Transcript Gravitational Waves from Warped Extra

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
Which Weak Scale Physics?
Strong first order phase transitions
Example: transition to RS1 phase
RS1: 2 brane model with five-dimensional
bulk warped geometry
Plan
Review Warped Geometry as solution to
hierarchy problem
Cosmology of Warped Geometry
Gravity Waves from 1st Order Phase
Transitions
Put it all together
REVIEW
Traditional route to extra
dimensions
Changed in 1990’s: Branes
With branes, we’ve found:
New way to hide dimensions
New concept of our place in the
universe
New way to explain weakness of gravity
Standard Model of Particle Physics
Rests on Unstable Foundation
Barnett Newman: Broken Obelisk
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
RS1 Warped Spacetime Geometry
to address hierarchy problem
•Two branes
•Gravity concentrated on
Gravitybrane
•But we live on a second
brane:
•The Weakbrane
Natural for gravity to be weak
ds2=dr2+e-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
Everything rescaled in warped
geometry!
Can understand
weakness of gravity as
things being bigger
and lighter on the
Weakbrane
Particles in bulk: rescaled masses
Planck
106 TeV
1000 TeV
TeV
TeV physics Testable: KK modes
Kaluza-Klein
particles
Definite mass
spectrum and
“spin”-2
collider signals would be dramatically different
H. Davoudiasl, J. Hewett, T. Rizzo
Collider signals could be spectacular
Can we probe in other ways?
(And conceivably higher energy scales?)
Alternatively…Gravitational Waves!
COSMOLOGY OF
RS1
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
AdS-Schwarschild
horizon
Weak
scale
High Temperature phase
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
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 situation—hierarchy with no very large
parameter
Mass squared determines hierarchy
RS1/GW potential
Radion minimization:
•With an additional brane term:
e~m2/4k2
What happens?
At critical temperature, RS phase is favored
Below this temperature expect a first order phase
transition
Radion starts at m=0 and evolves to m=mTeV
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
Bubbles connecting two phases
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)3~N2/16p2, need N large
GRAVITY WAVES
ST
FROM 1 ORDER
PHASE
TRANSITIONS: RS1
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 a>0.2
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
Signal function of a, b
SIGNAL AS FUNCTION OF
NUCLEATION TEMP
Particular Model
Reach
LISA Sensitivity
But Perturbativity Constraints
Phase transition only completes in
borderline perturbative region
k largish (need k/M5<1)
e largish (more a problem for GW)
v1~N
dT1 often big
Nucleation temperature not too low
We investigate dTmn< L3 k2
Constraints: e>0
Constraints: e<0
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
Conclusions
First order phase transition for RS1
Introduces constraints—cannot 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