dark energy cosmology inpe winter school september 12-16, 2005 robert caldwell dartmouth college
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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 2005data: Riess et al, ApJ 607 (2004) 665
Fluid Flow: Raychaudhuri Equation
v = 4-velocity of test particles
metric in subspace orthogonal to vvorticity
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 locationsKamionkowski & 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 galaxiesCastro et al, PRD 68 (2003) 127301 Grishchuck-Zeldovich test with WMAPDonoghue et al, PRD 71 (2005) 043002 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 momentCOBE
Kogut et al, PRD 55 (1997)1901
Bianchi VIIh template
Tiny anisotropies can produce ~10-5 temperature
fluctuations
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/0505157Vale, astro-ph/0509039
Homogeneity and Isotropy
Measurements of the Cosmic Microwave Background probe matter and energy on the
largest scalesStandard 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 Theorem If all observers see an almost isotropic cmb then the universe is almost FLRWMaartens 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 realistic spacetime
Photon beams suffer de/magnification
Photon number is conserved
Gunn, ApJ 150 (1967) 737Kantowski, ApJ 155 (1969) 89Turner et al, ApJ 284 (1984) 1Frieman, astro-ph/9608068Holz & Wald, PRD 58 (1998) 063501Wang, 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 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
Cosmology 1922: Friedmann1925: Lemaitre1929: Robertson1936: Walker
homogeneous, isotropic metric
homogeneous, isotropic source
Einstein: world-matter is homogeneous on large scales, but inhomogeneities are possible on small scales
Background Equations