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