In this paper we discuss analytically the luminosity distance – redshift relation in various generalized Randall-Sundrum type II brane-world models described by Eq. We give in Fig 1 a diagram containing a classification of these theories and how they emerge as different limits from each other. Notably, the BRANE2 branch contains cosmological models which self-accelerate at late-times. Both the original Randall-Sundrum type II model and the DGP model are contained as special subcases. These are called the BRANE1 branch for ε = -1 and BRANE2 for ε = 1 in the terminology of, respectively]. In a cosmological setup the square root of this equation can be taken, leading to a set of modified Friedmann and Raychaudhuri equations, which however contain a sign ambiguity ε = ☑ due to the involved square root. This implies that in certain sense the degree of nonlinearity of the theory is squared. ( 29) of ), which contains the square of the Einstein tensor G ab. In these models the role of the effective Einstein equation ( 2) is taken by a more complicated equation (see for example Eq. Generalizations of the DGP model are discussed covariantly in and when the embedding is symmetric, and in when it is asymmetric. The ghost modes withstand even the introduction of a second brane. This model however suffers from linear instabilities (ghost modes in the perturbations), as shown for de Sitter branes. The induced gravity correction couples to the 5-dimensional Einstein-Hilbert action with the coupling constant γ κ ˜ 2 / κ 2 The simplest of such models, the DGP model was introduced in. These can be regarded as brane-world models enhanced with the first quantum-correction arising from the interaction of the brane matter with bulk gravity. The possible modifications of gravitational dynamics are even more versatile in the so-called induced gravity models. There is also possible to replace dark matter with geometric effects in the interpretation of galactic rotation curves, weak lensing and galaxy cluster dynamics. Both early cosmology and gravitational collapse are essentially modified in these theories. Otherwise it can be called a Weyl fluid.Ī review of many aspects related to the theories described by the effective Einstein equation ( 2) can be found in. In a cosmological context and suppressing any energy exchange between the brane and the bulk, this latter term generates the so-called dark radiation. Supplementing this by the pull-back to the brane of the bulk energy momentum tensor Π ˜ a b which is The effective Einstein equation (for the case of symmetric embedding and no other contribution to the bulk-energy-momentum than a bulk cosmological constant) was first given in a covariant form in. Its projections to our observable 4-dimensional universe (the brane) are the twice contracted Gauss equation, the Codazzi equation and an effective Einstein equation, the latter being obtained by employing the junction conditions across the brane. In this generalized Randall-Sundrum type II (RS) theory, the brane has a tension λ and gravitational dynamics is governed by the 5-dimensional Einstein equation. In contrast with standard model fields, these evolve in the whole 5-dimensional bulk. The curved generalizations of the model presented in have evolved into a 5-dimensional alternative to general relativity, in which gravity has more degrees of freedom. The so-called brane-world models, motivated by string/M-theory, containing our observable 4-dimensional universe (the brane) as a hypersurface, were introduced in and, the latter model allowing for a non-compact extra dimension. Originally pioneered by Kaluza and Klein, such theories contained compact extra dimensions. Modifications of the gravitational interaction could also occur by enriching the space-time with extra dimensions. However the parameter range, in which the latter is in goood agrement with the supernova data, also presents stability problems. Quite remarkably, supernova data, which in the traditional interpretation yield to the existence of dark energy, can be explained by certain f(R) or inverse curvature gravity models. However in spite of the successes, certain problems were signaled on smaller scales. These theories are compatible with the Large scale structure of the Universe. There is no widely accepted explanations for the nature of any of the dark matter or dark energy (even the existence of the cosmological constant remains unexplained).Īn alternative to introducing dark matter would be to modify the law of gravitation, like in MOND and its relativistic generalization. Dark energy could be simply a cosmological constant Λ, or quintessence or something entirely different. At present the Universe is considered a general relativistic Friedmann space-time with flat spatial sections, containing more than 70% dark energy and at about 25% of dark matter.
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