Transcript BBN: elements CMB weak lens supernova galaxy surveys P_k

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
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.
 1 | data   1 P(1 2 3 ... n | data )d1d 2 ..d n
• BUT: Large n-integrals very hard to compute!
• If we instead sample from P( {ө} | data) then it is easy:
1
 1 | data  
N

1(i )
i
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
Samples in
6D parameter
space
WMAP1 CMB data
alone
color = optical depth
Background parameters and geometry
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•
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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…
Local parameters
• When is now (Age or TCMB, H0, Ωm etc. )
Astrophysical parameters
• Optical depth tau
• Cluster number counts, etc..
General perturbation parameters
General regular perturbation
Scalar
Adiabatic
-isocurvature-
(observed)
Matter density
Cancelling matter density
(unobservable in CMB)
Neutrino density
(contrived)
Neutrino velocity
(very contrived)
Vector
Neutrino vorticity
(very contrived)
Tensor
Gravitational waves
Amplitudes, spectral indices, correlations…
CMB Degeneracies
WMAP 3
WMAP 1
All
TT
ns < 1 (2 sigma)
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+prior
Red: full WMAP
ns < 1 at ~3 sigma (no tensors)?
Rule out naïve HZ model
Secondaries that effect adiabatic spectrum ns constraint
SZ Marginazliation
Spergel et al.
Black: SZ marge; Red: no SZ
Slightly LOWERS ns
CMB lensing
For Phys. Repts. review see
Lewis, Challinor : astro-ph/0601594
Theory is robust: can be modelled very accurately
CMB lensing and WMAP3
Black: with
red: without
- increases ns
not included in Spergel et al analysis
opposite effect to SZ marginalization
LCDM+
Tensors
No evidence from tensor modes
-is not going to get much better
from TT!
So:
ns =1
ns < 1
or tau is high
or there are tensors
or the model is wrong
or we are quite unlucky
CMB Polarization
Current 95% indirect limits for LCDM given WMAP+2dF+HST+zre>6
WMAP1ext
Lewis, Challinor : astro-ph/0601594
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
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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
-0.53<B<0.43
WMAP1+2df+CMB+BBN+HST
Gordon, Lewis: astro-ph/0212248
-0.42<B<0.25
WMAP3+2df+CMB
Degenerate CMB parameters
Assume Flat, w=-1
WMAP3 only
Use other data to break
remaining 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
CMB (WMAP1ext) with galaxy lensing (+BBN prior)
CFTHLS
Contaldi, Hoekstra, Lewis: astro-ph/0302435
Spergel et al
SDSS Lyman-alpha
The Lyman-alpa plots I showed
were wrong
LUQAS
white: LUQAS (Viel et al)
SDSS (McDonald et al)
SDSS, LCDM no tensors:
ns = 0.965 ± 0.015
s8 = 0.86 ± 0.03
ns < 1 at 2 sigma
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