AS 4022 Cosmology

Lecture 9

Observational Cosmology

Discovery of “Dark Energy”

AS 4022 Cosmology

Age Crisis (~1995)

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H0 t0 =dx

x ΩM x 3 +ΩΛ + (1−Ω0) x2

1

∞

∫

observations : H0 = 72 ± 8 km s−1 Mpc−1

t0 ≥14 ± 2 Gyr old globular clusters H0 t0 ≥1.0 ± 0.15

H0 t0 =23

for ΩM ,ΩΛ( ) = (1,0)

Globular clusters older than the Universe ?Inconsistent with critical-density matter-only model :

Strong theoretical prejudice for inflation.Doubts about stellar evolution therory (e.g. convection).

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Ω0 =1( )

AS 4022 Cosmology

Deceleration parameter

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q ≡ −˙ ̇ R R˙ R 2

= −˙ ̇ R

R H 2

q0 ≡ −˙ ̇ R R˙ R 2

0

= −˙ ̇ R

R H 2

0

a(t) ≡ R(t)R0

=1+ H0 t − t0( ) − q0

2H0

2 t − t0( )2+ ...

˙ a = H a ˙ ̇ a = −q H 2a

Dimensionless measure of the

deceleration of the Universe

q0 > 0 => deceleration

q0 = 0 => coasting at constant velocity

q0 < 0 => acceleration

t - t0

R

q0 > 0

q0 < 0

AS 4022 Cosmology

Deceleration parameter

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q ≡ −˙ ̇ R R˙ R 2

= −˙ ̇ R

R H 2 q0 ≡ −˙ ̇ R R˙ R 2

0

= −˙ ̇ R

R H 2

0

Friedmann momentum equation :

˙ ̇ R = − 4π G3

ρ +3 pc 2

R +

Λ3

R

˙ ̇ R H0

2R= −

4π G3H0

2 ρ 1+ 3w( ) +Λ

3H02

ρ, p > 0 decelerate, Λ > 0 accelerates

Equation of state : p = wi ρi c 2

i∑

wR =13

wM = 0 wΛ = −1

q0 = −˙ ̇ R

R H 2

0

=1+ 3 wi

2

Ωi

i∑ =ΩR +

ΩM

2−ΩΛ €

ΩM€

ΩΛ

€

Ω= 1€

0

€

+1/ 2€

q0 = −1/ 2

t - t0

R

AS 4022 Cosmology

DecelerationParameter

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q0 ≡ −˙ ̇ R R˙ R 2

0

=ΩM

2−ΩΛ

Measure q0 via :

1 . DA(z)

( e.g. radio jet lengths )

2. DL(z)

( curvature of Hubble Diagram )

+1

0

q0 = -1

acceleration

deceleration

Matter decelerates

Vacuum (Dark) Energyaccelerates

Critical density matter-only --> q0=1/2.

AS 4022 Cosmology

Observable Distances

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angular diameter distance :

θ = lDA

DA =r0

(1+ z )=

c zH0

1− q0 + 32

z + ...

luminosity distance :

F = L4π DL

2 DL = r0 (1+ z ) =c zH0

1+1− q0

2z + ...

deceleration parameter :

q0 =ΩM

2−ΩΛ

Verify these low-z expansions.

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1993 - Angular Size of Radio Jets

Deceleration

as expected for

But, are radio jets

standard rods ?

Kellerman 1993

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for ΩΛ = 0

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q0 ~ +0.5

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(ΩM ,ΩΛ ) =(1,0)

€

ΩM€

ΩΛ

€

θ =l

DA(z )

AS 4022 Cosmology

Kellerman 1993

1993 - Angular Size of Radio Jets

Deceleration

as expected for

But, are radio jets

standard rods ?

€

θ =l

DA(z )

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q0 ~ +0.5

€

(ΩM ,ΩΛ ) =(1,0)

€

(ΩM ,ΩΛ ) =(0.3,0.7)

Also compatible withConcordance Model.

€

ΩM€

ΩΛ

AS 4022 Cosmology

Angular Diameter Distance

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ΩM€

ΩΛ

€

DA (z) =lθ

Similar redshift dependence.

AS 4022 Cosmology

Angular Diameter Distance

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ΩM€

ΩΛ

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DA (z) =lθ

Change jet length, closer still.

AS 4022 Cosmology

Hubble Diagram

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m = M + 5 log DL (z)Mpc

+ 25

+ A + K(z)m = apparent magM = absolute magA = extinction (dust in galaxies)K(z) = K correction( accounts for redshift of spectrarelative to observed bandpass )

DL(z) =c zH0

1+1− q0

2z + ...

slope = +5

vertical shift --> H0

curvature --> q0

log ( c z )

app

aren

t m

ag

deceleration( q0 > 0 )

acceleration( q0 < 0 )

faint

bright

AS 4022 Cosmology

Finding faint Supernovae

Observe 106 galaxies.

Again, 3 weeks later.

Find “new stars”.

Measure lightcurves.

Take spectra.

( Only rare Type IaSupernovae work ).

AS 4022 Cosmology

Hi-Z Supernova Spectra

SN II --- hydrogen lines

(collapse and rebound ofthe core of a massive star)

SN I --- no hydrogen lines

(no H-rich envelopesurrounding the core)

SN Ia --- best knownstandard candles

(implosion of 1.4 Msunwhite dwarf, probably dueto accretion in a mass-transfer binary system).

HαHβ

AS 4022 Cosmology

Calibrating“StandardBombs”

1. Brighter onesdecline more slowly.

2. Time runs slowerby factor (1+z).

AFTER correcting:Constant peak brightness

MB = -19.7

Observed peak magnitude:m = M + 5 log (d/Mpc) + 25gives the distance! Time ==>

Abs

olut

e m

agni

tude

M B

==

>

AS 4022 Cosmology

SN Ia at z ~ 0.8are ~25% fainterthan expected

Acceleration ( ! ? )

1. Bad Observations?

-- 2 independent teams agree

1. Dust ?

-- corrected using reddening

2. Stellar populations ?

-- earlier generation of stars

-- lower metalicity

3. Lensing?

-- some brighter, some fainter

-- effect small at z ~ 0.8

Reiss et al. 1998

Perlmutter et al. 1998

AS 4022 Cosmology

1998cosmologyrevolution

Acceleration ( ! ? )

matter-only modelsruled out

cosmological constantΛ > 0

“Dark Energy”

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if Ω0 =ΩM +ΩΛ =1 then ΩM ~ 0.3 ΩΛ ~ 0.7

AS 4022 Cosmology

HST Supernova SurveysHST surveys to find SN Ia beyond z = 1Tonry et al. 2004.

AS 4022 Cosmology

25 HST SN 1a beyond z = 1Reiss et al. 2007.

SNAP = SuperNova Acceleration Probe

1.5m wide-angle multi-colour spacetelescope --- 1000 SN 1a

(Not Yet Funded)

Most distant SupernovaSN 2007ff z =1.75