Cosmology OverviewCosmology OverviewDavid SpergelDavid Spergel

Lecture OutlineLecture Outline THEME: Observations suggest that the THEME: Observations suggest that the

simplest cosmological model, a simplest cosmological model, a homogenuous flat universe describes the homogenuous flat universe describes the universe on its largest scalesuniverse on its largest scales

I. General Relativity: Dynamics and Shape of the Universe

II. Metric Theory

III. Evidence for Isotropy

IV. Tests of Metric Theories

V. Open Questions and Future Observations

General Relativity: A ReviewGeneral Relativity: A Review

Space is not absolute. Only relative Space is not absolute. Only relative positions are meaningful.positions are meaningful.

Matter tells space how to curveMatter tells space how to curve Curvature of space tells matter how to Curvature of space tells matter how to

move: particles move on “straight lines”move: particles move on “straight lines”

Metric TheoryMetric Theory

Particles move on straight linesParticles move on straight lines

NEWTONIAN LIMIT:

Matter Distribution determines Matter Distribution determines curvature of spacecurvature of space

Riemann Tensor: Unique combination of second derivatives of metric

Ricci tensor Curvature Scalar

Einstein Equation

Newtonian limit of Einstein equation

GR from Least Action GR from Least Action PrinciplePrinciple

Least Action:

Once you start adding terms, there may be no stopping:

e.g., Carroll et al., astro-ph/0413001

What is this doing here?

Big Bang CosmologyBig Bang Cosmology

Homogeneous, isotropic universe

(flat universe)

Freidmann Equation

Pseudo-Newtonian Pseudo-Newtonian CosmologyCosmology

Differentiate Friedmann equation:

where

Homogeneous & Isotropic Homogeneous & Isotropic UniverseUniverse

HomogeneityHomogeneity

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IsotropyIsotropy

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MAP990045

Microwave Receiver

The Cosmic Microwave Background

and y distortion constraints

CMB is not a grey body! Not a sum of black bodies!

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Density fluctuation versus Density fluctuation versus scalescale

Quasar Correlation FunctionQuasar Correlation Function

Evolution of Scale FactorEvolution of Scale Factor

Matter:

Radiation

Vacuum Energy

Conformal Conformal Structure of Structure of Space-timeSpace-time

RedshiftRedshift

Supernova Supernova DurationDuration

Goldhaber et al. (2001) ApJ 558, 359

Molaro et al. (2002)

Expansion of the universe cools microwave background

CI thermometer

Hubble LawHubble Law

Krisciunas, Phillips and Suntzeff (2004) ApJL 602:81

Rulers and Standard CandlesRulers and Standard Candles

Luminosity Distance

Angular Diameter Distance

SupernovaSupernova

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Flat M.D. UniverseFlat M.D. Universe

D = 1500 Mpc for z > 0.5

VolumeVolume

Measuring DistancesMeasuring Distances

Closed UniversesClosed Universes

Distance MeasurementsDistance Measurements

The universe appears to be The universe appears to be remarkably simple in its remarkably simple in its

geometry if not its geometry if not its compositioncomposition