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Dark Energy Cosmology

Dark Energy Cosmology. Robert Caldwell Dartmouth College. INPE Winter School September 12-16, 2005. Recap: First Cosmological models. Einstein. Why no  ? Why not?. Gell-Man’s Totalitarian Principle: “Anything which is not prohibited is compulsory”.

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Dark Energy Cosmology

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  1. Dark Energy Cosmology Robert Caldwell Dartmouth College INPE Winter School September 12-16, 2005

  2. Recap: First Cosmological models Einstein Why no ? Why not? Gell-Man’s Totalitarian Principle: “Anything which is not prohibited is compulsory” Challenge to Physics & Astronomy, Experiment & Theory Tighten the evidence for  / Dark Energy Discover the physics responsible for  / Dark Energy …

  3. Cosmic Acceleration observations of type 1a supernovae indicate our universe is accelerating RC, Physics World, May 2005 data: Riess et al, ApJ 607 (2004) 665

  4. Fluid Flow: Raychaudhuri Equation v = 4-velocity of test particles metric in subspace orthogonal to v vorticity expansion shear flow lines as determined by fluid, geometry

  5. Stress-Energy flux of -momentum across a -surface Relativistic Perfect Fluid Relativistic Imperfect Fluid Weinberg, Ch 2, 15 Shear viscosity and heat conduction are incompatible with the symmetries of an isotropic, homogeneous spacetime.

  6. Homogeneity and Isotropy Measurements of the Cosmic Microwave Background probe matter and energy on the largest scales How to measure the CMB at remote cosmological locations Kamionkowski & Loeb, PRD 56 (1997) 4511 CMB photons scatter off the ionized gas in clusters The anisotropy pattern of at the cluster is imprinted in the resulting polarized pattern Hogg et al, ApJ 624 (2005) 54 homogeneity using SDSS galaxies Castro et al, PRD 68 (2003) 127301 Grishchuck-Zeldovich test with WMAP Donoghue et al, PRD 71 (2005) 043002 early-time isotropy with WMAP Other:

  7. Homogeneity and Isotropy COBE magnitude ofl = i+1 multipole moment Stoeger, Maartens, Ellis (and permutations) ApJ 443 (1995) 1; PRD 51 (1995) 1525; A&A 309 (1996) L7. Bianchi VIIh template Tiny  anisotropies can produce ~10-5 temperature fluctuations Kogut et al, PRD 55 (1997)1901

  8. CMB Fluctuation Spectrum

  9. Homogeneity and Isotropy WMAP features due to anisotropic structure? Jaffe et al, ApJ 629 (2005) 1 North vs. South? extrema not very extreme Larson & Wandelt, ApJ 613 (2004) 85 Effect of local structure? Tomita, astro-ph/0505157 Vale, astro-ph/0509039

  10. Homogeneity and Isotropy Measurements of the Cosmic Microwave Background probe matter and energy on the largest scales Standard Procedure: • assume homogeneity & isotropy • allow weak perturbations • compare with CMB to validate Alternative Procedure: • use observed isotropy of CMB • assume cosmological principle • deduce homogeneity & isotropy almost-EGS Theorem If all observers see an almost isotropic cmb then the universe is almost FLRW Maartens et al, PRD 51 (1995) 1525 Taking either approach, our universe is homogeneous and isotropic

  11. Propagation of Photon Beams All gravitational focusing and shearing effects on a beam of light rays are described by the geodesic deviation equation. photon 4-vector observed frequency Angular-diameter distance: Luminosity distance:

  12. Propagation of Photon Beams What is the refractive index of the large-scale universe? What g, Riem(g) is used to model geodesic deviations? Where is most of the matter in the universe? Is the beam empty or full? Photon paths extend over very large scales, but can still feel small-scale inhomogeneities

  13. Propagation of Photon Beams In a Robertson-Walker spacetime k=0: solution #1 BC: k=0: solution #2

  14. Propagation of Photon Beams In a realistic spacetime Photon beams suffer de/magnification Photon number is conserved standard formula valid on average • Matter is mostly localized in galaxies • Some light rays will be “empty beam” • Due to photon conservation, the average beam will produce a dL given by the R-W metric • The distribution of beam results is not Gaussian, but skewed toward empty or demagnified • In practice, many SNe per bin are needed to flux average Wang et al, ApJ 72 (2002) L15 a quick history: Gunn, ApJ 150 (1967) 737 Kantowski, ApJ 155 (1969) 89 Turner et al, ApJ 284 (1984) 1 Frieman, astro-ph/9608068 Holz & Wald, PRD 58 (1998) 063501 Wang, ApJ 536 (2001) 531

  15. Cosmology 1922: Friedmann 1925: Lemaitre 1929: Robertson 1936: Walker homogeneous, isotropic metric homogeneous, isotropic source Einstein: world-matter is homogeneous on large scales, but inhomogeneities are possible on small scales Background Equations

  16. Cosmology } require consistency relation: Define an equation-of-state: Idealization:

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