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8/3/2019 Wayne Hu- Dark Energy in Light of the CMB
http://slidepdf.com/reader/full/wayne-hu-dark-energy-in-light-of-the-cmb 1/57
Wayne Hu
February 2006, NRAO, VA
(or why H0 is the Dark Energy)
Dark Energy in Light of the CMB
8/3/2019 Wayne Hu- Dark Energy in Light of the CMB
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If its not dark, it doesn't matter!• Cosmic matter-energy budget:
Dark Energy
Dark Matter
Dark Baryons
Visible Matter
Dark Neutrinos
8/3/2019 Wayne Hu- Dark Energy in Light of the CMB
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CMB Cornerstone
• CMB temperature and polarization measures provide the high
redshift cornerstone to cosmological inferences on the dark matter and dark energy
WMAP: Bennett et al (2003)
Multipole moment (l)
l ( l
+ 1 ) C
l
/ 2 π
( µ K 2 )
Angular Scale
0
0
1000
2000
3000
4000
5000
6000
10
90 2 0.5 0.2
10040 400200 800 1400
Model
WMAP
CBI
ACBAR
TT Cross PowerSpectrum
8/3/2019 Wayne Hu- Dark Energy in Light of the CMB
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Is H0 Interesting?
• WMAP infers that in a flat Λ cosmology H0=72±5
• Key project measures H0=72±8• Are local H0 measurements still interesting?
8/3/2019 Wayne Hu- Dark Energy in Light of the CMB
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Is H0 Interesting?
• WMAP infers that in a flat Λ cosmology H0=72±5
• Key project measures H0=72±8• Are local H0 measurements still interesting?
• YES!!!
• CMB best measures only high-z quantites:
distance to recombination
energy densities and hence expansion rate at high z
8/3/2019 Wayne Hu- Dark Energy in Light of the CMB
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Is H0 Interesting?
• WMAP infers that in a flat Λ cosmology H0=72±5
• Key project measures H0=72±8• Are local H0 measurements still interesting?
• YES!!!
• CMB best measures only high-z quantites:
distance to recombination
energy densities and hence expansion rate at high z
• CMB observables then predict H0 for a given hypothesis about the dark energy (e.g. flat Λ)
• Consistency with measured value is strong evidence for dark energy
and in the future can reveal properties such as its equation of state
if H0 can be measured to percent precision
8/3/2019 Wayne Hu- Dark Energy in Light of the CMB
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CMB Acoustic Oscillations
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In the Beginning...
Hu & White (2004); artist:B. Christie / SciAm
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Gravitational Ringing
• Potential wells = inflationary seeds of structure
• Fluid falls into wells, pressure resists: acoustic
oscillations
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Seeing Sound
• Oscillations frozen at recombination
• Compression=hot spots, Rarefaction=cold spots
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Peaks in Angular Power
• The Anisotropy Formation Process
8/3/2019 Wayne Hu- Dark Energy in Light of the CMB
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Extrema=Peaks
• First peak = mode that just compresses
• Second peak = mode that compresses then rarefies
Θ+Ψ
∆ T / T
−|Ψ|/3Second
Peak
Θ+Ψ
time time
∆ T / T
−|Ψ|/3
Recombination Recombination
First
Peak
k 2=2k 1k 1=π/ soundhorizon
• Third peak = mode that compresses then rarefies then compresses
8/3/2019 Wayne Hu- Dark Energy in Light of the CMB
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Peak Location• Fundmental physical scale, the distance sound travels, becomes an
angular scale by simple projection according to the angulardiameter distance DA
θA = λA/DA
A = kADA
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Peak Location• Fundmental physical scale, the distance sound travels, becomes an
angular scale by simple projection according to the angulardiameter distance DA
θA = λA/DA
A = kADA
• In a at universe, the distance is simply DA= D ≡ η 0− η∗ ≈ η0, the
horizon distance, and kA = π/s∗ =√3π/η∗ so
θA ≈η∗
η0
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Peak Location• Fundmental physical scale, the distance sound travels, becomes an
angular scale by simple projection according to the angulardiameter distance DA
θA = λA/DA
A = kADA
• In a at universe, the distance is simply DA= D ≡ η 0− η∗ ≈ η0, the
horizon distance, and kA = π/s∗ =√3π/η∗ so
θA ≈η∗
η0
• In a matter-dominated universe η ∝ a1/2 so θA ≈ 1/30 ≈ 2 or
A≈200
8/3/2019 Wayne Hu- Dark Energy in Light of the CMB
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CMB & the Dark Energy• Universe is neither fully matter dominated at recombination nor at
the present due to radiation and dark energy
• Given a recombination epoch a∗ (depends mainly on temperature
and atomic physics) calculate the sound horizon
s∗ ≡ csdη = a∗
0
dacs
a2
H note that this depends mainly on the expansion rate H at a∗, i.e.
the matter-radiation ratio and secondarily on the baryon-photon ratio.
• Given a dark energy model, calculate the comoving distance to a∗
D =
1
a∗
da1
a2H
• Given a curvature calculate the angular diameter distance
DA = R sin(D/R)
8/3/2019 Wayne Hu- Dark Energy in Light of the CMB
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Dark Energy in the Power Spectrum
• Features scale with angular diameter distance
• Small shift but angle already measured to <1%
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Calibrating Standard Ruler
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Baryon & Inertia
• Baryons add inertia to
the fluid
• Equivalent to adding mass
on a spring
• Same initial conditions
• Same null in fluctuations
• Unequal amplitudes of
extrema
8/3/2019 Wayne Hu- Dark Energy in Light of the CMB
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time
∆ T
Low Baryons
–
A Baryon-meter
• Low baryons: symmetric compressions and
rarefactions
8/3/2019 Wayne Hu- Dark Energy in Light of the CMB
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time
∆ T
Baryon Loading
–
A Baryon-meter
• Load the fluid adding to gravitational force
• Enhance compressional peaks (odd) over
rarefaction peaks (even)
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time
|
|
∆ T
A Baryon-meter
• Enhance compressional peaks (odd) over
rarefaction peaks (even)
e.g. relative suppression of second peak
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Baryons in the Power Spectrum
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Radiation and Dark Matter
• Radiation domination:
potential wells created by CMB itself
• Pressure support⇒ potential decay⇒ driving
• Heights measures when dark matter dominates
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Driving Effects and Matter/Radiation
• Potential perturbation: k 2Ψ = –4πGa2δρ generated by radiation
• Radiation → Potential: inside sound horizon δρ / ρ pressure supported
δρ hence Ψ decays with expansion
Θ+Ψ
−Ψ
η
∆ T / T
Hu & Sugiyama (1995)
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Driving Effects and Matter/Radiation
• Potential perturbation: k 2Ψ = –4πGa2δρ generated by radiation
• Radiation → Potential: inside sound horizon δρ / ρ pressure supported
δρ hence Ψ decays with expansion
• Potential → Radiation: Ψ–decay timed to drive oscillation
–2Ψ + (1/3)Ψ = –(5/3)Ψ → 5x boost
• Feedback stops at matter domination
Θ+Ψ
−Ψ
η
∆ T / T
Hu & Sugiyama (1995)
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Driving Effects and Matter/Radiation
• Potential perturbation: k 2Ψ = –4πGa2δρ generated by radiation
• Radiation → Potential: inside sound horizon δρ / ρ pressure supported
δρ hence Ψ decays with expansion
• Potential → Radiation: Ψ–decay timed to drive oscillation
–2Ψ + (1/3)Ψ = –(5/3)Ψ → 5x boost
• Feedback stops at matter domination
Θ+Ψ
−Ψ
η
∆ T / T
Hu & Sugiyama (1995)
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Dark Matter in the Power Spectrum
8/3/2019 Wayne Hu- Dark Energy in Light of the CMB
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Fixing the Past; Changing the Future
8/3/2019 Wayne Hu- Dark Energy in Light of the CMB
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Fixed Deceleration Epoch• CMB determination of matter density controls all determinations
in the deceleration (matter dominated) epoch
• Current status: Ωmh2 = 0.14± 0.01 → 7%
• Distance to recombination D∗ determined to 1
47% ≈ 2%
• Expansion rate during any redshift in the deceleration epoch
determined to 7%
• Distance to any redshift in the deceleration epoch determined as
D(z) = D∗ − z∗
z
dz
H (z)• Volumes determined by a combination dV = D2
AdΩdz/H (z)
• Structure also determined by growth of fluctuations from z∗
• Ωmh2 can be determined to ∼ 1% in the future.
8/3/2019 Wayne Hu- Dark Energy in Light of the CMB
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Value of Local Measurements• With high redshifts xed, the largest deviations from the dark
energy appear at low redshift z ∼ 0
• By the Friedman equation H 2 ∝ ρ and difference between H (z)
extrapolated from the CMB H 0 = 37 and 72 is entirely due to the
dark energy in a at universe
•
With the dark energy density xed by H 0, the deviation from theCMB observed D∗ from the ΛCDM prediction measures the
equation of state (or evolution of the dark energy density)
pDE = wρDE
• Intermediate redshift dark energy probes can then test atness
assumption and the evolution of the equation of state: e.g.
w(a) = w0 + (1 − a)wa
8/3/2019 Wayne Hu- Dark Energy in Light of the CMB
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H 0 = Dark Energy
• Flat constant w dark energy model
• Determination of Hubble constant gives w to comparable precision
• For evolving w, equal precision on average or pivot w, equally
useful for testing a cosmological constant
-1
0.7
0.6
0.5
-0.8 -0.6 -0.4wDE
ΩDE
h
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Forecasts for CMB+ H 0
• To complement CMB observations with Ωmh2 to 1%, an H 0 of
~1% enables constant w measurement to ~2% in a flat universe
σ(ln H 0) prior
σ ( w )
Planck: σ(lnΩmh2)=0.009
0.010.01
0.1
0.1
8/3/2019 Wayne Hu- Dark Energy in Light of the CMB
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Sensitivity in Redshift
• Fixed distance to recombination DA( z~1100)
• Fixed initial fluctuation G
( z
~1100)• Constant w=wDE; (ΩDE adjusted - one parameter family of curves)
∆ DA /DA
∆G/G
∆ H -1 /H -1
∆wDE=1/3
0.1
0
0.1
0.2
-0.2
-0.1
1 z
8/3/2019 Wayne Hu- Dark Energy in Light of the CMB
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Sensitivity in Redshift
• SNIa high-z distance useful because it fixes the Hubble constant!
deceleration
epoch measures
Hubble constant
∆ DA /DA
∆( H 0 DA) /H 0 DA
∆ H 0
/H 0∆G/G
∆ H -1 /H -1
∆wDE=1/3
0.1
0
0.1
0.2
-0.2
-0.1
1 z
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Evolution of the Dark Energy
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Beyond Testing Λ• In the context of testing a cosmological constant, constraining a
constant w in a at universe is the most important rst test.
• CMB measurements are best complemented by H 0.
• A deviation between the CMB predicted H 0 and its measured
value in the form of a constant w = 1 is evidence against a at
ΛCDM model.
• However it does not necessarily indicate a constant w = 1 at
model is correct! w is measured as its average or pivot value, a
small spatial curvature can change the expansion rate.
• A positive detection of deviations from ΛCDM will require more
than H 0 to determine its physical origin.
• Investigate the role of H 0 planning for success...
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Sensitivity in Redshift
• Three parameter dark energy model: w( z=0)=w0; wa=-dw /da; ΩDE
•w
a sensitivity; (fixedw
0 = -1;Ω
DE adjusted)
deceleration
epoch measures
Hubble constant
∆ DA /DA
∆( H 0 DA) /H 0 DA
∆ H 0 /H 0∆G/G
∆ H -1 /H -1
∆wa=1/2; ∆w0=0
0.1
0
0.1
0.2
-0.2
-0.1
1 z
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D k E S i i i
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Dark Energy Sensitivity
• H 0 fixed (or ΩDE); remaining wDE-ΩT spatial curvature degeneracy
• Growth rate breaks the degeneracy anywhere in the accelerationregime including local measurements!
deceleration
epoch measures
Hubble constant
∆ DA /DA
∆( H 0 DA) /H 0 DA
∆G/G
∆ H -1 /H -1
0.1
0
0.01
0.02
-0.02
-0.01
1 z
∆wDE=0.05; ∆ΩT=-0.0033
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Supernovae
i f A l i
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Discovery of Acceleration• Distance-redshift to supernovae Ia indicates cosmological
dimming (acceleration)
compilation from High-z team
Supernova Cosmology Project
34
36
38
40
42
44
Ωm=0.3, ΩΛ=0.7
Ωm=0.3, ΩΛ=0.0
Ωm=1.0, ΩΛ=0.0
m
- M ( m
a g )
High-Z SN Search Team
0.01 0.10 1.00z
-1.0
-0.5
0.0
0.5
1.0
∆ ( m - M )
( m a g )
F f CMB H SNI
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Forecasts for CMB+ H 0+SNIa
• Supernova Ia (2000 out to z=1) with curvature marginalized
statistical errors only
w0
w a
-1.2
-0.4
-0.2
0
0.2
0.4
-1.0 -0.8
11%
3%
1%
H0
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Baryon Acoustic Oscillations
C l i l Di t
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Cosmological Distances
• Modes perpendicular to line of sight measure angular diameter
distance
Local: Eisenstein, Hu, Tegmark (1998) Cosmological: Cooray, Hu, Huterer, Joffre (2001)
k (Mpc–1)
0.05
2
4
6
8
0.1
P o w e r
Observed
l D A-1
CMB provided
D A
C l i l Di t
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Cosmological Distances
• Modes parallel to line of sight measure the Hubble parameter
Eisenstein (2003); Blake & Glazebrook (2003); Hu & Haiman (2003); Seo & Eisenstein (2003)
k (Mpc–1)
0.05
2
4
6
8
0.1
P o w e r
Observed
H/ ∆z
CMB provided
H
BAO D t ti i SDSS
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BAO Detection in SDSS
• Baryon oscillations detected in 2-pt correlation function
Eisenstein et al (2005)
F t f CMB H BAO
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Forecasts for CMB+ H 0+BAO
• Baryon oscillations (2000deg2 out to z=1.3 with spectroscopy)
with curvature marginalized statistical errors only
w0
w a
-1.2
-0.4
-0.2
0
0.2
0.4
-1.0 -0.8
11%
3%
1%
H0
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Cluster Abundance
Cl t Ab d
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Cluster Abundance
• Abundance of rare massive dark matter halos exponentially sensitive
to the growth of structure
• Dark energy constraints if clusters can be mapped onto halos
0.001
0.01
0.1
1
10
1011 1012 1013 1014 1015
M h (h-1 M )
M *
ρ0
dnh
d ln M h N ( M h)
ms
As
M th
σln M
z=0
Forecasts for CMB+H +Cl sters
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Forecasts for CMB+ H 0+Clusters
• Galaxy clusters (4000deg2 out to z=2 with photometric redshifts)
with curvature marginalized statistical errors only
w0
w a
-1.2
-0.4
-0.2
0
0.2
0.4
-1.0 -0.8
11%
3%
1%
H0
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Weak Gravitational Lensing
Lensing Observables
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Lensing Observables
• Correlation of shear distortion of background images: cosmic shear
•Cross correlation between foreground lens tracers and shear:
galaxy-galaxy lensing
cosmic
shear
galaxy-galaxy lensing
Halos and Shear
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Halos and Shear
Forecasts for CMB+H0+Lensing
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Forecasts for CMB+ H 0+Lensing
• Weak lensing (4000deg2 out to zmed=1 with photometric redshifts)
with curvature marginalized
w0
w a
-1.2
-0.4
-0.2
0
0.2
0.4
-1.0 -0.8
11%
3%
1%
H0
Prospects for Percent H0
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1500 13001400
1
2
3
4
0
F l u x D e n s i t y ( J y )
550 450 -350 -450
0.1 pc
2.9 mas
10 5 0 -5 -10Impact Parameter (mas)
-1000
0
1000
2000
L O S V e l o c i t y ( k m / s ) Herrnstein et al (1999)
NGC4258
Prospects for Percent H0
• Improving the distance ladder with SNIa (~3%, Riess 2005)
• Water maser proper motion, acceleration (~3%, VLBA Condon & Lo 2005; ~1% SKA, Greenhill 2004)
• Gravity wave sirens (~2% - 3x Adv. LIGO + GRB sat, Dalal et al 2006)
• Combination of dark energy tests: e.g. SNIa relative distances:
H 0 D( z) and baryon acoustic oscillations D( z)
Summary
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Summary
• CMB fixes energy densities, expansion rate and distances in the
deceleration epoch
• Strongest deviations due to the dark energy appear locally at z=0
• The single best complement to the CMB observables is H 0
for a flat cosmology in determining deviations in the equation of state from a cosmological constant
• Precision in H 0 equal to CMBΩmh2 optimal: 1% (masers, gw,..?)
• H 0 also improves the ability of any single intermediate redshift dark energy probe (SNIa, BAO, Clusters, WL) to measure the
evolution in the equation of state even in the SNAP/LST era
• Combinations of dark energy probes can themselves indirectly
d i H0
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