Post on 03-Feb-2016
description
Observational constraints and cosmological parameters
Antony LewisInstitute of Astronomy, Cambridge
http://cosmologist.info/
CMB PolarizationBaryon oscillationsWeak lensingGalaxy power spectrumCluster gas fractionLyman alphaetc…
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Cosmological parameters
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
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
WMAP1 CMB data alone
color = optical depth
Samples in6D parameterspace
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..
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…
WMAP 1 WMAP 3
ns < 1 (2 sigma)
CMB Degeneracies
TTAll
Main WMAP3 parameter results rely on polarization
CMB polarization
Page et al.
No propagation of subtraction errors to cosmological parameters?
WMAP3 TT with tau = 0.10 ± 0.03 prior (equiv to WMAP EE)
Black: TT+priorRed: full WMAP
ns < 1 at ~3 sigma (no tensors)?
Rule out naïve HZ model
Black: SZ marge; Red: no SZ Slightly LOWERS ns
SZ Marginazliation
Spergel et al.
Secondaries that effect adiabatic spectrum ns constraint
CMB lensing
For Phys. Repts. review see
Lewis, Challinor : astro-ph/0601594
Theory is robust: can be modelled very accurately
CMB lensing and WMAP3Black: withred: without
- increases ns
not included in Spergel et al analysisopposite effect to SZ marginalization
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!
Current 95% indirect limits for LCDM given WMAP+2dF+HST+zre>6
CMB Polarization
Lewis, Challinor : astro-ph/0601594
WMAP1ext WMAP3ext
Polarization only useful for measuring tau for near future
Polarization probably best way to detect tensors, vector modes
Good consistency check
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
Assume Flat, w=-1WMAP3 only
Degenerate CMB parameters
Use other data to breakremaining degeneracies
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
Contaldi, Hoekstra, Lewis: astro-ph/0302435
CMB (WMAP1ext) with galaxy lensing (+BBN prior)
Spergel et al
CFTHLS
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
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