observational constraints and cosmological parameters
DESCRIPTION
Observational constraints and cosmological parameters. Antony Lewis Institute of Astronomy, Cambridge http://cosmologist.info/. CMB Polarization Baryon oscillations Weak lensing Galaxy power spectrum Cluster gas fraction Lyman alpha etc…. +. Cosmological parameters. - PowerPoint PPT PresentationTRANSCRIPT
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Observational constraints and cosmological parameters
Antony LewisInstitute of Astronomy, Cambridge
http://cosmologist.info/
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CMB PolarizationBaryon oscillationsWeak lensingGalaxy power spectrumCluster gas fractionLyman alphaetc…
+
Cosmological parameters
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Bayesian parameter estimation
• Can compute P( {ө} | data) using e.g. assumption of Gaussianity of CMB field and priors on parameters
• Often want marginalized constraints. e.g.
nn ddddataPdata ..)|...(| 2132111
• BUT: Large n-integrals very hard to compute!
• If we instead sample from P( {ө} | data) then it is easy:
)(11
1| i
iNdata
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 alone
color = optical depth
Samples in6D parameterspace
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Local parameters• When is now (Age or TCMB, H0, Ωm etc. )
Background parameters and geometry• Energy densities/expansion rate: Ωm h2, Ωb h2,a(t), w..
• Spatial curvature (ΩK)
• Element abundances, etc. (BBN theory -> ρb/ργ)
• Neutrino, WDM mass, etc…
Astrophysical parameters
• Optical depth tau• Cluster number counts, etc..
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General regular perturbation
Scalar
Vector
Tensor
Adiabatic(observed)
Matter density
Cancelling matter density(unobservable in CMB)
Neutrino vorticity(very contrived)
Gravitational waves
Neutrino density(contrived)
Neutrino velocity(very contrived)
General perturbation parameters
-iso
curv
atu
re-
Amplitudes, spectral indices, correlations…
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WMAP 1 WMAP 3
ns < 1 (2 sigma)
CMB Degeneracies
TTAll
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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: TT+priorRed: full WMAP
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ns < 1 at ~3 sigma (no tensors)?
Rule out naïve HZ model
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Black: SZ marge; Red: no SZ Slightly LOWERS ns
SZ Marginazliation
Spergel et al.
Secondaries that effect adiabatic spectrum ns constraint
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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 WMAP3Black: withred: without
- increases ns
not included in Spergel et al analysisopposite effect to SZ marginalization
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LCDM+Tensors
ns < 1or tau is highor there are tensorsor the model is wrongor we are quite unlucky
ns =1 So:
No evidence from tensor modes-is not going to get much betterfrom TT!
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Current 95% indirect limits for LCDM given WMAP+2dF+HST+zre>6
CMB Polarization
Lewis, Challinor : astro-ph/0601594
WMAP1ext WMAP3ext
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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
Gordon, Lewis: astro-ph/0212248
WMAP3+2df+CMB
-0.53<B<0.43
WMAP1+2df+CMB+BBN+HST
-0.42<B<0.25
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Assume Flat, w=-1WMAP3 only
Degenerate CMB parameters
Use other data to breakremaining 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 (perturbations+angular 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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Contaldi, Hoekstra, Lewis: astro-ph/0302435
CMB (WMAP1ext) with galaxy lensing (+BBN prior)
Spergel et al
CFTHLS
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SDSS Lyman-alpha
white: LUQAS (Viel et al)SDSS (McDonald et al)
SDSS, LCDM no tensors:ns = 0.965 ± 0.015s8 = 0.86 ± 0.03
ns < 1 at 2 sigma
LUQAS
The Lyman-alpa plots I showed were wrong
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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 <1, or something interesting
• No evidence for running, esp. using small scale probes