Wilkinson Microwave Anisotropy Probe (WMAP) Three Year Results: Implications for Cosmology

TL;DR

The three-year WMAP results reinforce a flat ΛCDM cosmology with six primary parameters, tightly constraining $\Omega_m h^2$, $\Omega_b h^2$, $h$, $\tau$, $n_s$, and $\sigma_8$. Using Bayesian MCMC methods with improved polarization data, low-$\ell$ likelihoods, and SZ marginalization, the analysis finds $n_s<1$ and $\tau\sim0.1$, consistent with inflationary predictions. The study integrates diverse astronomical data, sharpening constraints on geometry, dark energy, neutrinos, and tensor modes, while finding no significant non-Gaussian signals. Overall, the ΛCDM model remains the standard cosmological paradigm, with external data providing robust cross-checks and guiding future tests of inflation and new physics.

Abstract

A simple cosmological model with only six parameters (matter density, Omega_m h^2, baryon density, Omega_b h^2, Hubble Constant, H_0, amplitude of fluctuations, sigma_8, optical depth, tau, and a slope for the scalar perturbation spectrum, n_s) fits not only the three year WMAP temperature and polarization data, but also small scale CMB data, light element abundances, large-scale structure observations, and the supernova luminosity/distance relationship. Using WMAP data only, the best fit values for cosmological parameters for the power-law flat LCDM model are (Omega_m h^2, Omega_b h^2, h, n_s, tau, sigma_8) = 0.1277+0.0080-0.0079, 0.02229+-0.00073, 0.732+0.031-0.032, 0.958+-0.016, 0.089+-0.030, 0.761+0.049-0.048). The three year data dramatically shrink the allowed volume in this six dimensional parameter space. Assuming that the primordial fluctuations are adiabatic with a power law spectrum, the WMAP data_alone_ require dark matter, and favor a spectral index that is significantly less than the Harrison-Zel'dovich-Peebles scale-invariant spectrum (n_s=1, r=0). Models that suppress large-scale power through a running spectral index or a large-scale cut-off in the power spectrum are a better fit to the WMAP and small scale CMB data than the power-law LCDM model; however, the improvement in the fit to the WMAP data is only Delta chi^2 = 3 for 1 extra degree of freedom. The combination of WMAP and other astronomical data yields significant constraints on the geometry of the universe, the equation of state of the dark energy, the gravitational wave energy density, and neutrino properties. Consistent with the predictions of simple inflationary theories, we detect no significant deviations from Gaussianity in the CMB maps.

Figures (26)

• Figure 1: The improvement in parameter constraints for the power-law $\Lambda$CDM model (Model M5 in Table \ref{['tab:how_many_parameters']}). The contours show the 68% and 95% joint 2-d marginalized contours for the $(\Omega_m h^2,\sigma_8)$ plane (left) and the $(n_s,\tau)$ plane (right). The black contours are for the first year WMAP data (with no prior on $\tau$). The red contours are for the first year WMAP data combined with CBI and ACBAR (WMAPext in spergel/etal:2003). The blue contours are for the three year WMAP data only with the SZ contribution set to 0 to maintain consistency with the first year analysis. The WMAP measurements of EE power spectrum provide a strong constraint on the value of $\tau$. The models with no reionization ($\tau=0$) or a scale-invariant spectrum ($n_s=1$) are both disfavored at $\Delta\chi^2_{eff}>6$ for 5 parameters (see Table \ref{['tab:how_many_parameters']}). Improvements in the measurement of the amplitude of the third peak yield better constraints on $\Omega_m h^2$.
• Figure 2: Comparison of the predictions of the different best fit models to the data. The black line is the angular power spectrum predicted for the best fit three-year WMAP only $\Lambda$CDM model. The red line is the best fit to the 1-year WMAP data. The orange line is the best fit to the combination of the 1-year WMAP data, CBI and ACBAR (WMAPext in spergel/etal:2003). The solid data points are for the 3 year data and the light gray data points are for the first year data.
• Figure 3: WMAP constraints on the reionization history. ( Left) The 68% and 95% joint 2-d marginalized confidence level contours for $x_e^0-z_{reion}$ for a power law $\Lambda$ Cold Dark Matter ($\Lambda$CDM) model with the reionization history described by equation \ref{['eq:reion']} and fit to the WMAP three year data. In equation \ref{['eq:reion']} we assume that the universe was partially reionized at $z_{\rm reion}$ to an ionization fraction of $x_e^0$, and then became fully ionized at $z=7$. ( Right) The 68% and 95% joint 2-d marginalized confidence level contours for $x_e^0-n_s$. This figure shows that $x_e^0$ and $n_s$ are nearly independent for a given value of $\tau$, indicating that WMAP determinations of cosmological parameters are not affected by details of the reionization history. Note that we assume a uniform prior on $z_{reion}$ in this calculation, which favors models with lower $x_e^0$ values in the right panel.
• Figure 4: The $\Lambda$CDM model fit to the WMAP data predicts the Hubble parameter redshift relation. The blue band shows the 68% confidence interval for the Hubble parameter, $H$. The dark blue rectangle shows the HST key project estimate for $H_0$ and its uncertainties freedman/etal:2001. The other points are from measurements of the differential ages of galaxies, based on fits of synthetic stellar population models to galaxy spectroscopy. The squares show values from jimenez/etal:2003 analyses of SDSS galaxies. The diamonds show values from simon/verde/jimenez:2005 analysis of a high redshift sample of red galaxies.
• Figure 5: The prediction for the small-scale angular power spectrum seen by ground-based and balloon CMB experiments from the $\Lambda$CDM model fit to the WMAP data only. The colored lines show the best fit (red) and the 68% (dark orange) and 95% confidence levels (light orange) based on fits of the $\Lambda$CDM models to the WMAP data. The points in the figure show small scale CMB measurements ruhl/etal:2003abroe/etal:2004kuo/etal:2004readhead/etal:2004dickinson/etal:2004. The plot shows that the $\Lambda$CDM model (fit to the WMAP data alone) can accurately predict the amplitude of fluctuations on the small scales measured by ground and balloon-based experiments.