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

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

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

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

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

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

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

CMB Fluctuation Spectrum

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/ Vale, astro-ph/

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 Taking either approach, our universe is homogeneous and isotropic almost-EGS TheoremIf all observers see an almost isotropic cmb then the universe is almost FLRW Maartens et al, PRD 51 (1995) 1525

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:

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

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

Propagation of Photon Beams In a realistic spacetime Photon beams suffer de/magnification Photon number is conserved Gunn, ApJ 150 (1967) 737 Kantowski, ApJ 155 (1969) 89 Turner et al, ApJ 284 (1984) 1 Frieman, astro-ph/ Holz & Wald, PRD 58 (1998) Wang, ApJ 536 (2001) 531 a quick history: Wang et al, ApJ 72 (2002) L15 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 d L 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

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

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