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Hitchhiker’s Guide to the Early Universe

Hitchhiker’s Guide to the Early Universe. Paul Stankus Oak Ridge RHIC/AGS Users’ Meeting June 20, 05. Contents Evidence for a Big Bang  Experimental  Theoretical  Basic Framework  A Smidgen of GR  Vacuum Energy and Inflation  Thermodynamics  Decoupling and Relics  The QGP Transition.

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Hitchhiker’s Guide to the Early Universe

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  1. Hitchhiker’s Guide to the Early Universe Paul Stankus Oak Ridge RHIC/AGS Users’ Meeting June 20, 05

  2. Contents Evidence for a Big Bang  Experimental  Theoretical  Basic Framework  A Smidgen of GR  Vacuum Energy and Inflation Thermodynamics  Decoupling and Relics  The QGP Transition If I can understand it, so can you!

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

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

  5. W. Freedman American t Us Freedman, et al. Astrophys. J. 553, 47 (2001) Galaxies Modern Hubble constant (2001) x Photons 1/H0 Original Hubble diagram ? vRecession = H0d 1929:H0 ~500 km/sec/Mpc 2001:H0 = 727 km/sec/Mpc 1/H0 ~ 1010 year ~ Age of the Universe?

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

  7. 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) Global Reference Frames Convenient Coordinate Systems E1 t E2 x E0 Photons E1 t’ E2 E0 Complete coordinate freedom! All physics is in gmn(x0,x1,x2,x3) x’ Photons

  8. Homogeneity = same at all points in space at some t = constant as seen by observers following dx = dy = dz = 0 Isotropy = same in all spatial directions as seen from any point (Convenient: want dt = dt, i.e., proper/subjective time, when dx = dy = dz = 0) Robertson-Walker Metric:

  9. t Us Galaxies at rest in the “Hubble flow” t=now Photons c t A photon’s period grows  a(t) Its coordinate wavelength Dc is constant; its physical wavelength a(t)Dc grows  a(t) Red shift! l(t2)/l(t1) = a(t2)/a(t1) 1+z t2 t1 c

  10. a(t)  a Friedmann-Robertson-Walker (FRW) cosmology Three basic solutions for a(t): • Relativistic gas, “radiation dominated” P/r = 1/3 ra-4a(t)t1/2 2. Non-relativistic gas, “matter dominated” P/r = 0 ra-3a(t)t2/3 3. “Cosmological-constant-dominated” or “vacuum-energy-dominated” P/r = -1 rconstant a(t)eHt“de Sitter space”

  11. Over- B. RiemannGerman G. Ricci-Curbastro Italian Formalized non-Euclidean geometry (1854) Tensor calculus (1888)

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

  13. Basic Thermodynamics Sudden expansion, fluid fills empty space without loss of energy. dE = 0 PdV > 0 thereforedS > 0 Gradual expansion (equilibrium maintained), fluid loses energy through PdV work. dE = -PdV thereforedS = 0 Isentropic

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

  15. Re-introduce “cosmological constant” L Generalizer(t)=rMatter(t)+L/8p P(t)=PMatter(t)-L/8p Cosmological constant acts like constant energy density, constant negative pressure, with EOS P/r = -1

  16. Friedmann 1 and 2: With freedom to choose r02 and L, we can arrange to have a’=a’’=0 universe with finite matter density Einstein 1917 “Einstein Closed, Static Universe” L disregarded after Hubble expansion discovered - but - “vacuum energy” acts just like L

  17. The New Standard Cosmology in Four Easy Steps Inflation, dominated by “inflaton field” vacuum energy Radiation-dominated thermal equilibrium Matter-dominated, non-uniformities grow (structure) Start of acceleration in a(t), return to domination by cosmological constant and/or vacuum energy. w=P/r +1/3 accdec t -1/3 -1 aeHt at1/2 at2/3 now

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

  19. Golden Rule 1: Entropy per co-moving volume is conserved Golden Rule 2: All chemical potentials are negligible Golden Rule 3: All entropy is in relativistic species Expansion covers many decades in T, so typically either T>>m (relativistic) or T<<m (frozen out) Kolb & Turner, The Early Universe, Westview 1990

  20. n Decoupling Nucleosynthesis e+e- Annihilation Golden Rule 4: Heavy quarks and bosons freeze out QCD Transition Mesons freeze out Kolb & Turner

  21. Golden Rule 5: Equilibrium is boring! Would you like to live in thermal equilibrium at 2.75oK? Example of e+e- annihilation transferring entropy to photons, after neutrinos have already decoupled (relics). That which survives: RelicsT>m butG>H (CMB photons, neutrinos, gravitons,dark matter?free quarks, magnetic monopoles…) RemnantsT<m butm≠0 (baryons g/B~1010, electrons, dark matter?) Weinberg, Gravitation and Cosmology, Wiley 1972

  22. The QCD quark-hadron transition is typically ignored by cosmologists as uninteresting Weinberg (1972): Considers Hagedorn-style limiting-temperature model, leads to a(t)t2/3|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 1012oK 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…”

  23. 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) Schutz, A First Course in General Relativity, Cambridge (1985) Misner, Thorne, Wheeler, Gravitation, W.H.Freeman (1973) Bartelmann & Schneider, “Weak Gravitational Lensing”, Physics Reports 340, 291-472 (2001)

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