Cosmic%20Microwave%20Radiation%20Anisotropies%20in%20brane%20worlds

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Cosmic Microwave Radiation Anisotropies in brane
worlds
Kazuya Koyama Tokyo University

• K. Koyama astro-ph/030310
• K. Koyama PRD 66 084003(2002)

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1. Introduction

• Brane World picture
• Standard model lives on a brane
• Gravity can propagate into bulk
• Observational signatures
• Extra-dimension can be observed only
  through gravitational interactions
• Can we observe extra-dimension using CMB
  experiments ?

Standard model
gravity
brane
bulk
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Randall Sundrum model
(Randall, Sundrum)

• Gravity on the brane in AdS5
• carries the information in the bulk
• 4D Equations for on the brane

(Shiromizu, Maeda, Sasaki)
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Cosmology

• Background universe

Perturbations
4D equations can determine the behavior of
At large scales, Weyl anisotropic stress cannot
be determined only by 4D equations
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• CMB anisotropies (SW effect)
• We cannot predict CMB anisotropies unless the
• behavior of Weyl anisotropic stress is known
• In this talk, we calculate
• Weyl anisotropic stress in two branes model at
  low energies
• Impact of dark radiation perturbation on CMB
  anisotropies

Red shift
(Langlois, Maartens, Sasaki, Wands)
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2.Large scale anisotropy on the brane
Black Hole
Moving brane in BH geometry Homogeneity and
isotropy AdS Schwartzshild bulk
Brane
Anisotropy on the brane anisotropy in the
bulk anisotropy on the brane Bulk and brane
is coupled
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• We know the metric for Ads-Schwartzsild
• metric near the brane
• Consider the perturbation of dark radiation
  

AdS spacetime perturbations (TT gauge)
anisotropic shear
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• In TT gauge, anisotropic perturbation
• can exist (5D graviton)
• In TT gauge, the brane location is perturbed

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• Junction condition relates matter perturbation on
  the brane to and perturbations
• Adiabatic condition on matter perturbations
• equation for

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• Solution for integration
  constant
• 
  
• Metric perturbations on the brane
• Curvature perturbation

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• Curvature perturbation is determined
• independently of
• Curvature perturbation brane dynamics
• ( FRW equation brane dynamics)
• Solution for curvature perturbation can be
  derived exactly at large scales (including ,
  at high energies)
• Anisotropic stress
• anisotropic stress on the brane
• coupled to anisotropic perturbation

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• Evolution equation for
• Junction condition at the brane
• Gradient expansion

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• Junction condition on the brane
• One more boundary condition is needed to
• specify
• Anisotropic stress is nothing but
• Behavior of anisotropic stress completely
  depends on the boundary condition in the bulk

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• The simplest case where we can determine
• another brane in the bulk
• Junction conditions

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• Solution for ,
• Anisotropic stress

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• Two branes model
• Shadow matter, radion affect the anisotropy of
  the brane at large scales
• CMB anisotropies provide
• useful constraints on the model
• Realistic model should be considered
• case is interesting
• Anisotropic stress associated with dark
• radiation does not depend on

(Rhodes, van der Bruck, Brax, Davis)
Toy model for anisotropic stress
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3.Effect of dark radiation on CMB anisotropies

• Dark radiation perturbation induces the
  isocurvature perturbation
• Weyl anisotropic stress gives distinguishable
  features to CMB anisotropies
• We use the result for
  to investigate
• the effect of dark radiation on CMB
  anisotropies

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Covariant formalism
Radion
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• Parameter
• amplitude of dark radiation perturbation
• isocurvature perturbation, anisotropic
  stress
• Due to Weyl anisotropic stress, the resultant
  CMB spectrum is different from simple mixtures
  of adiabatic and isocurvature perturbations
• Likelihood analysis Malkov Chain Monte Calro
  approach

(K. Koyama and K Ichiki in preparation)
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Summary

• Two branes model
• Shadow matter, radion affect large scale CMB
  anisotropies
• Extensions to general cases
• Construct realistic models
• stabilization mechanism
• or time dependent fundamental constant

(K. Koyama, R. Maartens, work in progress)
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• One brane model
• We should carefully investigate the
• boundary condition in the bulk
• Anisotropic stress boundary condition
• Validity of our modeling ?
• Anisotropic AdS-Schwartzshild spacetime
• Toy model where the above relation can be
• analytically examined in a whole spacetime
• (KK and K. Takahashi hep-th/0307073)