Observational constraints and cosmological parameters

TL;DR

The paper analyzes WMAP 3-year data to constrain cosmological parameters using Gaussian CMB statistics and MCMC sampling, showing that polarization data tightly constrain the optical depth $\tau$ and drive $n_s<1$ in basic models. Temperature data with a $\tau$ prior largely replicate these constraints, while secondary effects such as CMB lensing and the SZ contribution produce modest shifts, and joint data with Lyman-$\alpha$ favor a higher $\sigma_8$ without requiring new physics. Extended models including tensors or isocurvature modes find no strong evidence for departures from adiabatic $\Lambda$CDM, though tensor degeneracies can loosen the constraint on $n_s$ and isocurvature fractions remain allowed within bounds $-0.42< B<0.25$. Overall, WMAP 3-year data favor a simple, consistent cosmology but highlight mild tensions in $\sigma_8$ with some external probes and point to future measurements of $\tau$, the third peak, and large-scale $B$-modes as crucial for further tightening.

Abstract

I discuss the extraction of cosmological parameter constraints from the recent WMAP 3-year data, both on its own and in combination with other data. The large degeneracies in the first year data can be largely broken with the third year data, giving much better parameter constraints from WMAP alone. The polarization constraint on the optical depth is crucial to obtain the main results, including n_s < 1 in basic six-parameter models. Almost identical constraints can also be obtained using only temperature data with a prior on the optical depth. I discuss the modelling of secondaries when extracting parameter constraints, and show that the effect of CMB lensing is about as important as SZ and slightly increases the inferred value of the spectral index. Constraints on correlated matter isocurvature modes are not radically better than before, and the data is consistent with a purely adiabatic spectrum. Combining WMAP 3-year data with data from the Lyman-alpha forest suggests somewhat higher values for sigma_8 than from WMAP alone.

Figures (8)

• Figure 1: Constraints from WMAP 3-year temperature (points) and joint with polarization ($68\%$ and $95\%$ contours) for a basic six parameter $\Lambda$CDM model (no tensors). The points represent samples from the posterior distribution, and are coloured by the value of the optical depth $\tau$. Polarization constrains the optical depth, breaking the main flat-model degeneracy and suggesting $n_s<1$.
• Figure 2: Constraints from WMAP 3-year temperature (red), temperature and polarization (black), and temperature with a Gaussian prior on the optical depth $\tau=0.10\pm 0.03$ (blue). The top six parameters have flat priors and are sampled using MCMC, the bottom six parameters are derived.
• Figure 3: The theoretical unlensed (black) and smoother lensed (red) CMB temperature power spectra (top) and the difference (bottom blue) for a fiducial WMAP 3-year $\Lambda$CDM model with $n_s=0.95$, $\tau=0.09$. Green lines are unlensed but include the SZ spectrum from Ref. Komatsu:2002wc evaluated for fiducial parameters as used by the WMAP team (with marginalized amplitude) at 22.8GHz. At higher frequencies the SZ contribution is somewhat smaller.
• Figure 4: Six parameter WMAP 3-yr constraints with no secondary modelling (blue), marginalizing over SZ model amplitude (red) and marginalizing over SZ and including CMB lensing (black).
• Figure 5: Constraints on the spectral index $n_s$ and $\sigma_8$ from WMAP only (green), SDSS Lyman-$\alpha$ (blue, Ref. McDonald:2004xn), and the joint constraint (red). Contours enclose $68\%$ and $95\%$ of the probability, and the model is $\Lambda$CDM with no tensors. Lyman alpha only contours are for fixed best-fit joint values of the other parameters and dependent upon this prior: they give a visual clue to the direction and amount by which the data pull the joint constraints, but the absolute position of the contours is fairly meaningless.