Quantum fluctuations of bulk inflaton in inflationary brane world

Kobayashi, Shinpei; Koyama, K.; Soda, Jiro

doi:10.1016/s0370-2693(01)00137-x

Cited by 60 publications

(63 citation statements)

References 30 publications

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“…(1) (m, k) is determined by the primordial fluctuations and later evolutions [35], [36]. Further studies are needed to know the exact form of E (1) (m, k).…”

Section: Resultsmentioning

confidence: 99%

Bulk gravitational field and cosmological perturbations on the brane

Koyama

Soda

2001

Phys. Rev. D

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We investigate the effect of the bulk gravitational field on the cosmological perturbations on a brane embedded in the 5D Anti-de Sitter (AdS) spacetime. The effective 4D Einstein equations for the scalar cosmological perturbations on the brane are obtained by solving the perturbations in the bulk. Then the behaviour of the corrections induced by the bulk gravitational field to the conventional 4D Einstein equation are determined. Two types of the corrections are found. First we investigate the corrections which become significant at scales below the AdS curvature scales and in the high energy universe with the energy density larger than the tension of the brane. The evolution equation for the perturbations on the brane is found and solved. Another type of the corrections is induced on the brane if we consider the bulk perturbations which do not contribute to the metric perturbations but do contribute to the matter perturbations. At low energies, they have imaginary mass m 2 = −(2/3)k 2 in the bulk where k is the 3D comoving wave number of the perturbations. They diverge at the horizon of the AdS spacetime. The induced density perturbations behave as sound waves with sound velocity 1/ √ 3 in the low energy universe. At large scales, they are homogeneous perturbations that depend only on time and decay like radiation. They can be identified as the perturbations of the dark radiation. They produce isocurvature perturbations in the matter dominated era. Their effects can be observed as the shifts of the location and the height of the acoustic peak in the CMB spectrum.

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“…(1) (m, k) is determined by the primordial fluctuations and later evolutions [35], [36]. Further studies are needed to know the exact form of E (1) (m, k).…”

Section: Resultsmentioning

confidence: 99%

Bulk gravitational field and cosmological perturbations on the brane

Koyama

Soda

2001

Phys. Rev. D

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“…The main purpose of this article is to explore the effects of scalar fields with light modes in a BW cosmological setup of the RSII type [1]. To consider massless limit of scalar field in inflating BW is especially well motivated in the context of 'bulk inflaton' models [5,6,10,11,12], in which the dynamics of a bulk scalar drives inflation on the brane. In the simplest realizations, the brane geometry is close to dS and the bulk scalar is nearly massless.…”

Section: Introductionmentioning

confidence: 99%

Massless scalar fields and infrared divergences in the inflationary brane world

Pujolàs¹,

Tanaka²

2004

J. Cosmol. Astropart. Phys.

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We study the quantum effects induced by bulk scalar fields in a model with a de Sitter (dS) brane in a flat bulk (the Vilenkin-Ipser-Sikivie model) in more than four dimensions. In ordinary dS space, it is well known that the stress tensor in the dS invariant vacuum for an effectively massless scalar (m 2 eff = m 2 + ξR = 0 with R the Ricci scalar) is infrared divergent except for the minimally coupled case. The usual procedure to tame this divergence is to replace the dS invariant vacuum by the Allen Follaci (AF) vacuum. The resulting stress tensor breaks dS symmetry but is regular. Similarly, in the brane world context, we find that the dS invariant vacuum generates Tµν divergent everywhere when the lowest lying mode becomes massless except for massless minimal coupling case. A simple extension of the AF vacuum to the present case avoids this global divergence, but Tµν remains to be divergent along a timelike axis in the bulk. In this case, singularities also appear along the light cone emanating from the origin in the bulk, although they are so mild that Tµν stays finite except for non-minimal coupling cases in four or six dimensions. We discuss implications of these results for bulk inflaton models. We also study the evolution of the field perturbations in dS brane world. We find that perturbations grow linearly with time on the brane, as in the case of ordinary dS space. In the bulk, they are asymptotically bounded.

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“…Furthermore, in the low energy limit Hℓ ≪ 1 where H is the Hubble parameter of the brane and ℓ is the curvature radius of the bulk, as far as the spatially homogeneous dynamics is concerned, the dynamics on the brane has been found to be indistinguishable form the conventional slow-roll inflation [12]. It was also shown that the quantum fluctuations projected on the brane [10] as well as reheating after inflation [13] also mimic the 4-dimensional standard inflation, as long as we consider the low energy limit.…”

Section: Introductionmentioning

confidence: 99%

Geometry and cosmological perturbations in the bulk inflaton model

2003

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We consider a braneworld inflation model driven by the dynamics of a scalar field living in the 5-dimensional bulk, the so-called "bulk inflaton model", and investigate the geometry in the bulk and large scale cosmological perturbations on the brane. The bulk gravitational effects on the brane are described by a projection of the 5-dimensional Weyl tensor, which we denote by Eµν. Focusing on a tachionic potential model, we take a perturbative approach in the anti-de Sitter (AdS5) background with a single de Sitter brane. We first formulate the evolution equations for Eµν in the bulk. Next, applying them to the case of a spatially homogeneous brane, we obtain two different integral expressions for Eµν. One of them reduces to the expression obtained previously when evaluated on the brane. The other is a new expression that may be useful for analyzing the bulk geometry. Then we consider superhorizon scale cosmological perturbations and evaluate the bulk effects onto the brane. In the limit H 2 ℓ 2 ≪ 1, where H is the Hubble parameter on the brane and ℓ is the bulk curvature radius, we find that the effective theory on the brane is identical to the 4-dimensional Einstein-scalar theory with a simple rescaling of the potential even under the presence of inhomogeneities. In particular, it is found that the anticipated non-trivial bulk effect due to the spatially anisotropic part of Eµν may appear only at O(H 4 ℓ 4 ).

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Quantum fluctuations of bulk inflaton in inflationary brane world

Cited by 60 publications

References 30 publications

Bulk gravitational field and cosmological perturbations on the brane

Bulk gravitational field and cosmological perturbations on the brane

Massless scalar fields and infrared divergences in the inflationary brane world

Geometry and cosmological perturbations in the bulk inflaton model

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