Cosmological Energy Budget of Cosmological First Order Phase - - PowerPoint PPT Presentation
Energy Budget of Cosmological Energy Budget of Cosmological First Order Phase Transitions First Order Phase Transitions Jose Miguel No Jose Miguel No King's College London King's College London Making the EW Phase Transition
Jose Miguel No Jose Miguel No King's College London King's College London
Making the EW Phase Transition (Theoretically) Strong Making the EW Phase Transition (Theoretically) Strong
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Nucleation & Growth of Bubbles
Could be Detected by LISA
Electroweak Electroweak Phase Transition Phase Transition
Bubble Expansion & Interaction
Bubble Collisions & (anisotropic) Plasma Motions Produce Stochastic Gravitational Wave Signature
Large Interferometer Space Antenna Courtesy of David Weir
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= 0 = v
Bubble Wall
V+ T+ V- T- = 0 = v
Close to Phase Boundary Far from Phase Boundary
Energy-Momentum Conservation
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matching Across Bubble wall matching Across Bubble wall
Bubble Wall
V+ T+ V- T- = 0 = v
Wall Reference Frame
Perfect Fluid
Energy-Momentum Conservation Across Bubble Wall Steady State Bubble Expansion
Simple Ansatz for Fluid E.O.S.
(Bag E.O.S.)
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matching Across Bubble wall matching Across Bubble wall
V+ T+ V- T- = 0
Wall Reference Frame
Bubble Wall
Only if
Two Branches of Solutions
= v
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Fluid Motion Fluid Motion
Self-Similar Ansatz
Fluid MOTION Fluid TEMPERATURE = 0.577... Plasma Speed of Sound
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Fluid Motion Fluid Motion
Self-Similar Ansatz
Fluid MOTION Fluid TEMPERATURE
Fluid Velocity Eq. Matching Conditions on Bubble Wall
Solutions Solutions for
for Fluid Motion
Fluid Motion
”Bubble Expansion Modes”
Boundary conditions
= 0.577... Plasma Speed of Sound
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Fluid Motion Fluid Motion
Inspecting Inspecting
Is Single – Valued Function
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DEtonations DEtonations DEflagrations DEflagrations hybrids hybrids
Supersonic Fluid at Rest in Front of Wall Rarefaction Wave Behind Wall Subsonic Fluid at Rest Behind Wall Compression Wave in Front of Wall Supersonic Both Compression & Rarefaction Waves Ends in a Shock Front
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Deflagrations Deflagrations hybrids hybrids detonations detonations
= cte
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DEflagrations DEflagrations
Slow Moving Bubbles
Good for Baryogenesis
Fast Moving Bubbles
DEtonations DEtonations
Bad(?) for Baryogenesis
Local Symmetry Restoration
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Bubbles Expanding in Vacuum Bubbles Expanding in Thermal Plasma
Energy Liberated During the Phase Transition Acts as Source of Gravitational Waves Perfect Conversion of Liberated Energy into Kinetic Energy NOT Perfect Conversion of Liberated Energy into Kinetic Energy Efficiency Factor
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Bubbles Expanding in Vacuum Bubbles Expanding in Thermal Plasma
Energy Liberated During the Phase Transition Acts as Source of Gravitational Waves Perfect Conversion of Liberated Energy into Kinetic Energy NOT Perfect Conversion of Liberated Energy into Kinetic Energy Efficiency Factor
Depends on TN , vW , α
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Controls Energy Budget
Energy not transformed into plasma bulk motion ( 1- ) used to increase plasma thermal energy
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Controls Energy Budget
Energy not transformed into plasma bulk motion ( 1- ) used to increase plasma thermal energy
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e.g. Sound Waves as GW Source e.g. Sound Waves as GW Source
Gravitational Wave Amplitude Depends Quadratically on
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e.g. Sound Waves as GW Source e.g. Sound Waves as GW Source
Gravitational Wave Amplitude Depends Quadratically on
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e.g. Sound Waves as GW Source e.g. Sound Waves as GW Source
Gravitational Wave Amplitude Depends Quadratically on
Bubble Expansion Solutions
P . J. Steinhardt, Phys. Rev. D 25 (1982) 2074
, Phys. Rev. D 49 (1994) 2837
Efficiency Coefficients Energy Budget –
Implications for Baryogenesis
Courtesy of D. Weir (Stavanger) Courtesy of D. Weir (Stavanger)
GW Bubble soUrces GW Bubble soUrces Sound Waves Sound Waves
Hindmarsh, Huber, Rummukainen, Weir, Phys. Rev. Lett 112 (2014) 041301
Turbulence Turbulence
Caprini, Durrer, Servant, JCAP 0912 (2009) 024
The Next/Future step The Next/Future step Gravitational Wave Astronomy in Space
Large Interferometer Space Antenna
(success of eLISA Pathfinder) (success of eLISA Pathfinder)
2-5 2-5 3 3rd
rd Arm
Arm As of Sept. 2016
LISA LISA Sensitivity to BSM Sensitivity to BSM
for the (e) for the (e)
LISA Cosmology Working Group
LISA Cosmology Working Group
Caprini et al, JCAP 1604 (2016) 001