CMB: Sound Waves in the Early Universe · 2010. 12. 10. · CMB: Sound Waves in the Early Universe...
Transcript of CMB: Sound Waves in the Early Universe · 2010. 12. 10. · CMB: Sound Waves in the Early Universe...
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CMB: Sound Waves in the Early Universe Before recombination:
Universe is ionized. Photons provide enormous
pressure and restoring force. Photon-baryon perturbations
oscillate as acoustic waves.
After recombination: Universe is neutral. Photons can travel freely
past the baryons. Phase of oscillation at trec
affects late-time amplitude.
Today
Recombination & Last scattering
z ~ 1000 ~400,000 years
Ionized Neutral
Time
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Acoustic Oscillations in the CMB
Although there are fluctuations on all scales, there is a characteristic angular scale, ~ 1 degree on the sky, set by the distance sound waves in the photon-baryon fluid can travel just before recombination: sound horizon ~ cstls
Temperature map of the cosmic microwave background radiation
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WMAP
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Sound Waves Each initial overdensity (in dark
matter & gas) is an overpressure that launches a spherical sound wave.
This wave travels outwards at �57% of the speed of light.
Pressure-providing photons decouple at recombination. CMB travels to us from these spheres.
Eisenstein
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Standard ruler
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CMB
Hu Angular scale subtended by s
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Geometry of three-dimensional space
K>0 K=0 K<0
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CMB Maps
s θ
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Angular positions of acoustic peaks probe spatial curvature of the Universe
Hu ~1/θ
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Microwave Background Anisotropy�Probes Spatial Curvature
Boomerang (2001) Netterfield et al DASI (2001) Pryke et al
Data indicates nearly flat geometry if w =-1
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CMB Results
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WMAP3 Results
assuming w=-1
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as changing ΩDE
Assuming k=0
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=1-Ωm
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CMB shift parameter
CMB anisotropy constraint on Angular Diameter distance to last-scattering well approximated by:
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R = ΩmH02( )1/ 2 dz
H(z)0
zLS
∫ =1.715 ± 0.021
zLS =1089WMAP5 results Komatsu etal 2008
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SDSS only:
Nearby+SDSS:
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w = −0.92 ± 0.11(stat)−0.15+0.07(syst)
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w = −0.93± 0.13(stat)−0.32+0.10(syst)
SALT
MLCS
SALT
MLCS
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ΩM
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Standard ruler
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The Structure Formation Cookbook
1. Initial Conditions: A Theory for the Origin of Density Perturbations in the Early Universe Primordial Inflation: initial spectrum of density perturbations
2. Cooking with Gravity: Growing Perturbations to Form Structure Set the Oven to Cold (or Hot or Warm) Dark Matter Season with a few Baryons and add Dark Energy
3. Let Cool for 13 Billion years Turn Gas into Stars
4. Tweak (1) and (2) until it tastes like the observed Universe.
Pm(k)~kn, n~1
Pm(k)~T(k)kn
Pg(k)~b2(k)T(k)kn
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Cold Dark Matter Models
Power Spectrum of the Mass Density
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δ k( ) = d3∫ x ⋅ ei k ⋅ x δρ x( )
ρ
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δ k1( )δ k2( ) =
2π( )3P k1( )δ 3 k 1 + k 2( )
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Cold Dark Matter Models Theoretical Power Spectrum of the Mass Density
Ωmh =0.5
Ωmh =0.2 P ~ kn
P ~ k–3
keq ~ Ωmh
h/Mpc Non-linear Linear
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δ k( ) = d3∫ x ⋅ ei k ⋅ x δρ x( )
ρ
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δ k1( )δ k2( ) =
2π( )3P k1( )δ 3 k 1 + k 2( )
Power spectrum measurements probe cosmological parameters
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Sound Waves again Each initial overdensity (in dark matter &
gas) is an overpressure that launches a spherical sound wave.
This wave travels outwards at �57% of the speed of light.
Pressure-providing photons decouple at recombination. CMB travels to us from these spheres.
Sound speed plummets. Wave stalls at a radius of 150 Mpc.
Overdensity in shell (gas) and in the original center (DM) both seed the formation of galaxies. Preferred separation of 150 Mpc.
Eisenstein
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A Statistical Signal The Universe is a super-
position of these shells. The shell is weaker than
displayed. Hence, you do not expect to
see bulls’ eyes in the galaxy distribution.
Instead, we get a 1% bump in the correlation function.
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Origin of Baryon Acoustic Oscillations (BAO)
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Collision Term
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sound horizon scale
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kA=2π/s
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Simulation
plus Poisson errors: multiply by (1+1/nP)2
Assumes Gaussian errors (linear theory)
Fit with::
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Power Spectrum
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Correlation Function
Measure redshifts and angular positions
Convert to comoving separation using redshift-distance relation
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Dependence on w
Tangential Radial
Assuming constant Ωm
Measure kA to 1% plus known s yields w to ~5%
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SDSS Galaxy Distribution
SDSS Galaxy Distribution
Luminous Red Galaxies
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Large-scale Correlations of �SDSS Luminous Red Galaxies
Warning: Correlated Error Bars Eisenstein, etal
Redshift-space Correlation Function
Baryon Acoustic Oscillations seen in Large-scale Structure
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ξ(r) =
δ( x )δ( x + r )
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Model Comparison
Equality scale depends on (Ωmh2)-1.
Acoustic scale depends on (Ωmh2)-0.25.
Ωmh2 = 0.12
Ωmh2 = 0.13
Ωmh2 = 0.14
CDM with baryons is a good fit: χ2 = 16.1 with 17 dof. Pure CDM rejected at Δχ2 = 11.7
Ωbh2 = 0.00
Fixed Ωbh2=0.024 ns=0.98, flat
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Constraints
Spherically averaged correlation function probes
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DV (z) = (1+ z)2dA2 (z) cz
H(z)
1/ 3
SDSS : DV (z = 0.35) =1370 ± 64 MpcR0.35 = DV (0.35) /dA (zLS ) = 0.0979 ± 0.0036
A = DV (0.35)ΩmH0
2
0.35c= 0.469 ± 0.017
Eisenstein etal 2005
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Galaxy pair with separations Δz, Δθ :Δrc = cΔz /H(z) radial comoving separationΔrc = Δθ(1+ z)dA angular comoving separation
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SDSS only:
Nearby+SDSS:
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w = −0.92 ± 0.11(stat)−0.15+0.07(syst)
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w = −0.93± 0.13(stat)−0.32+0.10(syst)
SALT
MLCS
SALT
MLCS
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ΩM
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BAO from SDSS + 2dFGRS BAO detected at low redshift 0<z<0.3 (effective redshift 0.2) SDSS main + 2dFGRS
BAO detected at high redshift 0.15<z<0.5 (effective redshift 0.35) SDSS LRGs
BAO from combined sample (detected over the whole redshift range 0<z<0.5) All SDSS + 2dFGRS
Percival et al. 2007
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DV (z = 0.35)DV (z = 0.2)
=1.812 ± 0.060
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Cosmological constraints: BAO
Constraint from DV(0.35)/DV(0.2)
Constraint fitting s/DV with model for s
Constraint including distance to CMB dA(zLS)/DV
Consider two simple models: 1. ΛCDM 2. Flat, constant w
Percival et al. 2007
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Galaxy Clustering varies with Galaxy Type
How are each of them related to the underlying Dark Matter distribution?
BIAS
Caveat for inference of Cosmological Parameters from LSS
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Galaxy Clustering as a function of Galaxy Luminosity
bright
faint
Zehavi, etal Tegmark, etal Based on sample of ~200,000 galaxies
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Correct For Luminosity Bias
Vertical Shift: Constant Bias
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δngal L, x ( )ngal L( )
= b L( )δρ x ( )ρ
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Systematic Issues for BAO
Effects of non-linearities on BAO signal
Modeling redshift distortions precisely
Effects of (non-linear) galaxy bias
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Halos vs. Dark Matter
Real Space
Redshift Space
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III. Baryon Acoustic Oscillations
Systematics: photo-z’s, correlated photometric errors, non-linearity, scale-dependent bias
Fosalba & Gaztanaga
Galaxy Angular Correlation Function in Photo-z bins
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III. Baryon Acoustic Oscillations
Blake & Bridle
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DES Science Program Four Probes of Dark Energy • Galaxy Clusters
• ~100,000 clusters to z>1 • ~10,000 with SZE measurements from SPT • Sensitive to growth of structure and geometry
• Weak Lensing • Shape measurements of 300 million galaxies • Sensitive to growth of structure and geometry
• Baryon Acoustic Oscillations • 300 million galaxies to z = 1 and beyond • Sensitive to geometry
• Supernovae • 15 sq deg time-domain survey • ~3000 well-sampled SNe Ia to z ~1 • Sensitive to geometry
Forecast Constraints on DE Equation of State
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Photometric Redshifts
• Measure relative flux in multiple filters: track the 4000 A break
• Estimate individual galaxy redshifts with accuracy σ(z) < 0.1 (~0.02 for clusters)
• Precision is sufficient for Dark Energy probes, provided error distributions well measured.
Elliptical galaxy spectrum
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DES griz DES
10σ Limiting Magnitudes g 24.6 r 24.1 i 24.0 z 23.9
+2% photometric calibration error added in quadrature
Photo-z systematic errors under control using existing spectroscopic training sets to DES photometric depth: low-risk
Galaxy Photo-z Simulations
+VHS*
+Developed improved Photo-z & Error Estimates and robust methods of outlier rejection Oyaizu, Cunha, Lima, Frieman, Lin
DES griZY +VHS JHKs on ESO VISTA 4-m enhances science reach
*Vista Hemisphere Survey
Z 23.8 Y 21.6
J 20.3 H 19.4 Ks 18.3