1. Gravitational Waves from Warped Extra-Dimensional Geometry LR (with Geraldine Servant)

2. LISA 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

3. Which Weak Scale Physics? Strong first order phase transitions Example: transition to RS1 phase RS1: 2 brane model with five-dimensional bulk warped geometry

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

5. REVIEW REVIEW

6. Traditional route to extra dimensions

7. Changed in 1990’s: Branes

8. 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

9. Standard Model of Particle Physics Rests on Unstable Foundation Standard Model of Particle Physics Rests on Unstable Foundation Barnett Newman: Broken Obelisk

10. 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

11. RS1 Warped Spacetime Geometry to address hierarchy problem Two branes Gravity concentrated on Gravitybrane But we live on a second brane: The Weakbrane

12. ds 2 =dr 2 +e -kr (dx  dx    Small probability for graviton to be near the Weakbrane If we live anywhere but the Gravitybrane, gravity is naturally weak in warped geometry Natural for gravity to be weak

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

14. Particles in bulk: rescaled masses Planck 10 6 TeV 1000 TeV TeV

15. TeV physics Testable: KK modes TeV physics Testable: KK modes Kaluza-Klein particles Definite mass spectrum and “spin”-2

16. collider signals would be dramatically different H. Davoudiasl, J. Hewett, T. Rizzo

17. Collider signals could be spectacular Can we probe in other ways? (And conceivably higher energy scales?) Alternatively…Gravitational Waves!

18. COSMOLOGY OF RS1 COSMOLOGY OF RS1

19. 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

20. AdS-Schwarschild horizon Weak scale

21. High Temperature phase

22. 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

23. 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

24. RS1/GW potential Radion minimization: With an additional brane term:  ~m 2 /4k 2

25. 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

26. 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 Turns out strongly first order phase transition

27. Bubbles connecting two phases

28. Aside Why can we treat this as bubble 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 v 1 small, radion light need v 1 small, radion light High energies: holography High energies: holography (M/k) 3 ~N 2 /16  2, need N large (M/k) 3 ~N 2 /16  2, need N large

29. GRAVITY WAVES FROM 1 ST ORDER PHASE TRANSITIONS: RS1

30. Gravity waves from 1 st order Phase Transition Two sources of gravitational waves: Bubble collision and Turbulence Depends on two parameters (when strong)  : ratio of latent heat to radiation density at nucleation temperature  : ratio of latent heat to radiation density at nucleation temperature Need  0.2  :  : Need transition to be slow enough for signal Expect of order ln(M P /T*) due to nucleation condition (exponentially suppressed) So about right order

31. Signal function of 

33. SIGNAL AS FUNCTION OF NUCLEATION TEMP

34. Particular Model

35. Reach

36. LISA Sensitivity

37. But Perturbativity Constraints Phase transition only completes in borderline perturbative region k largish (need k/M 5 <1)  largish (more a problem for GW) v 1 ~N  T 1 often big  T 1 often big Nucleation temperature not too low We investigate  T  < L 3 k 2

38. Constraints:  >0

39. Constraints:  <0

40. 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

41. 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 Or change in slope Gravity waves new way of exploring weak scale physics Worth investigating further