Cosmological 1st Order Phase Transitions: Bubble Growth & Energy Budget

Transcription

1 Cosmological 1st Order Phase Transitions: Bubble Growth & Energy Budget Jose Miguel No (IPhT CEA Saclay) ULB, Brussels, January 28th 2011

2 Outline Introduction to 1st Order Phase Transitions: Bubble Nucleation & Growth in a Nutshell. Associated Cosmological Phenomena. Relevant Quantities. Formalism: Studying Bubble Growth: Matching Equations Across the Bubble Wall. Fluid Equations for the Plasma. + = Fluid Solutions. Distributing the Energy: ➍ Efficiency Coefficients. Fixing the Wall Velocity: Higgs Equation of Motion. Applications: ➏ Steady State vs Acceleration (Runaway). Energy Budget.

3 Why Bubbles? Phase Transitions in the Early Universe (i.e. Electroweak Phase Transition) 1st Order 2nd Order

4 Why Bubbles? Phase Transitions in the Early Universe (i.e. Electroweak Phase Transition) 1st Order 2nd Order If Phase Transition is 1st Order Nucleation of True Vacuum Bubbles in False Vacuum Sea

5 Bubble Nucleation & Growth in a Nutshell Nucleation: Small Bubbles Nucleating Constantly Due to Fluctuations When a Bubble Nucleates: EB = E + E = V de dr B < 0 S - 4 / 3 3 R R > RC + 4 R2 V S

6 Bubble Nucleation & Growth in a Nutshell Wall Growth: Why Does a Bubble Expand? p - -p + = V(0) - V( 0) > 0 =0 = 0 Net Pressure on Wall p + p - Net Force on Wall Fdr

7 Bubble Nucleation & Growth in a Nutshell Wall Growth: Why Does a Bubble Expand? p - -p + = V(0) - V( 0) > 0 Bubbles Expand in Plasma =0 Net Pressure on Wall = 0 p p + Net Force on Wall - Fdr Friction! Wall M=0 M 0 Particles Gain Mass When Crossing Wall Friction Force Particle Distributions f (p) a Away from Equilibrium Close to Wall Ffr Balances Fdr

8 Bubble Growth in Cosmological Phase Transitions Relevant for: Electroweak Baryogenesis. Production of a Stochastic Background of Gravitational Waves. Primordial Magnetic Fields. Etc...

9 Electroweak Baryogenesis: 1st Order Phase Transition Departure from Equilibrium (3rd Sakharov Condition) Suppresion of Sphaleron Rate in Broken Phase /T 1 < > bsph

10 Electroweak Baryogenesis: 1st Order Phase Transition Departure from Equilibrium (3rd Sakharov Condition) Suppresion of Sphaleron Rate in Broken Phase /T 1 < > Viable Baryogenesis: nb Generated by CP / Diffusion Ahead of Bubble Wall cs V < diff = D w (cs Speed of Sound in Plasma / (Vw)2 ssph ( diff )-1 s Sph ) ( diff ) ssph ( diff )-1-1 Suppressed nb V (few) 10 w Favoured -2 bsph

11 Stochastic Background of Gravitational Waves: Bubble Nucleation, Growth & Percolation.

12 Stochastic Background of Gravitational Waves: Bubble Nucleation, Growth & Percolation. Possible Gravitational Wave sources: Bubble Collisions: Turbulence in the Plasma. Magnetic Fields. Efficiency Coefficient for Converting GW ~ 2 GW ~ V 4 W Phase Transition Energy into Kinetic Energy for GW Detectable by LISA?

13 Summary of Relevant Quantities Phase Transition EW Baryogenesis: V Gravitational Wave Production: < > w V w /T Bubble Growth

14 Summary of Relevant Quantities Phase Transition EW Baryogenesis: V Gravitational Wave Production: < > w V w /T Bubble Growth STUDY of BUBBLE GROWTH in 1st ORDER PHASE TRANSITIONS P. J. Steinhardt, Phys. Rev. D 25 (1982) 2074 Study Plasma Behaviour (V w Use Friction to fix V. w Free Parameter).

15 Matching Equations Across the Bubble Wall. Combined system Higgs Wall - Plasma : Energy-Momentum Conserved Across Bubble Wall + Steady State (Wall Reference Frame)

16 Matching Equations Across the Bubble Wall. Combined system Higgs Wall - Plasma : Energy-Momentum Conserved Across Bubble Wall + Steady State (Wall Reference Frame) =0 V + T + Wall = 0 V - T - Bag Approximation:

17 With Detonations (+) Deflagrations (-) Only if

18 With Detonations (+) Deflagrations (-) Only if

19 Fluid Equations for the Plasma. Velocity Profile for the Plasma Energy-Momentum Conservation (Similarity Solution)

20 Fluid Equations for the Plasma. Velocity Profile for the Plasma Energy-Momentum Conservation (Similarity Solution)

21 Boundary Conditions V+, V- ( ) + Fluid Equations ( ) Fluid Solutions. Subsonic Deflagrations - w + Detonations V =V >V >c w + - w s. Fluid at Rest Behind Bubble Wall. Supersonic V s >V + + T =T + Both Compression and Rarefaction Wave. - T >T N. Fluid at Rest in Front of Bubble Wall. w Rarefaction Wave Behind Wall. Hybrids V >c =V w Compression Wave in Front of Wall. c >V =V >V s V N

22 Fluid Profiles

23 As Wall Velocity increases: ( N = cte) Deflagrations Evolve Into Hybrids Hybrids Evolve Into Detonations

24 ➍ Efficiency Coefficients. Gravitational Wave Production from Bubble Collisions Depends on:

25 ➍ Efficiency Coefficients. Gravitational Wave Production from Bubble Collisions Depends on: Vacuum Bubbles: Perfect Conversion of Available Energy into Kinetic Energy

26 ➍ Efficiency Coefficients. Gravitational Wave Production from Bubble Collisions Depends on: Vacuum Bubbles: Perfect Conversion of Available Energy into Kinetic Energy Bubbles in Plasma: Conversion of Available Energy into Kinetic Energy is NOT Perfect Efficiency Coefficient M. Kamionkowski, A. Kosowsky and M. S. Turner, Phys. Rev. D 49 (1994) 2837 Energy not Transformed into Kinetic Bulk Motion, Used to Increase Thermal Energy of Plasma

27 Previously, Chapman Jouguet Condition Assumed: V = c P. J. Steinhardt, Phys. Rev. D 25 (1982) 2074 Jouguet Detonations - s

28 Previously, Chapman Jouguet Condition Assumed: V = c - P. J. Steinhardt, Phys. Rev. D 25 (1982) 2074 s Jouguet Detonations M. Kamionkowski, A. Kosowsky and M. S. Turner, Phys. Rev. D 49 (1994) 2837

29 Previously, Chapman Jouguet Condition Assumed: V = c - P. J. Steinhardt, Phys. Rev. D 25 (1982) 2074 s Jouguet Detonations M. Kamionkowski, A. Kosowsky and M. S. Turner, Phys. Rev. D 49 (1994) 2837 However, Chapman Jouguet Condition { Chemical Combustion Cosmological Phase Transitions M. Laine, Phys. Rev. D 49 (1994) 3847

30 Previous Result ( ) Extended to the (, N w J. R. Espinosa, T. Konstandin, J. M. No and G. Servant, JCAP 1006:028 (2010) N) Plane.

31 Higgs Equation of Motion. (Needed to Fix w) G. D. Moore and T. Prokopec, Phys. Rev. D 52 (1995) J. Ignatius, K. Kajantie, H. Kurki-Suonio and M. Laine, Phys. Rev. D 49 (1994) So far, w is a Free Parameter Need to Determine it.

32 Higgs Equation of Motion. (Needed to Fix w) G. D. Moore and T. Prokopec, Phys. Rev. D 52 (1995) J. Ignatius, K. Kajantie, H. Kurki-Suonio and M. Laine, Phys. Rev. D 49 (1994) So far, w is a Free Parameter Need to Determine it. Higgs EoM:

33 Higgs Equation of Motion. (Needed to Fix w) G. D. Moore and T. Prokopec, Phys. Rev. D 52 (1995) J. Ignatius, K. Kajantie, H. Kurki-Suonio and M. Laine, Phys. Rev. D 49 (1994) So far, w is a Free Parameter Need to Determine it. Higgs EoM: Departure from Equilibrium of Particle Distributions close to the Wall Driving Force Friction Force

34 Higgs Equation of Motion. (Needed to Fix w) G. D. Moore and T. Prokopec, Phys. Rev. D 52 (1995) J. Ignatius, K. Kajantie, H. Kurki-Suonio and M. Laine, Phys. Rev. D 49 (1994) So far, w is a Free Parameter Need to Determine it. Higgs EoM: Departure from Equilibrium of Particle Distributions close to the Wall Driving Force Friction Force If Fdr = Ffr (Friction Balances Pressure) Steady State If Fdr > Ffr Acceleration

35 ➏ Steady State vs Acceleration (Runaway) I. Previously Believed: Ffr ~ w w lim True for w 1 w 1 (Ffr ~ Ffr = w w~ w) G. D. Moore and T. Prokopec, Phys. Rev. D 52 (1995)

36 ➏ Steady State vs Acceleration (Runaway) I. Previously Believed: Ffr ~ w w lim True for w 1 w 1 (Ffr ~ Ffr = w w~ w) G. D. Moore and T. Prokopec, Phys. Rev. D 52 (1995) However: w 1 Ffr Ffr max = cte D. Bodeker and G. D. Moore, JCAP 0905:009 (2009) If Fdr < Ffr max Steady State (Friction If Balances Pressure) Fdr > Ffr max Runaway Bubble Wall (Acceleration) w) (Up to Possible Log( Corrections)

37 Steady State vs Acceleration (Runaway) II. Phenomenological Approach: ~ Friction Higgs EoM (in Possible Runaway Behaviour Parameter (Calculable from Theory) Wall frame): J. R. Espinosa, T. Konstandin, J. M. No and G. Servant, JCAP 1006:028 (2010)

38 Steady State vs Acceleration (Runaway) III. W in the (, N) Plane (, w ) in the (, N) Plane N

39 Energy Budget. J. R. Espinosa, T. Konstandin, J. M. No and G. Servant, JCAP 1006:028 (2010) N < (, ) Plasma Bulk Motion 1 w w N (, ) Plasma Thermal Energy N

40 Energy Budget. J. R. Espinosa, T. Konstandin, J. M. No and G. Servant, JCAP 1006:028 (2010) N N < > (, ) Plasma Bulk Motion 1 w w N (, ) Plasma Thermal Energy N N Higgs Field (Wall Acceleration), with Plasma Bulk Motion + Thermal Energy, with =1

41 Bonus: Possible Hydrodynamic Obstruction. T. Konstandin and J. M. No, ArXiv: Steady State Solution Suppose Subsonic W Deflagration (T+ > TN) As Wall Moves, Reheats Plasma in Front (T+ > TN). As As T+ Raises, F W Increases, T+ Raises (T+ dr If Heating Effect Drives T Tc Decreases (F dr if if W ). T+ ). Average T on the Bubble Wall If Fdr 0 for W < cs Hydrodynamic Obstruction!!

42 Conclusions Efficiency coefficient ➋ Runaway Bubble Walls (, w N ) Obtained Energy Budget of Phase Transitions Energy Stored in the Higgs Field Qualitative Modification of the Energy Budget Possible Consequences for Gravitational Wave Spectrum (Turbulence) Possible Hydrodynamic Obstruction to Supersonic w Allows to Estimate Subsonic w Without Knowing Friction Favors Electroweak Baryogenesis Scenarios

43 Conclusions Efficiency coefficient ➋ Runaway Bubble Walls (, w N ) Obtained Energy Budget of Phase Transitions Energy Stored in the Higgs Field Qualitative Modification of the Energy Budget Possible Consequences for Gravitational Wave Spectrum (Turbulence) Possible Hydrodynamic Obstruction to Supersonic w Allows to Estimate Subsonic w Without Knowing Friction Favors Electroweak Baryogenesis Scenarios Thank You!