Gravitational waves from the sound of a first-order phase transition With M. Hindmarsh, K. Rummukainen, D. Weir arXiv:1304.2433 Stephan Huber, University of Sussex PLANCK 2013 Bonn, May 2013

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

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??

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 ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●

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

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)

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

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

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

Envelope approximation 6 model T. Konstandin, S.H. ‘08 GW ~ f-1.8  GW ~ f-1 Does the envelope approximation also hold in the presence of a fluid? (related to small bubbles)

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?

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

(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)

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

detonation deflagration

10243 Lattice Fluid energy

GW production No real difference between detonations and deflagrations

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

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

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?

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