Quantization of scalar perturbations in brane-world inflation

Abstract

We consider a quantization of scalar perturbations about a de Sitter brane in a 5-dimensional anti-de Sitter (AdS) bulk spacetime. We first derive the second order action for a master variable $\Omega$ for 5-dimensional gravitational perturbations. For a vacuum brane, there is a continuum of normalizable Kaluza-Klein (KK) modes with $m>3H/2$. There is also a light radion mode with $m=\sqrt{2}H$ which satisfies the junction conditions for two branes, but is non-normalizable for a single brane model. We perform the quantization of these bulk perturbations and calculate the effective energy density of the projected Weyl tensor on the barne. If there is a test scalar field perturbation on the brane, the $m^2=2H^2$ mode together with the zero-mode and an infinite ladder of discrete tachyonic modes become normalizable in a single brane model. This infinite ladder of discrete modes as well as the continuum of KK modes with $m>3H/2$ introduce corrections to the scalar field perturbations at first-order in a slow-roll expansion. We derive the second order action for the Mukhanov-Sasaki variable coupled to the bulk perturbations which is needed to perform the quantization and determine the amplitude of scalar perturbations generated during inflation on the brane.

14 pages

References in corpus (29)

• A Large Mass Hierarchy from a Small Extra Dimension
• An Alternative to Compactification
• The Einstein Equations on the 3-Brane World
• Non-conventional cosmology from a brane-universe
• Brane-world gravity
• Chaotic inflation on the brane
• Bent Domain Walls as Braneworlds
• Brane World Cosmology - Gauge-Invariant Formalism for Perturbation
• Brane cosmology: an introduction
• Brane World Cosmology
• Gravitational waves from inflation on the brane
• Brane-world creation and black holes
• Cosmological Perturbations in Brane-World Theories: Formalism
• Gauge-invariant gravitational perturbations of maximally symmetric spacetimes
• Large-scale cosmological perturbations on the brane
• Evolution of Cosmological Perturbations in the Brane World
• On Brane World Cosmological Perturbations
• Cosmological perturbations in the bulk and on the brane
• Gravity waves from inflating brane or Mirrors moving in adS${}_5$
• Bulk Gravitational Field and Cosmological Perturbations on the Brane
• Radion on the de Sitter brane
• Quantum Fluctuations of Bulk Inflaton in Inflationary Brane World
• Primordial gravitational waves in inflationary braneworld
• Cosmic Microwave Radiation Anisotropies in Brane Worlds
• Scalar perturbations from brane-world inflation
• Cosmic vorticity on the brane
• Inflationary slow-roll formalism and perturbations in the Randall-Sundrum Type II braneworld
• Quantum Radion on de Sitter branes
• Bulk gravitational field and dark radiation on the brane in dilatonic brane world

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