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Register a new userModels for the Brane-Bulk Interaction: Toward Understanding Braneworld Cosmological Perturbation
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Using some simple toy models, we explore the nature of the brane-bulk interaction for cosmological models with a large extra dimension. We are in particular interested in understanding the role of the bulk gravitons, which from the point of view of an observer on the brane will appear to generate dissipation and nonlocality, effects which cannot be incorporated into an effective (3+1)-dimensional Lagrangian field theoretic description. We explicitly work out the dynamics of several discrete systems consisting of a finite number of degrees of freedom on the boundary coupled to a (1+1)-dimensional field theory subject to a variety of wave equations. Systems both with and without time translation invariance are considered and moving boundaries are discussed as well. The models considered contain all the qualitative feature of quantized linearized cosmological perturbations for a Randall-Sundrum universe having an arbitrary expansion history, with the sole exception of gravitational gauge invariance, which will be treated in a later paper.
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For a cosmological Randall-Sundrum braneworld with anisotropy, i.e., of Bianchi type, the modified Einstein equations on the brane include components of the five-dimensional Weyl tensor for which there are no evolution equations on the brane. If the bulk field equations are not solved, this Weyl term remains unknown, and many previous studies have simply prescribed it ad hoc. We construct a family of Bianchi braneworlds with anisotropy by solving the five-dimensional field equations in the bulk. We analyze the cosmological dynamics on the brane, including the Weyl term, and shed light on the relation between anisotropy on the brane and Weyl curvature in the bulk. In these models, it is not possible to achieve geometric anisotropy for a perfect fluid or scalar field -- the junction conditions require anisotropic stress on the brane. But the solutions can isotropize and approach a Friedmann brane in an anti-de Sitter bulk.
We calculate the entanglement entropy of scalar perturbations due to gravitational non-linearities present in any model of canonically-coupled, single-field ekpyrosis. Specifically, we focus on a recent model of improved ekpyrosis which is able to generate a scale-invariant power spectrum of curvature perturbations and gravitational waves as well as have a non-singular bounce due to an S-brane at the end of ekpyrotic contraction. By requiring that the entanglement entropy remians subdominant to the thermal entropy produced during reheating, we get an upper bound on the energy scale of the bounce.
We consider a model with two parallel (positive tension) 3-branes separated by a distance $L$ in 5-dimensional spacetime. If the interbrane space is anti-deSitter, or is not precisely anti-deSitter but contains no event horizons, the effective 4-dimensional cosmological constant seen by observers on one of the branes (chosen to be the visible brane) becomes exponentially small as $L$ grows large.
Braneworld inflation is a phenomenology related to string theory that describes high-energy modifications to general relativistic inflation. The observable universe is a braneworld embedded in 5-dimensional anti de Sitter spacetime. Whe the 5-dimensional action is Einstein-Hilbert, we have a Randall-Sundrum type braneworld. The amplitude of tensor and scalar perturbations from inflation is strongly increased relative to the standard results, although the ratio of tensor to scalar amplitudes still obeys the standard consistency relation. If a Gauss-Bonnet term is included in the action, as a high-energy correction motivated by string theory, we show that there are important changes to the Randall-Sundrum case. We give an exact analysis of the tensor perturbations. They satisfy the same wave equation and have the same spectrum as in the Randall-Sundrum case, but the Gauss-Bonnet change to the junction conditions leads to a modified amplitude of gravitational waves. The amplitude is no longer monotonically increasing with energy scale, but decreases asymptotically after an initial rise above the standard level. Using an approximation that neglects bulk effects, we show that the amplitude of scalar perturbations has a qualitatively similar behaviour to the tensor amplitude. In addition, the tensor to scalar ratio breaks the standard consistency relation.
We apply the effective field theory approach to the coupled metric-inflaton system, in order to investigate the impact of higher dimension operators on the spectrum of scalar and tensor perturbations in the short-wavelength regime. In both cases, effective corrections at tree-level become important when the Hubble parameter is of the order of the Planck mass, or when the physical wave number of a cosmological perturbation mode approaches the square of the Planck mass divided by the Hubble constant. Thus, the cut-off length below which conventional cosmological perturbation theory does not apply is likely to be much smaller than the Planck length. This has implications for the observability of trans-Planckian effects in the spectrum of primordial perturbations.
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