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14/05/22 Chris Pearson : Observational Cosmology 2: The Cosmic Background - ISAS -2004 1 THE COSMIC BACKGROUND “My goal is simple. It is complete understanding of the universe, why it as it is and why it exists as all.” — Stephen Hawking. Observational Cosmology: 2. Observational Cosmology: 2. The Cosmic Background The Cosmic Background

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Observational Cosmology: 2. The Cosmic Background. “My goal is simple. It is complete understanding of the universe, why it as it is and why it exists as all.” — Stephen Hawking. 2.1: The Isotropic Background. Is the Universe really homogeneous & isotropic ?? - Olbers Paradox revisited. - PowerPoint PPT Presentation

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Page 1: “My goal is simple

22/04/23 Chris Pearson : Observational Cosmology 2: The Cosmic Background - ISAS -2004

1

THE COSMIC BACKGROUND

“My goal is simple. It is complete understanding of the universe, why it as it is and why it exists as all.”

  — Stephen Hawking.

Observational Cosmology: 2.Observational Cosmology: 2.The Cosmic The Cosmic BackgroundBackground

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THE COSMIC BACKGROUND

2.1: The Isotropic Background2.1: The Isotropic BackgroundIs the Universe really homogeneous & isotropic ?? - Olbers Paradox revisited

Heinrich Olbers 1826 (Thomas Digges 1576)WHY IS THE SKY SO DARK ?The Sky should be the average surface brightness of a star !!!

Solution: The Universe has a finite age Not all the light has had time to reach us yet !

This is the optical Olbers Paradox….BUT … What if Mr Olber had microwave eyes ?

The sky would be uniformly bright at =5cmAt a constant temperature of 2.73K

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THE COSMIC BACKGROUND

2.1: The Isotropic Background2.1: The Isotropic BackgroundIs the real Universe really homogeneous and isotropic ??

ActualTemperatureDistribution

1 / 1000 Temperaturevariation

1 / 100, 000 Temperaturevariation

4c m

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THE COSMIC BACKGROUND

2.1: The Isotropic Background2.1: The Isotropic BackgroundThe discovery of the microwave Background

These photons are the redshifted relic or ashes of the Big Bang Originally high energy gamma rays, these primordial photons have cooled to be 2.73K 2mm microwaves today

• 1964: Penzias & Wilson - • Bell Laboratries Satellite Telecommunications at microwave wavelengths ~ 7.35cm• Found a value of 3.5K higher temperature than expected when turning antenna to blank sky• Serendipitously discover the 2.73K microwave background radiation

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THE COSMIC BACKGROUND

HHH

H

Last Scattering

HH

HH

De-coupling

2.2: The Origin of the Microwave 2.2: The Origin of the Microwave BackgroundBackgroundRecombination and Decoupling

zT

tR

• matter in thermal equilibrium with the radiation. photons and

electrons to interact via Thompson scattering

pe-

p pp

e-

e- e-

recombination•Temperature drops then p+e-H

recombination

• Eventually interactions stop allowing the photons to flow freely on scales of the horizon de-coupling

QuickTime¢‚∞˙ YUV420 codec æ–√‡ «ÿ¡¶±‚∞°

¿Ã ±◊∏≤¿ª ∫∏±‚ ¿ß«ÿ « ø‰«’¥œ¥Ÿ.

• Era at which any photon last scattered off any electron

surface of last scattering

BIG BANG

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THE COSMIC BACKGROUND2.2: The Origin of the Microwave 2.2: The Origin of the Microwave BackgroundBackground

The Surface of Last Scattering

After Recombination and Decoupling the photons are no longer bound to matter and can stream freely

Photons from the Big Bang fill the universe and we observe them as the 2.7K microwave background.

These photons are the redshifted relic or ashes of the Big Bang Last time photons interacted Surface of Last Scattering

This also means that we can not observe the Universe when it was younger than ~400,000 years

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THE COSMIC BACKGROUND2.2: The Origin of the Microwave 2.2: The Origin of the Microwave BackgroundBackground

The Relic BackgroundEnergy density of radiation

ε =ρc2 = aT 4 ⇒ εγ ,o

= ρ oc2 = aTo

4 ≈ 0.26MeVm−3 ~ 5x10−5 ρ c

a = radiation constant = 4.73x10−3 MeVm−3K−4

εb,o = Ωb,oρ cc2 ⇒ 0.04 3Ho

2c 2

8πG

⎛ ⎝ ⎜

⎞ ⎠ ⎟= 0.04(5200MeVm−3) ≈ 208MeVm−3

Energy density of the matter

• Today : Energy density in Baryons is 800 times energy density in photons• But : Number density of Baryons to photon is 1 in 109

nγ ,o ≈εγ ,o

hυ 2mm

≈ 4x108 m−3Photon Number Density

nb,o ≈εb,o

mproton

= 0.22m−3Baryon Number density

η =nb,o

nγ ,o

≈ 0.224x108 ≈ 5.5x10−10

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THE COSMIC BACKGROUND2.2: The Origin of the Microwave 2.2: The Origin of the Microwave BackgroundBackgroundThe Physics of Recombination

Temperature drops then p+e-H recombination depends on I. Ionization energy of Hydrogen =13.6eVII. The baryon/photon ratio, η~5x10-10

But even at lower temperatures sufficient photons with appropriate ionization energy

Number densities of particles as a function of To given by Boltzmann function

nH = gHmH kT2πh2

⎛ ⎝ ⎜

⎞ ⎠ ⎟3 / 2

e−

m H c 2

kT

np = gp

mpkT2πh2

⎛ ⎝ ⎜

⎞ ⎠ ⎟3 / 2

e−

m p c 2

kT

ne = gemekT2πh2

⎛ ⎝ ⎜

⎞ ⎠ ⎟3 / 2

e−

me c 2

kT

⎪ ⎪ ⎪ ⎪

⎪ ⎪ ⎪ ⎪

nH

npne

= gH

gpge

mH

mpme

⎝ ⎜ ⎜

⎠ ⎟ ⎟

3 / 2kT

2πh2

⎛ ⎝ ⎜

⎞ ⎠ ⎟−3 / 2

e−

(m H −m p −me )c 2

kT

Therefore define the fractional ionization

χ =np

np + nH

=np

nb

= ne

nb

np = number of unbound protons

nH = number of bound protonsnb = number of baryonsne = number of electrons

⎨ ⎪ ⎪

⎩ ⎪ ⎪

H binding energy = Q = (mp+me-mH)c2

mp~ mH

Statistical weights mp= me=2, mH=4SAHA EQUATION

nH

npne

= mekT2πh2

⎛ ⎝ ⎜

⎞ ⎠ ⎟−3 / 2

eQkT

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THE COSMIC BACKGROUND2.2: The Origin of the Microwave 2.2: The Origin of the Microwave BackgroundBackgroundThe Physics of Recombination

IonizationFraction

χ =np

np + nH

=np

nb

⇒nH = 1− χ

χnp

η =np

χnγ

⎨ ⎪ ⎪

⎩ ⎪ ⎪

1

2

nH

npne

= mekT2πh2

⎛ ⎝ ⎜

⎞ ⎠ ⎟−3 / 2

eQkTSaha

Equation 3

εBB (ν )dν = 16π 2hc 3

ν 3dνehν / kT −1

⇒ nγ = 2.404π 2

kThc ⎛ ⎝ ⎜

⎞ ⎠ ⎟3

Black Body Energy Density Distribution 4

1− χχ 2 = 3.84 kT

mec2

⎛ ⎝ ⎜

⎞ ⎠ ⎟−3 / 2

eQkT

Between temperatures of To~5000 2000, Ionization fraction drops 1 0

Quadratic in χ

24

31

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THE COSMIC BACKGROUND2.2: The Origin of the Microwave 2.2: The Origin of the Microwave BackgroundBackgroundThe Physics of Recombination

DecouplingOptical Depth

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THE COSMIC BACKGROUND2.2: The Origin of the Microwave 2.2: The Origin of the Microwave BackgroundBackgroundThe Physics of Recombination

Epoch of Recombination (kT~Q) To ~ 3740Kz ~ 1370, z ~ 200T ~ 240kyr, t ~ 70kyr

Epoch of Decoupling (~H) To ~ 3000z ~ 1089, z ~ 195T ~ 379,000yr, t ~ 118ky

10-26

10-24

10-22

10-20

10-18

10-16

10-14

10-12

10-10

10-8

10-6

0.0001

0.01

1

1250 2500 3750 5000 6250 7500

Fractional Ionization as function of Temperature

Ionization

Temperature (K)

χ(T)

χ(z)

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THE COSMIC BACKGROUND

2.3: Observations of the CMB2.3: Observations of the CMBTemperature Fluctuations

Observations of CMB Fluctuations in Temperature

At the level of T ~ 10-3 : Observe Dipole Anisotropy

Early Universe was highly homogenous

Subtract Dipole DistortionAt the level of T ~ 10-5 : Observe complicated fluctuations

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THE COSMIC BACKGROUND

2.3: Observations of the CMB2.3: Observations of the CMBTemperature Fluctuations - Isotropy and Homogeneity

Early Universe was highly homogenous

• 1989: COBE• Cosmic Microwave Background Explorer• Diffuse Infrared Background Experiment • DIRBE 0.001mm < l < 0.24mm• Far Infrared Absolute Spectrometer • FIRAS 0.1mm < l < 10mm• Differential Microwave Radiometer• DMR l= 3.3, 5.7, 9.6mm

COBE

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THE COSMIC BACKGROUND

2.3: Observations of the CMB2.3: Observations of the CMBTemperature Fluctuations - The Dipole Anisotropy

At the level of 10-3 : Observe Dipole AnisotropyOne half of sky seemingly blue shifted to higher temperaturesOne half of sky seemingly red shifted to lower temperatures

Net motion of COBE wrt frame of reference in which CMB is isotropic

Like the Ether ?

1+ cos )

Doppler Effect? 1) increases energy of photons seen in direction of motion ~ 1+cosDoppler Effect? 2) d, interval of frequencies also increased ~ 1+cos =v/c Net D

oppler

Effect ZERO!

1) Sweeps up cdt+vdtcos more photons in direction of travel 1+cos 2) Abberation effect (solid angle for moving observer decreases) (1+cos

I () = (1+cos Ie (e)

To(θ) = TCMB(1+ β cosθ)

1+ β

• COBE - Earth correction ~ 8 kms-1

• Earth - Sun correction ~ 30 kms-1

• Sun - Galactic Centre correction ~ 220 kms-1

• Galaxy - Local Group ~ 80 kms-1

• Local Group moving towards Hydra at v~630±20kms-1 ~ 0.002c

There is no quadrapole moment

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THE COSMIC BACKGROUND

2.3: Observations of the CMB2.3: Observations of the CMBTemperature Fluctuations

• Early Universe was highly homogenous• Planck Time ~ quantum fluctuations• Inflation ~ amplified fluctuations macroscopic• Fluctuations frozen until zdec• Fluctuations in the density (ρρ)~3(TT)

TT

(θ,φ) =T(θ,φ) − T

T

δTT ⎛ ⎝ ⎜

⎞ ⎠ ⎟2

COBE ,DMR

1/ 2

≈1x10−5T1(1,1) T2(2,2)

T1T2 = almYlm (θ,φ)m=−l

l

∑l= 0

∑ ,

alm2 1/ 2

= δT1

T1

δT2

T2

= Cl (θ)

Temperature fluctuations defined of surface of sphere Expand as spherical harmonics

Cl() = Correlation function (mean product over all points seperated by )Value of Cl() as a function of (0< <180o) gives a complete statistical description of the CMB

QuickTime™ and aSorenson Video decompressorare needed to see this picture.

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THE COSMIC BACKGROUND

T = l(l +1)2π

⎛ ⎝ ⎜

⎞ ⎠ ⎟

1/ 2

Cl

2.3: Observations of the CMB2.3: Observations of the CMBTemperature Fluctuations

T1T2 = almYlm (θ,φ)m=−l

l

∑l= 0

∑ , alm2 1/ 2

= δT1

T1

δT2

T2

= Cl (θ)

Expand Cl() in spherical harmonics(Pl = Legendre Polynomials)

C(θ) = 14π

(2l +1)l= 0

∑ ClPl cosθ

Cl() is scale dependent The value probed will depend on resolution of instrument

Individual Cl ’s probe structure on different angular scales given by =o / l l = 0 the monopolel = 1 the dipole (due to our motion wrt CMB)l = >1 fluctuations imprinted on SLS

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THE COSMIC BACKGROUND

2.3: Observations of the CMB2.3: Observations of the CMBHorizons and Fluctuations

• Particle horizon: the distance light can have traveled from t = 0 to any given time t • Event horizon: the distance light can travel from any given time t to t=∞ (or tmax). • Hubble Distance (Hubble Sphere): the distance beyond which recession velocity exceeds the speed of light.

r(z) = cRo

dzH(z)0

z∫ Comoving coordinate

rlc (te ) = c dtR(t)te

to∫ Past Light Cone

rp (t) = c dtR(t)o

t∫ Particle Horizon

rE (t) = c dtR(t)

Event Horizont

∞∫

DH = cH

The Hubble Distance

τ = dtR(t)0

t∫

Davis & Lineweaver 2003

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THE COSMIC BACKGROUND

BIGBANG INFLATION

2.3: Observations of the CMB2.3: Observations of the CMBHorizons and Fluctuations: Large Scale Fluctuations o

dA

L/2H

horizon

horizon

observer

observer

The Horizon Distance at recombination and decoupling (Surface of Last Scattering SLS)

dH ,SLS = R(tSLS )rp (t) = R(tSLS ) cdtR(t)o

tSLS∫ ~ 0.22MpcHorizon Distance given by particle horizon distance

Angular Diameter Distance at SLS

dA = Lδθ

( for z >>1) ≈ dH (to)z

~ 13Mpc

For scales = Horizon scale at last scattering,

L = dH,SLS⇒ δθ = θ H ~ 1o

Scales of o different origin to scales o

Spherical harmonics =o / lo Corresponds to l<180o Corresponds to l>180

Scales of o outside horizon fluctuations from inflation Gravitational effect of primordial density fluctuations

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THE COSMIC BACKGROUND

2.3: Observations of the CMB2.3: Observations of the CMBHorizons and Fluctuations: Sachs-Wolfe Effect

Scales of o outside horizon fluctuations from inflation Gravitational effect of primordial density fluctuations

∇2δΦ = 4πGδρ ≡ 4πGc 2 δε

Fluctuations in density fluctuations in gravitational potential Gravitational Wells

Poisson eqn

At surface of last scattering:

Red spots - higher temperature - potential maxima

Blue spots - lower temperature - potential minima

• Photon a local potential minima (bottom of well) has to climb out lose energy Redshift•Photon a local potential maxima (top of well) falls in gain energy Blueshift

TT

= 13

δΦc 2

SACHS - WOLFE EFFECT (1967)

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THE COSMIC BACKGROUND

BIGBANG INFLATION

2.3: Observations of the CMB2.3: Observations of the CMBHorizons and Fluctuations: Small Scale Fluctuations o

horizon

horizon

• Scales of o are inside the horizon baryons & photons• Baryons and photons fall into DM potential well

Generally (l=180) corresponds to potential wells in which Baryon/photon fluid had just reached max compression at time of decoupling (fundamental mode of oscillation).

Compression

Pressure

Expansion

AcousticOscillations

Overtones (l<180)

Fundamental

l = 180

At decoupling• Baryon/photon fluid in max compression high ρ,T• Baryon/photon fluid in max expansion low ρ,T

These potential wells had sizes of ~ dH,SLS (seen as H today)

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THE COSMIC BACKGROUND

2.3: Observations of the CMB2.3: Observations of the CMBHorizons and Fluctuations

Multipole (l) Angular scale ()

60’

6’

600’

Pow

er in

the

fluct

uatio

nsl2 C

l(2)

1/2

Savage 2003

Different angular scales probing different Physical processes

odd peaks max compression

even peaksmax rarefaction

Dobbs 2003

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THE COSMIC BACKGROUND

2.3: Observations of the CMB2.3: Observations of the CMBCMB Experiments

Different angular scales probing different Physical processes.

http://planck.mpa-garching.mpg.de/Planck/experiments.html

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THE COSMIC BACKGROUND

2.3: Observations of the CMB2.3: Observations of the CMBCMB Experiments

1965 : CMB Discovery (Penzias & Wilson)

1977 : CMB Dipole Observed (Smoot et al)

1989 : CMB anisotropies observed (COBE)

2001 : Fundamental acoustic peak observed (Boomerang, Maxima)

2002 : Secondary acoustic peaks observed (Maxima,Boomerang DASI)

2002 : CMB Polarization (E-modes) observed (DASI)

2001 : Acoustic Peaks mapped (WMAP)

2005 ? : Discovery of B-modes ? (Polar Bear)

2007? : Characterize E-modes, Discovery of B-modes ? (Planck)

2015? : Discovery of B-modes ? (CMBPOL Einstein Probe Satellite)

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THE COSMIC BACKGROUND

2.3: Observations of the CMB2.3: Observations of the CMBWMAP

QuickTime¢‚∞˙ Sorenson Video æ–√‡ «ÿ¡¶±‚∞°

¿Ã ±◊∏≤¿ª ∫∏±‚ ¿ß«ÿ « ø‰«’¥œ¥Ÿ.

• Wilkinson Microwave Anisotropy Probe (2001 at L2) • Detailed full-sky map of the oldest light 380,000yr old in Universe. • It is a "baby picture" of the 380,000yr old Universe• Probe the CMB fluctuation Spectrum below the horizon scale• ~ 900 - 0.2 (l=2-1000)

~ 70 ~ 0.20

QuickTime™ and aSorenson Video decompressorare needed to see this picture.

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THE COSMIC BACKGROUND

2.3: Observations of the CMB2.3: Observations of the CMBWMAP

QuickTime¢‚∞˙ Sorenson Video æ–√‡ «ÿ¡¶±‚∞°

¿Ã ±◊∏≤¿ª ∫∏±‚ ¿ß«ÿ « ø‰«’¥œ¥Ÿ.

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THE COSMIC BACKGROUND

Red - warm Blue - cool

2.3: Observations of the CMB2.3: Observations of the CMBResolving the Different Cosmological World Models

fundemental 1st harmonic• Relative heights and locations of these peaks signatures of properties of the gas at this time

Open Universe - photons move on faster diverging paths => angular scale is smaller for a given size

Peak moves to smaller angular scales (larger values of l)

*** THE UNIVERSE IS FLAT ***

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THE COSMIC BACKGROUND

2.3: Observations of the CMB2.3: Observations of the CMBResolving the Different Cosmological World Models

Wandelt et al. 2004

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THE COSMIC BACKGROUND

2.3: Observations of the CMB2.3: Observations of the CMBPolarization measurements

•CMB SLS gravity wave amplitude B (curl) mode component to CMB polarization•The smoking gun of inflation•Extend observations from 380,000yrs 10-35 s after Big Bang !!•Combination of Scalar, Vector & Tensor fields carry information on temperature anisotropies, acoustic peaks, cosmological parameter.

•Information on epoch of re-ionization

DASI polarization measurement 2002

Stokes vector S=(I,Q,U,V) characterizies Stokes vector S=(I,Q,U,V) characterizies the intensity and polarization of light.the intensity and polarization of light.

Q=IQ=I00-I-I9090

U=IU=I+45+45-I-I-45-45

V=IRCP-ILCP Unpolarized light Q=U=V=0Unpolarized light Q=U=V=0polarized light, Qpolarized light, Q22+U+U22+V+V22=1=1CMB Polarization V=0CMB Polarization V=0

CMB photons may be polarizedCMB photons may be polarized

•Inflation Gravitational wave background

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THE COSMIC BACKGROUND

2.3: Observations of the CMB2.3: Observations of the CMB

Hu et al. astro-ph/0210096

~100mK

~4mK RMS

≤300nK

1 degree

TemperatureE (Tensor)-modes

B (curl)-modes

B-mode amplitude is Determined only by the energy scale of inflation. Characterized by Tensor to scalar ratio ~ < 0.71 (WMAP

Polarization measurements

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THE COSMIC BACKGROUND2.4: Background Light 2.4: Background Light ComponentsComponents

Backgrounds or Foregrounds? (signals or noise?)

• Cosmic Microwave Background Radiation CMBR 3K, peaks at 5cm• Our Atmosphere: Sunlight scattered through atmosphere• Zodiacal Light: Dust in plane of Solar System illuminated by Sun peaks at

60m• Galactic emission from dust, peaks at about 100m• Emission from hot gas, Synchrotron & free-free radio emission• Extra galactic contributions from Radio Sources, Galaxies• S-Z Compton scattering of CMBR photons by relativistic e- in cluster gas

The total integrated background light comes from many sources

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THE COSMIC BACKGROUND2.4: Background Light 2.4: Background Light ComponentsComponentsBackgrounds or Foregrounds? (signals or noise?)

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THE COSMIC BACKGROUND2.4: Background Light 2.4: Background Light ComponentsComponents

Infrared Cirrus

B100 Contours at 1 and 2 MJy/sr

• Extended whispy neutral interstellar dust in the Milky Way heated by the interstellar radiation field.• Cirrus emission peaks at far IR wavelengths (100µm) but was detected in all 4 IRAS bands• The galactic cirrus is a function of galactic latitude and is serious for wavelengths longer than 60µm.

P ∝ d3 ∝ k 3

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THE COSMIC BACKGROUND2.4: Background Light 2.4: Background Light ComponentsComponentsConfusion to extragalactic sources

• Extragalactic Background• The superposition of sources below the flux limit / resolution of the instrument

Iν = Sν0

∫ dN(Sν )dS

dS ≡ dSν dN(s

∑ Sν )

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THE COSMIC BACKGROUND2.4: Background Light 2.4: Background Light ComponentsComponentsContributions to the Extragalactic Background

Optical

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THE COSMIC BACKGROUND2.4: Background Light 2.4: Background Light ComponentsComponentsBackgrounds or Foregrounds? (signals or noise?)

CMBGalactic HI (correlated)Galactic HI (uncorrelated)Galactic SynchrotronExtragalactic Radio SourcesExtragalactic IR Sources

Instrument on sky noise level

Bouchet 1999

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THE COSMIC BACKGROUND

2.5: Summary2.5: SummarySummary

The CMB is strong vindication for the Hot Big Bang Theory

The CMB• Isotropic to one part in 105 - An ideal Black Body• Shows a Dipole distortion due to the motion of the Earth wrt CMB frame• After Dipole Subtraction shows fluctuations on 30K

The epoch of recombination and decoupling define the Surface of Last Scattering (SLS)• The SLS is the last time the CMB interacated with matter• The SLS is a fossil of the 380,000yr old Universe• Primoridial density fluctuations are imprinted on the SLS

The Fluctuations in the CMB has 2 origins• On scales > 1 degree Primordial Fluctuations from Inflation (Sachs Wolfe effect)• On scales < 1 degree acoustic oscillations in the baryon-photon plasma

Decomposing the CMB fluctuations into spherical harmonics• Plot the fluctuation power as a function of angular size• Discriminate between different world models• WMAP - THE UNIVERSE IS FLAT !

Foreground (contamination)• Zodiacal Light• Discriminate between different world models• Extragalactic Background (unresolved galaxies)• ***** One man’s noise is another man’s signal *****

BUT….

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THE COSMIC BACKGROUND

2.5: Summary2.5: SummarySummary

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THE COSMIC BACKGROUND

2.5: Summary2.5: SummarySummary

Observational Cosmology Observational Cosmology 2. The Cosmic Background2. The Cosmic Background 終終

次:次:Observational Cosmology Observational Cosmology

3. Structure Formation3. Structure Formation