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Gravitational Waves from Warped Extra-Dimensional Geometry. LR (with Geraldine Servant). 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. - PowerPoint PPT Presentation
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Gravitational Waves from Gravitational Waves from Warped Extra-Dimensional Warped Extra-Dimensional
GeometryGeometry
LR (with Geraldine Servant)LR (with Geraldine Servant)
LISA and the Weak ScaleLISA and the Weak Scale
LISA band 10-4 – 10-2 mHz
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
Which Weak Scale Physics?Which Weak Scale Physics?
Strong first order phase transitionsStrong first order phase transitions
Example: transition to RS1 phaseExample: transition to RS1 phase
RS1: 2 brane model with five-dimensional RS1: 2 brane model with five-dimensional bulk warped geometrybulk warped geometry
PlanPlan
Review Warped Geometry as solution to Review Warped Geometry as solution to hierarchy problemhierarchy problem
Cosmology of Warped GeometryCosmology of Warped Geometry
Gravity Waves from 1Gravity Waves from 1stst Order Phase Order Phase TransitionsTransitions
Put it all togetherPut it all together
REVIEWREVIEW
Traditional route to extra Traditional route to extra dimensionsdimensions
Changed in 1990’s: BranesChanged in 1990’s: Branes
With branes, we’ve found:With branes, we’ve found:
New way to hide dimensionsNew way to hide dimensions
New concept of our place in the New concept of our place in the universeuniverse
New way to explain weakness of gravityNew way to explain weakness of gravity
Standard Model of Particle PhysicsStandard Model of Particle PhysicsRests on Unstable Foundation Rests on Unstable Foundation
Barnett Newman: Broken Obelisk
Hierarchy Problem: One of the Hierarchy Problem: One of the Chief PuzzlesChief Puzzles
New ideas might provide deeper connections among masses and forces
Need “fine-tuning” to get very different masses
RS1 RS1 Warped Spacetime Geometry Warped Spacetime Geometry to address hierarchy problemto address hierarchy problem
•Two branes
•Gravity concentrated on Gravitybrane
•But we live on a second brane:
•The Weakbrane
dsds22=dr=dr22+e+e-kr-kr(dx(dx dx dx
Small probability for Small probability for graviton to be near the graviton to be near the WeakbraneWeakbrane
If we live anywhere but If we live anywhere but the Gravitybrane, gravity the Gravitybrane, gravity is naturally weak in is naturally weak in warped geometrywarped geometry
Natural for gravity to be weakNatural for gravity to be weak
Everything rescaled in warped Everything rescaled in warped geometry!geometry!
Can understand Can understand weakness of gravity as weakness of gravity as things being bigger and things being bigger and lighter on the lighter on the WeakbraneWeakbrane
Particles in bulk: rescaled massesParticles in bulk: rescaled masses
Planck 106 TeV 1000 TeV TeV
TeV physics Testable: KK modesTeV physics Testable: KK modes
Kaluza-Klein Kaluza-Klein particlesparticles
Definite mass Definite mass spectrum and spectrum and “spin”-2“spin”-2
collider signals would be dramatically different
H. Davoudiasl, J. Hewett, T. Rizzo
Collider signals could be spectacularCollider signals could be spectacularCan we probe in other ways?Can we probe in other ways?(And conceivably higher energy scales?)(And conceivably higher energy scales?)
Alternatively…Gravitational Waves!Alternatively…Gravitational Waves!
COSMOLOGY OF COSMOLOGY OF RS1RS1
Cosmological Evolution Cosmological Evolution
(Creminelli, Nicolis, Rattazzi)(Creminelli, Nicolis, Rattazzi)
Universe starts off at high temperatureUniverse starts off at high temperature
No evidence of Weakbrane No evidence of Weakbrane
Temperature too high to experience weak Temperature too high to experience weak scale phenomenascale phenomena
High temperature: AdS-SchwarschildHigh temperature: AdS-Schwarschild
Weak brane physics shielded by a horizonWeak brane physics shielded by a horizon
AdS-SchwarschildAdS-Schwarschild
horizonWeak scale
High Temperature phaseHigh Temperature phase
Low Temperature PhaseLow Temperature Phase
RS1 geometryRS1 geometry
Second brane emerges at ~TeV scaleSecond brane emerges at ~TeV scale
Key is stabilization mechanismKey is stabilization mechanism
Radion field: determines spacing between Radion field: determines spacing between branesbranes
Require that radion is stabilized at about Require that radion is stabilized at about TeV TeV
Goldberger-Wise StabilizationGoldberger-Wise Stabilization
Need to set distance between the branes
Requires competing effects
Potential terms want branes close
Gradient terms want branes far
Get optimal situation—hierarchy with no very large parameter
Mass squared determines hierarchy
RS1/GW potentialRS1/GW potential
Radion minimization:Radion minimization:
•With an additional brane term:
~m2/4k2
What happens?What happens?
At critical temperature, RS phase is favored
Below this temperature expect a first order phase transition
Radion starts at =0 and evolves to =TeV
Phase TransitionPhase Transition
AdS-S and RS1 are both local minima of AdS-S and RS1 are both local minima of free energyfree energyFrom 4D perspective, expect transition From 4D perspective, expect transition through bubble nucleationthrough bubble nucleationFrom 5D perspective, spherical brane From 5D perspective, spherical brane patches on horizon patches on horizon Coalesce to form WeakbraneCoalesce to form Weakbrane Turns out strongly first order phase Turns out strongly first order phase transitiontransition
Bubbles connecting two phasesBubbles connecting two phases
AsideAside
Why can we treat this as bubble Why can we treat this as bubble nucleation in four dimensions nucleation in four dimensions
when truly a five-dimensional set-up?when truly a five-dimensional set-up? Low energies: radion dominates potential, Low energies: radion dominates potential,
need vneed v11 small, radion light small, radion light High energies: holographyHigh energies: holography
(M/k)(M/k)33~N~N22/16/1622, need N large, need N large
GRAVITY WAVES GRAVITY WAVES FROM 1FROM 1STST ORDER ORDER PHASE PHASE TRANSITIONS: RS1TRANSITIONS: RS1
Gravity waves from 1Gravity waves from 1stst order Phase order Phase TransitionTransition
Two sources of gravitational waves:Two sources of gravitational waves:Bubble collision and TurbulenceBubble collision and TurbulenceDepends on two parameters (when strong)Depends on two parameters (when strong) : ratio of latent heat to radiation density at : ratio of latent heat to radiation density at nucleation temperaturenucleation temperatureNeed Need 0.20.2 : : Need transition to be slow enough for signalNeed transition to be slow enough for signalExpect of order ln(MExpect of order ln(MPP/T*) due to nucleation /T*) due to nucleation condition (exponentially suppressed)condition (exponentially suppressed)So about right orderSo about right order
Signal function of Signal function of
SIGNAL AS FUNCTION OF SIGNAL AS FUNCTION OF NUCLEATION TEMPNUCLEATION TEMP
Particular ModelParticular Model
ReachReach
LISA SensitivityLISA Sensitivity
But Perturbativity ConstraintsBut Perturbativity Constraints
Phase transition only completes in Phase transition only completes in borderline perturbative regionborderline perturbative region
k largish (need k/Mk largish (need k/M55<1)<1)
largish (more a problem for GW)largish (more a problem for GW)
vv11~N~N
TT11 often big often big
Nucleation temperature not too lowNucleation temperature not too lowWe investigate We investigate TT< L< L33 k k22
Constraints: Constraints: >0>0
Constraints: Constraints: <0<0
CommentsComments
Truly borderlineTruly borderline
Could be better or worseCould be better or worse
Plus:Plus:
De Wolfe, Freedman, Karch have shown De Wolfe, Freedman, Karch have shown RS can work with sizable back reactionRS can work with sizable back reaction
And sizable vev for GW field: Kofman et alAnd sizable vev for GW field: Kofman et al
Nonetheless need to take results with Nonetheless need to take results with some cautionsome caution
ConclusionsConclusions
First order phase transition for RS1First order phase transition for RS1Introduces constraints—cannot have very small Introduces constraints—cannot have very small AdS curvatureAdS curvatureBut in region where transition can take placeBut in region where transition can take placeStrong gravity wave signalStrong gravity wave signalTwo peak structure—Two peak structure— Or change in slopeOr change in slopeGravity waves new way of exploring weak scale Gravity waves new way of exploring weak scale physicsphysicsWorth investigating furtherWorth investigating further
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