Exactly solvable model for cosmological perturbations in dilatonic brane worlds

Department of Physics, The University of Tokyo, Tōkyō, Japan
Physical review D: Particles and fields (Impact Factor: 4.86). 07/2003; 68(10). DOI: 10.1103/PhysRevD.68.103512
Source: arXiv


We construct a model where cosmological perturbations are analytically solved based on dilatonic brane worlds. A bulk scalar field has an exponential potential in the bulk and an exponential coupling to the brane tension. The bulk scalar field yields a power-law inflation on the brane. The exact background metric can be found including the back-reaction of the scalar field. Then exact solutions for cosmological perturbations which properly satisfy the junction conditions on the brane are derived. These solutions provide us an interesting model to understand the connection between the behavior of cosmological perturbations on the brane and the geometry of the bulk. Using these solutions, the behavior of an anisotropic stress induced on the inflationary brane by bulk gravitational fields is investigated. Comment: 30 pages, typos corrected, reference added

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Available from: Keitaro Takahashi, May 12, 2013
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    • "In refs. [15],[17]-[20], 5D solutions that also include the dynamics of a bulk scalar field were found for the case of a single brane. In these papers the search for solutions was simplified by assuming that the – 6 – metric functions and the bulk scalar were separable functions of t and y, which we will justify. "
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    ABSTRACT: We show that the radion in a warped geometry bounded by two branes can have a potential suitable for inflation. Our construction is based upon a solution known in string theory as the linear dilaton, in which the back-reaction from a bulk scalar \Phi is exactly accounted for. The radion, stabilized by \Phi, is much heavier than the TeV scale and its couplings to the standard model are much more suppressed than in the usual Randall-Sundrum solution. We present a new formalism for obtaining approximate time-dependent solutions, based on perturbing the exact solution to the coupled Einstein and scalar field equations in the bulk. It allows the radion potential to be computed directly in terms of the brane potentials for \Phi. We show that simple exponential potentials on the branes can lead to a 4D radion potential with a flattened hilltop form, yielding inflation with a spectral index of typically n_s=0.96 and no higher than 0.99. With more complicated brane potentials, the descent from the hilltop can be a linear potential, giving a tensor-to-scalar ratio as large as r=0.07 with n_s=0.974. The couplings of the radion to the standard model particles are dictated by general covariance, so the details of reheating are explicitly calculable, leading to a reheat temperature of at least 10^7 GeV. The quantum corrections to the inflaton potential from its couplings to matter are also calculable and are shown to be small, so that the prediction for the shape of the potential is under theoretical control, even with superPlanckian field excursions.
    Preview · Article · Nov 2011 · Journal of High Energy Physics
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    • "In this work we develop a gravi-dilaton brane-world with a non-trivial dynamics on the brane (a lot of papers have been written generalizing the standard RS solution to a more general framework in which a scalar field is included, see for example [12] [13] [14] [15] [16] [17]. In particular, following our previous work [9], we consider a higher-dimensional p-brane (with p > 3) coupled with a bulk dilaton. "
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    ABSTRACT: We consider a braneworld model in which an anisotropic brane is embedded in a dilatonic background. We solve the background solutions and study the behavior of the perturbations when the universe evolves from an inflationary Kasner phase to a Minkowski phase. We calculate the massless mode spectrum, and find that it does not differ from what expected in standard four-dimensional cosmological models. We then evaluate the spectrum of both light (ultrarelativistic) and heavy (nonrelativistic) massive modes, and find that, at high energies, there can be a strong enhancement of the Kaluza-Klein spectral amplitude, which can become dominant in the total spectrum. The presence of the dilaton, on the contrary, decrease the relative importance of the massive modes. Comment: 18 pages, 4 figures, Typos corrections
    Preview · Article · Jan 2006 · Physical review D: Particles and fields
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    ABSTRACT: Abstract The braneworld paradigm provides a tool for including the extra dimensions proposed by string theory into cosmology,in a simple way. With ordinary matter confined to a surface or brane, the extra dimension(s) introduce new degrees of freedom corresponding to the bulk geometry and bulk energy density. After presenting the derivation of the governing equations for braneworlds of co-dimension 1 (that is, with 1 extra dimension), this thesis will look at examples,of how a non-zero bulk energy-momentum,tensor can affect the cosmological evolution on the brane. In such braneworld models, particle interactions at high energies will produce 5- dimensional gravitons that escape into the bulk. Under the assumption,that all these gravitons are emitted radially, this emission can be modelled using a Vaidya-AdS5 space- time. In Chapter 4 we investigate the dynamics of this model, and find the exact solution of the field equations. We use a dynamical systems approach to analyze global features of the phase space of solutions. In Chapter 5, we generalise the previous radiating braneworld model by allowing for a breaking of Z2 symmetry, via different bulk cosmological constants and different initial black hole masses on either side of the brane. One of the notable features of asymmetry,is a suppression of the asymptotic level of dark radiation, which means that nucleosynthesis constraints are easier to satisfy. There are also models,where the radiation escapes to infinity on one or both sides, rather than falling into a black hole, but these models can have negative energy density on the brane.
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