1. Gravitational waves from the sound of a first-order phase transition
With M. Hindmarsh, K. Rummukainen, D. Weir arXiv:
Stephan Huber, University of Sussex
PLANCK 2013
Bonn, May 2013

2. Outline ● introduction ● pure scalar field: envelope approximation
● scalar + fluid: full numerical simulations
● Gravitational wave production: dominated by sound waves
● Summary & outlook

3. We are surrounded by a constant Higgs field
This field was not present at high temperatures in the early universe
How did it come about?
Are there observable relics?
Gravitational waves?
Primordial magnetic fields?
Baryon asymmetry?
First order electroweak phase transition
Other first oder phase transitions??

4. Bubbles H(z) vw broken phase symmetric phase ● ● ● ● ● ● ● ● ● ● ● ● ●
temperature Tc
vev in the broken phase vc
vc/Tc>1?
wall width Lw
wall velocity vw ● ● ● ● ● vw ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●

5. The strength of the PT Thermal potential: ● Boson loops:
SM: gauge bosons
strong PT: mh<40 GeV (no top)
never (with realistic top mass)
Lattice: crossover for mh>80 GeV → the SM has NO phase transition
Kajantie, Laine, Rummukainen, Shaposhnikov 1996
Csikor, Fodor, Heitger 1998

6. The strength of the PT Thermal potential: ● Boson loops:
SM: gauge bosons
SUSY: light stops
2HDM: extra Higgses
● tree-level: extra singlets: λSH2, NMSSM, etc.
● replace H4 by H6, etc.
● other phase transitions (not electroweak)

7. GW’s are a unique window to the early cosmos
Gravitational waves
LISA / eLISA
GW’s are a unique window to the early cosmos
sources of GW‘s: direct bubble collisions
turbulence
magnetic fields
sound waves
key parameters: available energy
typical bubble radius
vb wall velocity
Grojean, Servant ‘06

8. How to compute the GW spectrum:
We model the universe as a scalar plus perfect fluid
Eqn. for the metric perturbations:
need to project onto the transverse traceless part: hij
power in GW’s per logarithmic frequency interval:
resulting spectrum has to redshifted to the present time

9. The envelope approximation: Kosowsky, Turner 1993
Energy momentum tensor of expanding
bubbles modelled by expanding infinitely
thin shells,
cutting out the overlap
 very non-linear!
Tested by colliding two pure scalar bubbles
Recent scalar field theory simulation:
Child, Giblin 2012

10. Envelope approximation
6 model
T. Konstandin, S.H. ‘08
GW ~ f  GW ~ f-1
Does the envelope approximation also hold in the presence of a fluid?
(related to small bubbles)

11. Including the fluid: Turbulence? (Reynolds number is huge)
How to model turbulence?
Different groups used different assumptions on velocity correcations
Turbulence: Kosowsky, Mack, Kahniashvili ’01
Dolgov, Grasso, Nicolis ’02
Turbulence: Caprini, Dürrer ’06
Collisions: Kamionkovski, Kosowsky, Turner ‘93
strong PT: α~1, but radius gets larger (fewer bubbles, growing larger)
→ stronger signal, but at smaller f !!
discrepancy between Dol. and CD!
double peak structure?

12. To arrive at a reliable GW spectrum
Numerical simulation
To arrive at a reliable GW spectrum

13. (Thermal scalar potential)
We performed the first 3d simulation of a scalar + relativistic fluid system:
(Thermal scalar potential)
(Scalar eqn. of motion)
(eqn. for the energy density)
(eqn. for the momentum density)
(eqn. for the metric perturbations)

14. Types of single bubble solutions:
Espinosa, Konstandin, No, Servant‘10
Efficiency coefficients: how much energy goes to the fluid motion (not into heat)
Scalar energy is irrelevant

15. detonation
deflagration

16. 10243
Lattice
Fluid energy

17. GW production
No real difference between detonations and deflagrations

18. GW Spectrum Transverse and longitudinal part of the fluid stress
Logitudinal part dominates  Basically sound waves

19. Strength of the GW signal:
simulation
env. appr.
Enhancement by
What sets τs ? Hubble time?

20. Summary ► gravitational waves are unique window to the early cosmos
► first order phase transition generate a GW signal which is potentially observable (EWPT, mHz peak, eLISA?)
► first 3d numerical simulation of scalar + fluid
GW production by sound waves
no sign of turbulence
► outlook: reliable predication for the peak power and shape
what replaces the envelope approximation?
can one distinguish a thermal from a non-thermal transition via GW’s?

21. SM + higher-dim. operators
Zhang ‘93
Grojean et al. ‘04
maybe related to strong dynamics at the TeV scale, such as technicolor or gravity?
(or simply comes from integrating out extra scalars)
two parameters, (λ, M ) ↔ (mh, M)
λ can be negative → bump because of |H|4 and |H|6