Cosmological Parameters and the WMAP data Antony Lewis CfA, Harvard / CITA, Toronto Standard assumptions – what are the parameters? Unexpected features, validity of assumptions? Low quadrupole, cut-off/running/dark energy Asymmetries features of WMAP analysis

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 uses CAMB ( to generate C lhttp://cosmologist.info/cosmomchttp://camb.info Lewis, Bridle: astro-ph/

Cosmological Parameters: combining CMB+Weak Lensing Contaldi, Hoekstra, Lewis: astro-ph/ WMAP+ACBAR+CBI+VSA with RCS + weak BBN prior

Vanilla Universe marginalized parameter constraints Good agreement with more conservative independent CMB+2dF analysis large compared to WMAPext+2dF (0.134±0.006) flat, massless neutrinos, cosmological constant, power law power spectrum, …

WMAP TT power spectrum at low l Pseudo-Cl data points from compared to theoretical power law model (mean over realizations)

Low quadrupole? Standard models Observed Likelihood of theoretical value given observed value WMAP Pseudo-C l : C 2 = 123 Tegmark cleaned map: C 2 = 184 (kp2 cut, Pseudo-Cl estimator on map from astro-ph/ ) Foreground uncertainty: Likelihood modelling:

Running n s ? 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

Cut-off in initial power spectrum? P(k)=0 for k k c Bridle, Lewis, Weller, Efstathiou: astro-ph/

Contributions to the quadrupole ISW Last scattering k MPc Total ΔkΔk

Changing ISW is tricky… E.g. Dark energy with w > -1,c s 2 <1 or w<-1, c s 21 give less ISW than cosmological constant Weller, Lewis: astro-ph/ Bean, Doré: astro-ph/ No simple theoretical model gives a very low quadrupole The low value is not that unlikely in a realisation of a standard model

P(k) on smaller scales Bridle, Lewis, Weller, Efstathiou: astro-ph/

Asymmetry of low multipoles? after Eriksen et al astro-ph/ : l <~31 shows unlikely asymmetry: evaluate binned C l 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/ find quadrupole and octopole alignment is unlikely at 1/60 level

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 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 C l not consistent with Gaussian expectations? Do outliers bias results?... Versions of TE power spectrum

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.

In two bins… 1<l<18 17<l<31

No power in northern hemisphere 3-point function? Eigenmodes: Measured and marginalized errors from simulations: