Observational constraints and cosmological parameters

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Observational constraints and cosmological
parameters
Antony Lewis Institute of Astronomy,
Cambridge http//cosmologist.info/
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CMB PolarizationBaryon oscillations Weak
lensing Galaxy power spectrum Cluster gas
fraction Lyman alpha etc

Cosmological parameters
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Bayesian parameter estimation

• Can compute P( ? data) using e.g. assumption
  of Gaussianity of CMB field and priors on
  parameters
• Often want marginalized constraints. e.g.

• BUT Large n-integrals very hard to compute!
• If we instead sample from P( ? data) then it
  is easy

Use Markov Chain Monte Carlo to sample
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Markov Chain Monte Carlo sampling

• Metropolis-Hastings algorithm
• Number density of samples proportional to
  probability density
• At its best scales linearly with number of
  parameters(as opposed to exponentially for brute
  integration)

• Public WMAP3-enabled CosmoMC code available at
  http//cosmologist.info/cosmomc (Lewis, Bridle
  astro-ph/0205436)
• also CMBEASY AnalyzeThis

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WMAP1 CMB data alonecolor optical depth
Samples in6D parameterspace
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Local parameters
Background parameters and geometry

• Energy densities/expansion rate Om h2, Ob
  h2,a(t), w..
• Spatial curvature (OK)
• Element abundances, etc. (BBN theory -gt ?b/??)
• Neutrino, WDM mass, etc

• When is now (Age or TCMB, H0, Om etc. )

Astrophysical parameters

• Optical depth tau
• Cluster number counts, etc..

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General perturbation parameters
-isocurvature-
Amplitudes, spectral indices, correlations
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WMAP 1
CMB Degeneracies
WMAP 3
All
TT
ns lt 1 (2 sigma)
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Main WMAP3 parameter results rely on polarization
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CMB polarization
Page et al.
No propagation of subtraction errors to
cosmological parameters?
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WMAP3 TT with tau 0.10 0.03 prior (equiv to
WMAP EE)
Black TTpriorRed full WMAP
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ns lt 1 at 3 sigma (no tensors)?
Rule out naïve HZ model
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Secondaries that effect adiabatic spectrum ns
constraint
SZ Marginazliation
Spergel et al.
Black SZ marge Red no SZ
Slightly LOWERS ns
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CMB lensing
For Phys. Repts. review see
Lewis, Challinor astro-ph/0601594
Theory is robust can be modelled very accurately
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CMB lensing and WMAP3
Black withred without - increases ns
not included in Spergel et al analysisopposite
effect to SZ marginalization
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LCDMTensors

• No evidence from tensor modes
• is not going to get much betterfrom TT!

ns lt 1 or tau is high or there are tensors or the
model is wrong or we are quite unlucky
So
ns 1
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CMB Polarization
Current 95 indirect limits for LCDM given
WMAP2dFHSTzregt6
WMAP1ext
WMAP3ext
Lewis, Challinor astro-ph/0601594
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Polarization only useful for measuring tau for
near future Polarization probably best way to
detect tensors, vector modes Good consistency
check
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Matter isocurvature modes

• Possible in two-field inflation models, e.g.
  curvaton scenario
• Curvaton model gives adiabatic correlated CDM
  or baryon isocurvature, no tensors
• CDM, baryon isocurvature indistinguishable
  differ only by cancelling matter mode

Constrain B ratio of matter isocurvature to
adiabatic
-0.53ltBlt0.43
-0.42ltBlt0.25
WMAP32dfCMB
WMAP12dfCMBBBNHST
Gordon, Lewis astro-ph/0212248
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Degenerate CMB parameters
Assume Flat, w-1
WMAP3 only
Use other data to break remaining degeneracies
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Galaxy lensing

• Assume galaxy shapes random before lensing

Lensing

• In the absence of PSF any galaxy shape estimator
  transforming as an ellipticity under shear is an
  unbiased estimator of lensing reduced shear
• Calculate e.g. shear power spectrum constrain
  parameters (perturbationsangular at late times
  relative to CMB)
• BUT- with PSF much more complicated- have to
  reliably identify galaxies, know redshift
  distribution- observations messy (CCD chips,
  cosmic rays, etc)- May be some intrinsic
  alignments- not all systematics can be
  identified from non-zero B-mode shear- finite
  number of observable galaxies

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CMB (WMAP1ext) with galaxy lensing (BBN prior)
CFTHLS
Contaldi, Hoekstra, Lewis astro-ph/0302435
Spergel et al
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SDSS Lyman-alpha
white LUQAS (Viel et al)SDSS (McDonald et al)
The Lyman-alpa plots I showed were wrong
SDSS, LCDM no tensors ns 0.965 0.015 s8
0.86 0.03 ns lt 1 at 2 sigma
LUQAS
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Conclusions

• MCMC can be used to extract constraints quickly
  from a likelihood function
• CMB can be used to constrain many parameters
• Some degeneracies remain combine with other
  data
• WMAP3 consistent with many other probes, but
  favours lower fluctuation power than lensing,
  ly-alpha
• ns lt1, or something interesting
• No evidence for running, esp. using small scale
  probes