First Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Determination of Cosmological Parameters

TL;DR

The paper tests whether a simple flat ΛCDM cosmology with nearly scale-invariant adiabatic fluctuations can reproduce WMAP TT/TE data and remain consistent with other astronomical measurements. Using Bayesian MCMC, it first fits a six-parameter model to WMAP data, then combines with smaller-scale CMB and large-scale structure data to test extensions, including a running spectral index, dark energy w, non-flat geometries, and neutrinos. The results reinforce the standard model: h≈0.71, Ω_b h^2≈0.022–0.024, Ω_m h^2≈0.135, τ≈0.17, n_s≈0.93, σ8≈0.84, with limited room for additional physics such as significant tensor modes, nonzero neutrino masses, or large deviations in w from -1. The analysis also identifies intriguing discrepancies at the largest scales and discusses how future CMB polarization and LSS data could clarify these tensions and further constrain new physics.

Abstract

WMAP precision data enables accurate testing of cosmological models. We find that the emerging standard model of cosmology, a flat Lambda-dominated universe seeded by nearly scale-invariant adiabatic Gaussian fluctuations, fits the WMAP data. With parameters fixed only by WMAP data, we can fit finer scale CMB measurements and measurements of large scle structure (galaxy surveys and the Lyman alpha forest). This simple model is also consistent with a host of other astronomical measurements. We then fit the model parameters to a combination of WMAP data with other finer scale CMB experiments (ACBAR and CBI), 2dFGRS measurements and Lyman alpha forest data to find the model's best fit cosmological parameters: h=0.71+0.04-0.03, Omega_b h^2=0.0224+-0.0009, Omega_m h^2=0.135+0.008-0.009, tau=0.17+-0.06, n_s(0.05/Mpc)=0.93+-0.03, and sigma_8=0.84+-0.04. WMAP's best determination of tau=0.17+-0.04 arises directly from the TE data and not from this model fit, but they are consistent. These parameters imply that the age of the universe is 13.7+-0.2 Gyr. The data favors but does not require a slowly varying spectral index. By combining WMAP data with other astronomical data sets, we constrain the geometry of the universe, Omega_tot = 1.02 +- 0.02, the equation of state of the dark energy w < -0.78 (95% confidence limit assuming w >= -1), and the energy density in stable neutrinos, Omega_nu h^2 < 0.0076 (95% confidence limit). For 3 degenerate neutrino species, this limit implies that their mass is less than 0.23 eV (95% confidence limit). The WMAP detection of early reionization rules out warm dark matter.

Figures (17)

• Figure 1: This figure compares the best fit power law $\Lambda$CDM model to the WMAP temperature angular power spectrum. The gray dots are the unbinned data.
• Figure 2: This figure compares the best fit power law $\Lambda$CDM model to the WMAP TE angular power spectrum.
• Figure 3: This figure shows the likelihood function of the WMAP TT + TE data as a function of the basic parameters in the power law $\Lambda$CDM WMAP model. ($\Omega_b h^2$, $\Omega_m h^2$, $h$, $A$, $n_s$ and $\tau$.) The points are the binned marginalized likelihood from the Markov chain and the solid curve is an Edgeworth expansion of the Markov chains points. The marginalized likelihood function is nearly Gaussian for all of the parameters except for $\tau$. The dashed lines show the maximum likelihood values of the global six dimensional fit. Since the peak in the likelihood, $x_{ML}$ is not the same as the expectation value of the likelihood function, $<x>$, the dashed line does not lie at the center of the projected likelihood.
• Figure 4: This plot shows the contribution to $2 \ln {\cal L}$ per multipole binned at $\Delta l = 15$. The excess $\chi^2$ comes primarily from three regions, one around $\ell \sim 120$, one around $\ell\sim 200$ and the other around $\ell \sim 340$.
• Figure 5: Spectral Index Constraints. Left panel: the $n_s-\tau$ degeneracy in the WMAP data for a power-law $\Lambda$CDM model. The TE observations constrain the value of $\tau$ and the shape of the $C_l^{TT}$ spectrum constrain a combination of $n_s$ and $\tau$. Right panel: $n_s-\Omega_b h^2$ degeneracy. The shaded regions show the joint one and two sigma confidence regions.