The Cosmic Microwave Background

Based partly on slides Joe Mohr

(University of Chicago)

History of the Universe:

superluminal inflation,particle plasma, atomic plasma,recombination,structure formation

Outline1. Introduction

» Relic radiation

» Penzias and Wilson at Bell Labs

2. Blackbody radiation

» Electromagnetic spectrum

» Lamps, stars and people

» Effects of expansion

3. COBE and WMAP

» Nature of the bkgd radiation

» Uniformity of background

» Detecting our motion

» Seeds of structure formation

4. Review

Implications of an Expanding Universe

Reactions to an expanding universe» Gamow predicts (1940’s) hot, dense early phase

» Novikov predicts (1962) relic radiation from hot, dense phase

» Dicke was interested in finding a radiation background

Arno Penzias and Robert Wilson» Study radio emission at 7cm

» Bell Labs in New Jersey

» Discover background in 1965

– temperature is 3 Kelvin

– isotropic

» Dicke explained significance

Penzias and Wilson with radio horn

Effects of Expansion on Light As the universe expands, light wavelengths stretch with space. Photons gravitationally

red shifted or simply stretched with the expanding space.

Sphere courtesy Wayne Hu

Temperature is directly proportional to wavelength. The effective temperature of a blackbody spectrum decreases as the wavelength stretches.

Galaxy velocities: Doppler shifts or universal expansion?

m~1/a3

r~1/a4

where a=characteristic scale size of universe

Extrapolation into the PastPresent day

» Universe cold (3K) with low matter density» one hydrogen atom per 10 cubic meters» 400 million CMB photons per cubic meter» CMB photons and matter rarely interact - transparent» typical matter in form of atoms and molecules

Recombination or last scattering surface» universe hot (3,000K) and a billion times denser» photon energy high enough to ionise atoms and molecules» plasma of e-, p+ and (plus trace He3, deuterium, Li and

Be)» CMB photons coupled to matter through collisions

Pre-recombination» universe even hotter and denser» CMB photons coupled to matter through collisions» Early universe hot enough for pair creation, neutrino

opacity and many particle processes.

Tim

e

EarlyUniverse

Present

13 Gyr

0.5 Myr

<1 yr

A Pictorial History of the CMB

Observer

Last Scattering Surfacewhere recombination of

electrons and protonstakes place.

Edge of Observable Universe- distance light

could have traveled over age of universe.

Blackbody light

Blackbody light

The Observable Universe

Blackbody light emitted in the surface of last scattering travels in all directions. We only see that portion which happens to set off in a direction that leads it into one of our detectors.

Blackbody RadiationEvery opaque object emits blackbody radiation

Blackbody spectrum

»Continuous spectrum, depends only on temperature– Hotter bodies brighter, bluer, shorter – Cooler bodies dimmer, redder, longer

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P = P(ω)dω =π 2k 4

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⎝ ⎜

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⎠ ⎟∫ T 4 =σT 4

Stefan-Boltzmann Law

Planck radiation law

Blackbody Radiation Cont’d

=Stefan-Boltzmann Constant 5.67 x 10-8 Wm2T-4

10K: 0.56mW/m2

300K: 450W/m2

1000K: 56kW/m2

104K : 560MW/m2

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hωkT

~ 3At peak

Cosmic Background Explorer (COBE)

NASA satellite designed to test nature of cosmic background radiation

Three instruments

» FIRAS- Far Infrared Absolute Spectrophotometer

– measure CMB spectrum

» DMR- Differential Microwave Radiometers

– measure variations in temperature on the sky

» DIRBE- Diffuse Infrared Background Experiment

Image courtesy COBE homepage.

FIRAS Spectrum of CMB

Theoretical blackbody spectrum34 observations over-plotted

largest deviation 0.03%

T=2.728+/-0.004 K

Image courtesy COBE homepage.

Imaging the Globe with the COBE DMR

Image of the world

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Imaging the Globe with the COBE DMR

Image of the world

Image with COBE angular resolution

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Imaging the Globe with the COBE DMR

Image of the world

Image with COBE angular resolution

Image with COBE measurement noise

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Imaging the Globe with the COBE DMR

Image of the world

Image with COBE angular resolution

Image with COBE measurement noise

COBE-like image smoothed to reduce noise

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COBE DMR ImageThe sky temperature with range from 0-4 KelvinMicrowave background is very uniform at ~3 Kelvin

Image courtesy COBE homepage.

COBE DMR Image: 1,000X ZoomThe sky temperature with range from 2.724-2.732 Kelvin

– blue is 2.724 K and red is 2.732 K

Dipole pattern in temperature indicates motion– Doppler Effect at level of ~0.005 K

– Solar system is traveling at ~400 km/s with respect to CMB

Image courtesy COBE homepage.

COBE DMR Image: 25,000X Zoom

The sky temperature ranging from 2.7279-2.7281 Kelvin– blue is 2.7279 K and red is 2.7281 K

Dipole variation from Solar system motion removedRed emission along equator is galactic emissionOther fluctuations are likely cosmic in origin

Image courtesy COBE homepage.

COBE DMR Image: Galaxy and Dipole Removed

Image courtesy COBE homepage.

Amplitude of temperature fluctuations is 30K +/-3 K in 10 degree patches.(1 part in 105)

WMAP reduced in resolution to COBE

WMAP All Sky Image 2002 galaxy removed

WMAP half sky image and examples of fluctuations on varying scales

The Angular Power Spectrum of the CMB

1999 Image Analysis: theory and experiment

Analysis of CMB Images

Angular Power Spectrum

Gravitational EnhancementBefore recombination dark matter fluctuations

with scale size matching the fundamental acoustic wave cause increased clumping of baryons and photons. Photons from the troughs are red shifted.

By the time of recombination the excess density regions have been heated enough that the phase is reversed and the temperature fluctuations are 3 times enhanced.

Second Harmonic Gravitational Suppression

For even harmonics of the acoustic wave, the same initial condition (cooler troughs) leads to density increase and heating well before recombination.

Because of the shorter scale size there is enough time for pressure (blue arrows) to act to oppose gravity (white arrows), thus suppressing the second peak.

Summary Microwave background observed

» Penzias and Wilson at Bell Labs in 1965 with sensitive radio telescope» NASA Cosmic Background Explorer (COBE) satellite in early 1990’s» NASA WMAP Microwave Anisotropy Probe 2002» CMB photons have travelled 13 billion years to reach us

Nature of cosmic background radiation» precise blackbody spectrum with temperature of 2.725K» highly uniform temperature

– small dipole: evidence for our motion at ~400 km/s– anisotropies: 1 part in 105 if you examine 10 degree patches of sky

-image analysis consistent with detailed cosmological model involving acoustic oscillations in early universe

Universe hot and dense enough to behave as blackbody in past» Fluctuations over non-causally connected regions implies inflation» Fluctuations over causally connected regions allows determination of mass

density, dark matter and dark energy

» See Wayne Hu Sciama lecture, animations and Sci Am Feb 2004

The Electromagnetic Spectrum

Images from “Imagine the Universe!” site at Goddard Space Flight Center http://imagine.gsfc.nasa.gov/docs/homepage.html

LightWaves ParticlesPhotons

electron

photon

EnergyWavelengthFrequency

Photons and electronsscatter off one another like billiard balls.

Stellar SpectrumSimple Model of a Star

Fusion in thecenter of the staris energy source.

Hot, dense gas cools byemitting blackbody radiation. The Sunemits blackbody rad-iation with an effectivetemperature of 5,500 K.

Atoms in the cooler, lower density sur-face gas absorb lightat specific wave-lengths, creatingabsorption lines.

Observed stellar spectrum. Notethe large number of absorptionlines.

Magnesium

Sodium

Calcium

Wavelength

Inte

ns i

ty

Infrared Emission from Living Things

Infrared image of a cat. Orange is brighter(and warmer) and blue is dimmer (and cooler).Note the warm eyes and cold nose.

Images from IPAC at the Jet Propulsion Laboratory. The cat image comes courtesy of SE-IR corporation.

Infrared image of a man with sunglasses anda burning match. Black is dim (cold) and white it bright (hot).

Compton LecturesFoundations of the Hot Big Bang Model

» 1 “Observing the Expansion of the Universe”

» 2 “The Cosmic Microwave Background (CMB)”

» 3 “Creation of the Elements in the Early Universe”

» 4 “The Dark Night Sky, Causality and Geometry”

» 5 “A Timeline for the Universe”

Current Topics in Observational Cosmology

» 6 “Mapping the Large Scale Structures in the Nearby Universe”

» 7 “Observing the Seeds of Structure Formation in the CMB”

» 8 “Detecting Dark Matter with the Chandra X-ray Satellite”

» 9 “Measuring the Size and Geometry of the Universe”

» 10 “Using Shadows in the CMB to Map the Edge of the Universe”