Gravitational Waves from Warped ExtraDimensional Geometry

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Gravitational Waves from Warped Extra-Dimensional
Geometry

• LR (with Geraldine Servant)

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LISA and the Weak Scale
Gravity waves thought of as a new way of probing
astrophysics Cosmology perhaps inflation? But
also might be a way of probing the weak scale
LISA band 10-4 10-2 mHz
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Which Weak Scale Physics?

• Strong first order phase transitions
• Example transition to RS1 phase
• RS1 2 brane model with five-dimensional bulk
  warped geometry

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Plan

• Review Warped Geometry as solution to hierarchy
  problem
• Cosmology of Warped Geometry
• Gravity Waves from 1st Order Phase Transitions
• Put it all together

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• REVIEW

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Traditional route to extra dimensions
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Changed in 1990s Branes
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• With branes, weve found
• New way to hide dimensions
• New concept of our place in the universe
• New way to explain weakness of gravity

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Standard Model of Particle PhysicsRests on
Unstable Foundation
Barnett Newman Broken Obelisk
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Hierarchy Problem One of the Chief Puzzles
New ideas might provide deeper connections among
masses and forces Need fine-tuning to get
very different masses
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RS1 Warped Spacetime Geometry to address
hierarchy problem

• Two branes
• Gravity concentrated on Gravitybrane
• But we live on a second brane
• The Weakbrane

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Natural for gravity to be weak

• ds2dr2e-kr(dxm dxn hmn)
• Small probability for graviton to be near the
  Weakbrane
• If we live anywhere but the Gravitybrane, gravity
  is naturally weak in warped geometry

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Everything rescaled in warped geometry!
Can understand weakness of gravity as things
being bigger and lighter on the Weakbrane

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Particles in bulk rescaled masses
Planck 106 TeV
1000 TeV TeV
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TeV physics Testable KK modes

• Kaluza-Klein particles
• Definite mass spectrum and spin-2

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collider signals would be dramatically different
H. Davoudiasl, J. Hewett, T. Rizzo
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• Collider signals could be spectacular
• Can we probe in other ways?
• (And conceivably higher energy scales?)
• AlternativelyGravitational Waves!

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• COSMOLOGY OF RS1

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Cosmological Evolution

• (Creminelli, Nicolis, Rattazzi)
• Universe starts off at high temperature
• No evidence of Weakbrane
• Temperature too high to experience weak scale
  phenomena
• High temperature AdS-Schwarschild
• Weak brane physics shielded by a horizon

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AdS-Schwarschild
horizon
Weak scale
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High Temperature phase
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Low Temperature Phase

• RS1 geometry
• Second brane emerges at TeV scale
• Key is stabilization mechanism
• Radion field determines spacing between branes
• Require that radion is stabilized at about TeV

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Goldberger-Wise Stabilization
Need to set distance between the branes Requires
competing effects Potential terms want branes
close Gradient terms want branes far Get optimal
situationhierarchy with no very large
parameter Mass squared determines hierarchy
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RS1/GW potential

• Radion minimization

• With an additional brane term

em2/4k2
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What happens?
At critical temperature, RS phase is
favored Below this temperature expect a first
order phase transition Radion starts at m0 and
evolves to mmTeV
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Phase Transition

• AdS-S and RS1 are both local minima of free
  energy
• From 4D perspective, expect transition through
  bubble nucleation
• From 5D perspective, spherical brane patches on
  horizon
• Coalesce to form Weakbrane
• Turns out strongly first order phase transition

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Bubbles connecting two phases
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Aside

• Why can we treat this as bubble nucleation in
  four dimensions
• when truly a five-dimensional set-up?
• Low energies radion dominates potential,
• need v1 small, radion light
• High energies holography
• (M/k)3N2/16p2, need N large

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• GRAVITY WAVES FROM 1ST ORDER PHASE TRANSITIONS
  RS1

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Gravity waves from 1st order Phase Transition

• Two sources of gravitational waves
• Bubble collision and Turbulence
• Depends on two parameters (when strong)
• a ratio of latent heat to radiation density at
  nucleation temperature
• Need agt0.2
• b
• Need transition to be slow enough for signal
• Expect of order ln(MP/T) due to nucleation
  condition (exponentially suppressed)
• So about right order

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Signal function of a, b
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(No Transcript)
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SIGNAL AS FUNCTION OF NUCLEATION TEMP
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Particular Model
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Reach
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LISA Sensitivity
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But Perturbativity Constraints

• Phase transition only completes in borderline
  perturbative region
• k largish (need k/M5lt1)
• e largish (more a problem for GW)
• v1N
• dT1 often big
• Nucleation temperature not too low
• We investigate dTmnlt L3 k2

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Constraints egt0
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Constraints elt0
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Comments

• Truly borderline
• Could be better or worse
• Plus
• De Wolfe, Freedman, Karch have shown RS can work
  with sizable back reaction
• And sizable vev for GW field Kofman et al
• Nonetheless need to take results with some caution

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Conclusions

• First order phase transition for RS1
• Introduces constraintscannot have very small AdS
  curvature
• But in region where transition can take place
• Strong gravity wave signal
• Two peak structure
• Or change in slope
• Gravity waves new way of exploring weak scale
  physics
• Worth investigating further