scale factor R and the proper time τ on the brane.…”