BRANEWORLD COSMOLOGICAL PERTURBATIONS Roy Maartens University of Portsmouth Tokyo IT October 2003.
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Transcript of BRANEWORLD COSMOLOGICAL PERTURBATIONS Roy Maartens University of Portsmouth Tokyo IT October 2003.
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BRANEWORLD COSMOLOGICALPERTURBATIONS
Roy Maartens
University of PortsmouthTokyo ITOctober 2003
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testing the braneworld scenario cosmology as a probe of theory
braneworld observational signature?
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RS braneworldwhy does gravity not leak into 5D? cosmological constant in bulk 5 < 0how is brane protected against 40 + 5 4 =0 Minkowski brane in anti de Sitter bulk
5D gravitons effective mass m on brane (massive KK modes)
nonlocal KK effects
t>05
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field equationsgravitational action
RS solution 4-Minkowski in 5-AdS
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massive KK modes metric perturbation
TT-gauge (4D)
perturbed 5D field equation
separate into modes
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solution
zero mode
massive modes
RS1: m > 0 discrete spectrumRS2: m > 0 continuous spectrumgravitational potential
m=0 m>0
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general braneworldGauss equation
Codazzi equation
junction equations
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induced 4D Einstein tensor
high-energy
high or low energy 5D graviton - massive KK effects
KK/ Weyl anisotropic stress must be determined by 5D equations
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KK stresses from brane matter matter obeys brane and bulk do not exchange energy not true if scalar field/radiation in bulkBianchi identity
KK stresses sourced by perturbations - inhomogeneity and anisotropic stress
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standard 4D perturbation picture
t
inflation
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brane-worldperturbations
bulk
0-mode + KK modes
KK anisotropy
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inflation on the brane4D inflaton, high-energy inflation
high-energy assists slow-rollbrane slow-roll parameters
new possibility - steep inflation
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brane matter perturbations decouple from bulk metric perturbation (large scales)curvature perturbation can be found (large scales)
then
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tensor perturbations from inflationperturbed de Sitter brane
wave equation separable (H constant)
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solutions
mass gap above 0-mode
massive modes decay during inflation0-mode has increased amplitude at high energy
but tensor/ scalar is reduced!
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spectrum of normalizable statesdiscrete zero mode (4D) m=0massive KK continuum m>3H/2 only zero-mode excited during inflationevolution after inflation0-mode re-enters Hubble KK modes generated (5D gravitons bulk)loss of energy damping(Koyamas talk)
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spectral indices scalar perturbations same form as GR
tensor perturbations
compare GR
but consistency condition has the same form
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RS2 + induced gravitybrane matter / bulk graviton couplingquantum correction to gravitational actioncurvature term induced on brane
modifies gravity at large scales/ low energiesbut also removes RS high-energy correctionearly universe at high energy = GR +
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scalar perturbations
less power since need to check curvature perturbations
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tensor perturbations from inflationsame bulk equations same modesbut boundary conditions different:
giving
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RS2+Gauss-Bonnet gravitymost general 5D action with 2nd order equationsquantum/ stringy correction to gravity
modifies gravity at high energies
suggests lower scalar perturbationsbut curvature perturbation must be checked
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tensor perturbations from inflationbulk equation different
but bulk wave equation has same form
but boundary conditions differentjunction conditions cubic in extrinsic curvature!but same form of boundary condition as in IG:
giving
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curvature perturbation
matter conservation
curvature perturbation determined (on large scales)
CMB scalar anisotropies
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Sachs-Wolfe
adiabatic (matter) +isocurvature (dark radiation) + Weyl anisotropic stress terms
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gradient expansion curvature radius on the brane curvature radius in the bulk
To find - need boundary conditions - shadow/ regulator brane Low energy approximation
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background
Friedmann equationsdark radiationradion
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radionlow-energy solution
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effective equations on +ve tension branescalar-tensor theory
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cosmological perturbations
on large scales
Weyl anisotropic stress given by radion
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define new variablesthen
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brane displacements
bulk anisotropic perturbation physical meaning of variables
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simple toy model
Weyl anisotropic stress
completely compensates entropy perturbation
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further work
choose physical shadow matter
dark radiation in background
one-brane case: needs suitable boundary/ initial conditions