37

Astronomia2017-18

Parte VCosmologia

A.Penzias & R.Wilson (1965)Nobel Prize 1978A.Penzias & R.Wilson (1965)Nobel Prize 1978

BIG BANGt 0

T ∞

HERE and NOWt ~ 13.8 x 109 yr

T = 2.725 K

Last scattering surface

t ~ 3.8 x 105 yrT ~ 3000 K

Cosmic neutrinos1 s

5.000 yrsMatter domination

3 min Nucleosinthesis

Annihilation e+ e-

1 µsBaryogenesis

380.000 yrs Neutral atoms

TRANSPARENTUNIVERSE

4310 s−

Quantum gravity???

Grand unification??

1 nsHiggs

3510 s−Inflation?

0.01 ns Electroweak transition

Cosmic Microwave Background

Thermal History of the Universe

R Mρ ρ ρ ρΛ= + +

const.ρΛ =3

,00

M M

a

aρ ρ

−

=

4

,00

R R

a

aρ ρ

−

=

ρΛ

If it is a cosmic relic from an early hot phase, then:

Blackbody spectrum

Highly isotropic

Diffuse backgrounds through EM spectrum

λ = 1 m λ = 1 cm

1

12/2

3

−=

kThec

hB νν

ν

Blackbody radiation

Planck law:

Cosmic Microwave Background

At recombination radiation has a thermal spectrum with T ~ 3000 K. 1

2

3

1exp2

)(−

−

=kT

h

c

hB

ννν

At time t, number of photons in volume V(t) with frequencies between ν and ν+dν is:

)(1

)(4

)( tVh

dBc

tdNV νννπ=

Energy density of thermal radiation is

ννπργ ∫= dBc

)(4

ννπνdtV

kT

h

c)(1exp

81

3

2 −

−

=

Show that thermal radiation, filling the Universe, maintains a thermal spectrum as the Universe expands.

)'()( tdNtdN VV =

Now consider some later time t’ > t. If there have been no photon-producing/absorbing interactions, the number of photons in the volume remains the same:

However:(a) the volume has increased with the expansion ofthe Universe

)(

)'()()'(

3

3

ta

tatVtV =

Substitute for V(t), ν and dν in formula for dN(t), and use the fact that dN(t’) = dN(t)

(b) each photon has been redshifted:

)'(

)('

ta

tadd νν =

)'(

)('

ta

taνν =

Cosmic Microwave Background

3

3

( ')( ') ( )

( )

a tV t V t

a t= ( )

'( ')

a td d

a tν ν=( )

'( ')

a t

a tν ν=

')'(1'

'exp

'8)'(

1

3

2

ννπνdtV

kT

h

ctdNV

−

−

=

ννπνdtV

kT

aah

ctdNV )(1

'

)'/(exp

8)'(

1

3

2 −

−

=

)'()( tdNtdN =)(

)'('

ta

taTT =

After expansion (a a’) CMB has thermal spectrum with a lower temperature:

)'(

)('

ta

taTT = 0( ) (1 )T z T z= +

)'/()/')((1'

)'/(exp

)'/(8)'( 3

1

3

22

aadaatVkT

aah

c

aatdNV ννπν −

−

=

ννπνdtV

kT

h

ctdNV )(1exp

8)(

1

3

2 −

−

=Compare to:

Cosmic Microwave Background

Densità di energia della radiazione

Energy density associated with a blackbody filed:

3

2 /

2 1

1h kT

hB

c eγ νν=

−3

3 /

4 8

1h kT

hB d d

c c eγ ν νπ π νρ ν ν= =

−∫ ∫5 4

4 4 34 -32 3 2 2

1 24.8 10 g cm

15

kT T

c h c cγπ σρ −

= = ≈ ×

2.726 KTγ =Stefan-Boltzman law

55 10C

γγ

ρρ

−Ω = ≈ ×

229 -303

10 g cm8c

H

Gρ

π−= ≈

1964: Princeton group (Dicke, Peebles, Roll & Wilkinson) predict primordial thermal radiation and plan experiment to detect it

South Pole1989-19921.5-90 GHz radiometers

Absolute calibration

Free-space LHe-cooled blackbody Load

Low frequency CMB spectrum

Sky radiation

Ground screen

Sun schield

Horn antennaFWHM ~ 20°

Total power receiver

LHe absolute calibrator

COBEFIRAS

The CMB spectrum

Planck law

1e

12/2

3

−=

kThc

hB νν

ν

∫∫ −== ννπνπρ νν d

ec

hdB

c kThR 1

84/

3

3

525 106.4103.2 −−− ×≈×≈=Ω hC

RR ρ

ρ

High precision in cosmology!

K 002.0725.20 ±=T

zc

zth

Tight limits on energy releases in the early universe

Constraints on distortions

No distortions observed Upper limits

COBECosmic Background Explorer

Mission:

Launch:November 1989

Orbit:900 km LEO

Spinning Spacecraft

Experiments:

DMR:CMB Anisotropy

FIRAS:CMB Spectrum

DIRBE:IR Background

COBECosmic Background Explorer

FIRASFar InfraRed Absolute Spectrophotometer

COBE/FIRAS schematic

• Differential Michelson interferometer (internal reference blackbody)

• Absolute calibration: external blackbody (ε > 0.9999, Mather et al. 1999).

• Frequency range: 60-600GHz, spectral resolution: 5%

Frequency selection

Relative reference

Sky & absolute

calibration

COBE-FIRAS

λ = 0.5cm, ν = 60GHz λ = 0.05cm, ν = 600GHz

“Precision cosmology” with the CMB has been already demonstrated