1. Paul Stankus Oak Ridge RHIC/AGS Users’ Meeting June 20, 05 Hitchiker’s Guide: QGP in the Early Universe Paul Stankus Oak Ridge Nat’l Lab APS 06 April Meeting

2. Contents Big Bang Basic Framework Nuclear Particles in the Early Universe; Limiting Temperature? Thermal Quarks and Gluons; Experimental Evidence If I can understand it, so can you!

3. Henrietta Leavitt American Distances via variable stars Edwin Hubble American Galaxies outside Milky Way The original Hubble Diagram “A Relation Between Distance and Radial Velocity Among Extra- Galactic Nebulae” E.Hubble (1929)

4. US Now Slightly Earlier As seen from our position:As seen from another position: Recessional velocity  distance Same pattern seen by all observers!

5. Original Hubble diagram Freedman, et al. Astrophys. J. 553, 47 (2001) 1929: H 0 ~500 km/sec/Mpc 2001: H 0 = 72  7 km/sec/Mpc Photons t x Us Galaxies ? v Recession = H 0 d 1/H 0 ~ 10 10 year ~ Age of the Universe? 1/H 0 W. Freedman Canadian Modern Hubble constant (2001)

6. H.P. Robertson American A.G. Walker British W. de Sitter Dutch Albert Einstein German A. Friedmann Russian G. LeMaitre Belgian Formalized most general form of isotropic and homogeneous universe in GR “Robertson-Walker metric” (1935-6) General Theory of Relativity (1915); Static, closed universe (1917) Vacuum-energy- filled universes “de Sitter space” (1917) Evolution of homogeneous, non- static (expanding) universes “Friedmann models” (1922, 1927)

7. Robertson-Walker Metric H. Minkowski German “Henceforth space by itself, and time by itself, are doomed to fade away into mere shadows, and only a kind of union of the two will preserve an independent reality" (1907) Minkowski Metric

8. t  t1t1 t2t2 Photons Us Galaxies at rest in the “Hubble flow” t t=now  Galaxies Photons Hubble Constant A photon’s period grows  a(t) Its coordinate wavelength  is constant; its physical wavelength a(t)  grows  a(t) (t 2 )/ (t 1 ) = a(t 2 )/a(t 1 )  1+z Cosmological Red Shift Robertson-Walker Coordinates

9. w=P/w=P/ -1/3 +1/3 a(t)  e Ht a(t)  t 1/2 a(t)  t 2/3 t now acc dec Inflation, dominated by “inflaton field” vacuum energy Radiation-dominated thermal equilibrium Matter-dominated, non-uniformities grow (structure) Acceleration in a(t), domination by cosmological constant and/or vacuum energy. a(t) depends on pressure/energy: The New Standard Cosmology in Four Easy Steps

10. Basic Thermodynamics Sudden expansion, fluid fills empty space without loss of energy. dE = 0 PdV > 0 therefore dS > 0 Gradual expansion (equilibrium maintained), fluid loses energy through PdV work. dE = -PdV therefore dS = 0 Isentropic Adiabatic Hot Cool

11. Golden Rule 1: Entropy per co-moving volume is conserved Golden Rule 3: All chemical potentials are negligible Golden Rule 2: All entropy is in relativistic species Expansion covers many decades in T, so typically either T>>m (relativistic) or T<<m (frozen out) Golden Rule 4:

12. g *S 1 Billion o K 1 Trillion o K Start with light particles, no strong nuclear force

13. g *S 1 Billion o K 1 Trillion o K Previous Plot Now add hadrons = feel strong nuclear force

14. g *S 1 Billion o K 1 Trillion o K Previous Plots Keep adding more hadrons….

15. How many hadrons? Density of hadron mass states dN/dM increases exponentially with mass. Prior to the 1970’s this was explained in several ways theoretically Statistical Bootstrap Hadrons made of hadrons made of hadrons… Regge Trajectories Stretchy rotators, first string theory Broniowski, et.al. 2004 T H ~ 2  10 12 o K

16. Rolf Hagedorn German Hadron bootstrap model and limiting temperature (1965) Ordinary statistical mechanics: For thermal hadron gas (crudely set E i =M i ): Energy diverges as T --> T H Maximum achievable temperature? “…a veil, obscuring our view of the very beginning.” Steven Weinberg, The First Three Minutes (1977)

17. Karsch, Redlich, Tawfik, Eur.Phys.J.C29:549-556,2003  /T 4  g *S D. Gross H.D. Politzer F. Wilczek American QCD Asymptotic Freedom (1973) “In 1972 the early universe seemed hopelessly opaque…conditions of ultrahigh temperatures…produce a theoretically intractable mess. But asymptotic freedom renders ultrahigh temperatures friendly…” Frank Wilczek, Nobel Lecture (RMP 05) QCD to the rescue! Replace Hadrons (messy and numerous) by Quarks and Gluons (simple and few) Hadron gas Thermal QCD ”QGP” (Lattice)

18. Kolb & Turner, “The Early Universe” QCD Transition e + e - Annihilation Nucleosynthesis Decoupling Mesons freeze out Heavy quarks and bosons freeze out “Before [QCD] we could not go back further than 200,000 years after the Big Bang. Today…since QCD simplifies at high energy, we can extrapolate to very early times when nucleons melted…to form a quark-gluon plasma.” David Gross, Nobel Lecture (RMP 05) Thermal QCD -- i.e. quarks and gluons -- makes the very early universe tractable; but where is the experimental proof? g *S

19. National Research Council Report (2003) Eleven Science Questions for the New Century Question 8 is:

20. Also: BNL-AGS, CERN-SPS, CERN-LHC BNL-RHIC Facility

21. Low High Low High Density, Pressure Pressure Gradient Initial (10 -24 sec) Thermalized Medium Early Later Fast Slow Elliptic momentum anisotropy

22. PHENIX Data Fluid dynamics predicts momentum anisotropy correctly for 99% of particles produced in Au+Au Strong self-re-interaction Early thermalization (10 -24 sec) Low dissipation (viscosity) Equation of state P/  similar to relativistic gas What does it mean?

23. Beam energy High acceleration requires high P/  pressure/energy density. Hagedorn picture would be softer since massive hadrons are non-relativistic. Increase/saturate with higher energy densities. In Hagedorn picture pressure decreases with density. Momentum anisotropy increases as we increase beam energy & energy density What does it mean?

24. Thermal photon radiation from quarks and gluons? T i > 500 MeV Direct photons from nuclear collisions suggest initial temperatures > T H

25. 1. B violation 2. C,CP violation 3. Out of equilibrium Sakharov criteria for baryogenesis Most of the early universe is QCD! Dissipation could be relevant here: Mean Free Path ~ de Broglie Quantum Limit! “Perfect Fluid” Ideal gas  Ideal fluid Long mfpShort mfp High dissipationLow dissipation Data imply (D. Teaney, D. Molnar):

26. Conclusions The early universe is straightforward to describe, given simplifying assumptions of isotropy, homogeneity, and thermal equilibrium. Strong interaction/hadron physics made it hard to understand T > 100 MeV ~ 10 12 K. Transition to thermal QCD makes high temperatures tractable theoretically; but we are only now delivering on a 30-year-old promise to test it experimentally.

27. References Freedman & Turner, “Measuring and understanding the universe”, Rev Mod Phys 75, 1433 (2003) Kolb & Turner, The Early Universe, Westview (1990) Dodelson, Modern Cosmology, Academic Press (2003) Weinberg, Gravitation and Cosmology, Wiley (1972) Weinberg, The First Three Minutes, Basic (1977, 1993) Schutz, A First Course in General Relativity, Cambridge (1985) Misner, Thorne, Wheeler, Gravitation, W.H.Freeman (1973)

28. Backup material

29. Side-to-beam view Along-the-beam view Hot Zone Au+Au at √s NN = 200 GeV STAR Experiment at RHIC

30. Complete coordinate freedom! All physics is in g  (x 0,x 1,x 2,x 3 ) H. Minkowski German “Henceforth space by itself, and time by itself, are doomed to fade away into mere shadows, and only a kind of union of the two will preserve an independent reality" (1907) x t t’ x’ Photons E1E1 E1E1 E2E2 E2E2 E0E0 E0E0 B. Riemann German Formalized non- Euclidean geometry (1854)

31. a(t)  a Friedmann-Robertson-Walker (FRW) cosmology Three basic solutions for a(t): 1. Relativistic gas, “radiation dominated” P/  = 1/3  a -4 a(t)  t 1/2 2. Non-relativistic gas, “matter dominated” P/  = 0  a -3 a(t)  t 2/3 3. “Cosmological-constant-dominated” or “vacuum-energy-dominated” P/  = -1  constant a(t)  e Ht “de Sitter space”

32. Energy density (in local rest frame) Curvature Q: How does  change during expansion? Friedmann Equation 1 (  =0 version)

33. Friedmann Equation 2 (Isen/Iso-tropic fluid,  =0) However, this cannot describe a static, non-empty FRW Universe. Ac/De-celeration of the Universe’s expansion Necessity of a Big Bang!

34. Over- B. Riemann German Formalized non- Euclidean geometry (1854) G. Ricci- Curbastro Italian Tensor calculus (1888)

35. With freedom to choose r 0 2 and , we can arrange to have a’=a’’=0 universe with finite matter density Einstein 1917 “Einstein Closed, Static Universe”  disregarded after Hubble expansion discovered - but - “vacuum energy” acts just like  Friedmann 1 and 2:

36. Re-introduce “cosmological constant”  Generalize  (t)=  Matter (t) +  /8  P(t)=P Matter (t) -  /8  Cosmological constant acts like constant energy density, constant negative pressure, with EOS P/  = -1

37. T(t)T(t) a(t)a(t) (t)(t) t How do we relate T to a,  ? i.e. thermodynamics

39. The QCD quark-hadron transition is typically ignored by cosmologists as uninteresting Weinberg (1972): Considers Hagedorn-style limiting- temperature model, leads to a(t)  t 2/3 |lnt| 1/2 ; but concludes “…the present contents…depends only on the entropy per baryon…. In order to learn something about the behavior of the universe before the temperature dropped below 10 12o K we need to look for fossils [relics]….” Kolb & Turner (1990): “While we will not discuss the quark/hadron transition, the details and the nature (1st order, 2nd order, etc.) of this transition are of some cosmological interest, as local inhomogeneities in the baryon number density could possible affect…primordial nucleosythesis…”

40. Weinberg, Gravitation and Cosmology, Wiley 1972 Golden Rule 5: Equilibrium is boring! Would you like to live in thermal equilibrium at 2.75 o K? Example of e + e - annihilation transferring entropy to photons, after neutrinos have already decoupled (relics).