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 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

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/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 Robertson-Walker spacetime

k=0: solution #1

k=0: solution #2BC:

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

Cosmology

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

Idealization: