A field theoretical model for the QCD phase transition in the early universe

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1 A field theoretical model for the QCD phase transition in the early universe Rainer Stiele Institute for Theoretical Physics Heidelberg University International School on QGP and HIC : past, present, future Villa Gualino, Torino, Italy 7-12 March, 2011

2 A field theoretical model for the QCD phase transition in the early universe Rainer Stiele Institute for Theoretical Physics Heidelberg University In collaboration with Tillmann Boeckel, Simon Schettler, Jürgen Schaffner-Bielich Lisa Haas, Jan Pawlowski

3 The QCD phase transition in the early universe GSI, QCD in the early universe 1

4 The QCD phase transition in the early universe GSI, QCD in the early universe 1

5 Outline 1 Motivation 2 HICs vs. early universe: differences & similarities 3 Polyakov-loop-extended Quark-Meson model 4 Finite Isospin 5 Lepton Asymmetry 6 The Little Inflation scenario 7 Conclusions QCD in the early universe 2

6 Motivation Some microseconds after the Big Bang, the quarks and gluons were free and formed some kind of soup......a plasma of quarks and gluons Only afterwards they sticked together to form the matter. The physicists and myself we would like to know why and how these particles sticked together. La BD du LHC, QCD in the early universe 3

7 Motivation QCD in the early universe 4

8 Motivation NASA / WMAP Science Team, QCD in the early universe 5

9 HICs vs. early universe: differences & similarities Time scales time scale of strong interactions: s 1 fm /c Heavy Ion Colisions expansion time: s non-equilibrium effects Early Universe age of the universe 10 5 s local thermal equilibrium Heavy Ion Colisions Strongly interacting liquid Color glass condensate Early Universe Weakly interacting QGP radiation dominated fluid, slowly cooling by adiabatic expansion QCD in the early universe 6

10 Polyakov-loop-extended Quark-Meson model Grand canonical potential Ω = U (σ x, σ y ) + U ( Φ, Φ ) + Ω qq ( Φ, Φ, σx, σ y ) Mesonic Potential Chiral Symmetry Linear σ model Fit of meson phenomenology Polyakov-loop Potential (De)Confinement Fit to pure gauge thermodynamics Quark/antiquark, fermionic contribution Equations of motion order parameters Ω σ x = Ω σ y = Ω Φ = Ω Φ σ x= σ x,σ y= σ y,φ= Φ, Φ= Φ = 0 QCD in the early universe 7

11 Polyakov-loop-extended Quark-Meson model Order parameters & Phase Diagram 2 flavor 2+1 flavor QCD in the early universe 8

12 Polyakov-loop-extended Quark-Meson model Finite Isospin µ q = µ u + µ d 2 = µ B 3, µ I = µ u µ d = µ iso 2 2 QCD in the early universe 9

13 Polyakov-loop-extended Quark-Meson model Lepton Asymmetry l n l n l n γ n l n l s µ l + µ l T l, l 0.02 Stuke & Schwarz 2009, JCAP 11 µ I = 0, w/o leptons QCD in the early universe 10

14 Polyakov-loop-extended Quark-Meson model Lepton Asymmetry l nl n l n γ nl n l s µl + µ l T l, l 0.02 Phase diagram at finite lepton asymmetry: n C = 0 n e = n B/2 n νe = (1/2 + l/b) n B µ B = 3µ q µe 1 2 µνe Stuke & Schwarz 2009, JCAP 11 QCD in the early universe 10

15 The Little Inflation scenario Evolution path of the universe Boeckel & Schaffner-Bielich 2010, Phys. Rev. Lett. 105 QCD in the early universe 11

16 The Little Inflation scenario Cosmological consequences Bubble collision & turbulence gravitational waves Charged bubble collisions seeds of (extra)galactic magnetic fields Density and pressure structure formation Dilute dark matter density lower annihilation cross section Schettler, Boeckel & Schaffner-Bielich, 2010 arxiv , PRD in press QCD in the early universe 12

17 Summary HICs vs. early universe: isospin, leptons Include isospin & leptons to PQM in order to describe early universe Little Inflation scenario: 1st order QCD phase transition in early universe. Gravitaional waves, magnetic fields, power spectrum of density fluctuations, dark matter annihilation cross section Outlook: Include trace anomaly by dilatons Improvement of Polyakov-loop Potential by RG and lattice calculations In collaboration with Tillmann Boeckel, Simon Schettler, Jürgen Schaffner-Bielich, Lisa Haas, Jan Pawlowski QCD in the early universe 13

18 Thank You for Your attention! HICs vs. early universe: isospin, leptons Include isospin & leptons to PQM in order to describe early universe Little Inflation scenario: 1st order QCD phase transition in early universe. Gravitaional waves, magnetic fields, power spectrum of density fluctuations, dark matter annihilation cross section Outlook: Include trace anomaly by dilatons Improvement of Polyakov-loop Potential by RG and lattice calculations In collaboration with Tillmann Boeckel, Simon Schettler, Jürgen Schaffner-Bielich, Lisa Haas, Jan Pawlowski QCD in the early universe 13