The consequences for the brane cosmological evolution of energy exchange between the brane and the bulk are analyzed in detail, in the context of a non-factorizable background geometry with vanishing effective cosmological constant on the brane. A rich variety of brane cosmologies is obtained, depending on the precise mechanism of energy transfer, the equation of state of brane-matter and the spatial topology. An accelerating era is generically a feature of our solutions. In the case of low-density flat universe more dark matter than in the conventional FRW picture is predicted. Spatially compact solutions are found to delay their re-collapse.

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A novel idea is proposed for a natural solution of the dark energy and its cosmic coincidence problem. The existence of local antigravity sources, associated with astrophysical matter configurations distributed throughout the universe, can lead to a recent cosmic acceleration effect. Various physical theories can be compatible with this idea, but here, in order to test our proposal, we focus on quantum originated spherically symmetric metrics matched with the cosmological evolution through the simplest Swiss cheese model. In the context of asymptotically safe gravity, we have explained the observed amount of dark energy using Newton's constant, the galaxy or cluster length scales, and dimensionless order one parameters predicted by the theory, without fine-tuning or extra unproven energy scales. The interior modified Schwarzschild-de Sitter metric allows us to approximately interpret this result as that the standard cosmological constant is a composite quantity made of the above parameters, instead of a fundamental one. * Electronic address: gkofinas@aegean.gr † Electronic address: vzarikas@teilam.gr

New general spherically symmetric solutions have been derived with a cosmological "constant" Λ as a source. This Λ field is not constant but it satisfies the properties of the asymptotically safe gravity at the ultraviolet fixed point. The importance of these solutions comes from the fact that they describe the near to the centre region of black hole spacetimes as this is modified by the Renormalization Group scaling behaviour of the fields. The consistent set of field equations which respect the Bianchi identities is derived and solved. One of the solutions (with conventional sign of temporal-radial metric components) is timelike geodesically complete, and although there is still a curvature divergent origin, this is never approachable by an infalling massive particle which is reflected at a finite distance due to the repulsive origin. Another family of solutions (of both signatures) range from a finite radius outwards, they cannot be extended to the centre of spherical symmetry, and the curvature invariants are finite at the minimum radius. * Electronic address: gkofinas@aegean.gr † Electronic address: vzarikas@teilam.gr