cosmological parameters and the wmap data antony lewis cfa, harvard / cita, toronto standard...
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Cosmological Parameters and the WMAP data
Antony LewisCfA, Harvard / CITA, Toronto
http://cosmologist.info
• Standard assumptions – what are the parameters?
• Unexpected features, validity of assumptions?
• Low quadrupole, cut-off/running/dark energy• Asymmetries• ‘features’ of WMAP analysis
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MCMC sampling for parameter estimation
• MCMC sample points in cosmological parameter space drawn from the posterior distribution given the data P(parameters|data)
• Each sample gives an equally likely set of parameters given the data. “possible universes”
• Number density of samples proportional to probability density
• Just requires a function to compute likelihood for each set of parameters
• CosmoMC code at http://cosmologist.info/cosmomc uses CAMB (http://camb.info) to generate Cl
• Lewis, Bridle: astro-ph/0205436
Samples.py
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Cosmological Parameters:combining CMB+Weak Lensing
Contaldi, Hoekstra, Lewis: astro-ph/0302435
WMAP+ACBAR+CBI+VSA with RCS + weak BBN prior
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Vanilla Universe marginalized parameter constraints
Good agreement with more conservative independent CMB+2dF analysis
006.0144.0~2 hm
large compared to WMAPext+2dF (0.134±0.006)
flat, massless neutrinos, cosmological constant, power law power spectrum, …
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WMAP TT power spectrum at low l
Pseudo-Cl data points from http://lambda.gsfc.nasa.gov/
compared to theoretical power law model (mean over realizations)
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Low quadrupole?
Standard models
Observed
Likelihood of theoretical value given observed value
WMAP Pseudo-Cl: C2 = 123Tegmark cleaned map: C2 = 184(kp2 cut, Pseudo-Cl estimator on map from astro-ph/0302496)
Foreground uncertainty:
Likelihood modelling:
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Running ns?WMAP+CMB+2dF, with and without l =2,3,4 multipoles
Low quadrupole and octopole drive ~1 sigma evidence for running
Need small scale data more reliable than Lyman-α
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Cut-off in initial power spectrum?
P(k)=0 for k<kc ~ 3 x 10-4 Mpc-1
Slightly favoured by the data
Does not give very low quadrupolebecause of ISW contribution from larger k>kc
Bridle, Lewis, Weller, Efstathiou: astro-ph/0302306
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Contributions to the quadrupole
ISW
Last scattering
k MPc
Total
Δk
22 ||)(~ kkPC
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Changing ISW is tricky…
E.g. Dark energy with w > -1,cs2 <1 or
w<-1, cs2≥1 give less ISW than
cosmological constant
Weller, Lewis: astro-ph/0307104 Bean, Doré: astro-ph/0307100
No simple theoretical modelgives a very low quadrupole
The low value is not that unlikelyin a realisation of a standard model
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P(k) on smaller scales
Bridle, Lewis, Weller, Efstathiou: astro-ph/0302306
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Asymmetry of low multipoles?• after Eriksen et al
astro-ph/0307507:
l <~31 shows unlikely asymmetry:evaluate binned Cl on half sky as a function of axis: the lowest ratio of power on opposite two halves is small compared to simulations. Low power in N ecliptic hemisphere.
• Also astro-ph/0307282 find quadrupole and octopole alignment is unlikely at 1/60 level
Samples.py
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WMAP is great, but…• Foreground uncertainties significant at low l
– e.g. different analyses of TE power spectrum. Foreground uncertainties not included in likelihoods
• Pseudo-Cl estimators combined with maximum likelihood error bars not strictly correct
• Noise not included in TT likelihood at l<100, even though larger at l~<100 than l>~100
• Significant correlation between TT and TE power spectra neglected – bias on e.g.
• Likelihood approximation not valid for outlier points
• Is it valid to do parameter estimation with usual assumptions when Cl not consistent with Gaussian expectations? Do outliers bias results? ...
Versions of TE power spectrum
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Conclusions
• Standard ΛCDM cosmology fits the overall shape of the WMAP power spectrum and is consistent with other data
• Low quadrupole is not that unlikely in standard models, but favours models predicting low values by factor <~ 10
• Outlier points/asymmetries – quite strong evidence for analysis problems, foregrounds, or new physics
• Parameter constraints from naïve analysis may be misleading – should really understand unexpected features first.
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In two bins…
1<l<18
17<l<31
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No power in northern hemisphere 3-point function?
Eigenmodes:
Measured andmarginalized errorsfrom simulations: