Nine-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Cosmological Parameter Results (1212.5226v3)

Abstract: We present cosmological parameter constraints based on the final nine-year WMAP data, in conjunction with additional cosmological data sets. The WMAP data alone, and in combination, continue to be remarkably well fit by a six-parameter LCDM model. When WMAP data are combined with measurements of the high-l CMB anisotropy, the BAO scale, and the Hubble constant, the densities, Omegabh2, Omegach2, and Omega_L, are each determined to a precision of ~1.5%. The amplitude of the primordial spectrum is measured to within 3%, and there is now evidence for a tilt in the primordial spectrum at the 5sigma level, confirming the first detection of tilt based on the five-year WMAP data. At the end of the WMAP mission, the nine-year data decrease the allowable volume of the six-dimensional LCDM parameter space by a factor of 68,000 relative to pre-WMAP measurements. We investigate a number of data combinations and show that their LCDM parameter fits are consistent. New limits on deviations from the six-parameter model are presented, for example: the fractional contribution of tensor modes is limited to r<0.13 (95% CL); the spatial curvature parameter is limited to -0.0027 (+0.0039/-0.0038); the summed mass of neutrinos is <0.44 eV (95% CL); and the number of relativistic species is found to be 3.84+/-0.40 when the full data are analyzed. The joint constraint on Neff and the primordial helium abundance agrees with the prediction of standard Big Bang nucleosynthesis. We compare recent PLANCK measurements of the Sunyaev-Zel'dovich effect with our seven-year measurements, and show their mutual agreement. Our analysis of the polarization pattern around temperature extrema is updated. This confirms a fundamental prediction of the standard cosmological model and provides a striking illustration of acoustic oscillations and adiabatic initial conditions in the early universe.

• The paper demonstrates that combining nine-year WMAP data with external observations yields a precise six-parameter ΛCDM model fit.
• It achieves 1.5% precision on core parameters, confirms a 5σ spectral tilt, and reduces the parameter space volume by 68,000 times.
• The research further constrains extended parameters like neutrino mass and tensor-to-scalar ratio, reinforcing the robustness of the standard model.

Analyzing Nine-Year Wilkinson Microwave Anisotropy Probe Observations: Insights and Implications for Cosmological Parameters

The paper discussed in this paper reports cosmological parameter constraints derived from nine years of data collected by the Wilkinson Microwave Anisotropy Probe (WMAP). This paper marks the culmination of the WMAP mission, establishing a comprehensive cosmological model consistent with observations. The research combines WMAP data with other significant cosmological datasets—high-$l$ CMB anisotropy data from ACT and SPT, measurements of the baryon acoustic oscillation (BAO) scale, and determinations of the Hubble constant ($H_0$). These datasets synergistically contribute to refining the precision of various cosmological parameters.

Key Numerical Results and Implications

1. Six-Parameter Model Fit: The core findings show that the combined WMAP and external datasets align remarkably well with a six-parameter $\Lambda$CDM model. These parameters include the densities of baryonic and cold dark matter ($\Omega_bh^2$ and $\Omega_ch^2$), the cosmological constant ($\Omega_\Lambda$), the amplitude of the primordial fluctuations ($\Delta_{\cal R}^2$), the spectral index ($n_s$), and the reionization optical depth ($\tau$).
2. Parameter Precision: With the inclusion of additional datasets, WMAP provides a 1.5% precision on $\Omega_bh^2$, $\Omega_ch^2$, and $\Omega_\Lambda$. The data measures the amplitude of the primordial fluctuations to within 3% and confirms a spectral tilt at the $5\sigma$ level, verifying a deviation from a pure power law.
3. Volume Reduction: Since the onset of WMAP observations, there has been a factor of 68,000 reduction in the volume of the six-dimensional parameter space, underscoring the mission's significant contributions to cosmological precision.
4. Extended Parameter Constraints: The paper also explores constraints on parameters beyond the standard model, such as the tensor-to-scalar ratio ($r$), running spectral index ($dn_s/d\ln{k}$), neutrino mass ($\sum m_\nu$), and spatial curvature ($\Omega_k$). Particularly, it limits the tensor mode contribution to $r < 0.13$ (95% CL), and establishes an upper bound on the sum of neutrino masses, $\sum m_\nu < 0.44$ eV (95% CL).
5. Cosmic Consistency: The joint constraints on the effective number of relativistic species ($N_{\rm eff}$) and the primordial helium abundance ($Y_{\rm He}$) corroborate the predictions of Big Bang nucleosynthesis, supporting the standard cosmological model with $N_{\rm eff} = 3.84 \pm 0.40$.

Theoretical and Practical Implications

The research extends theoretical confidence in the prevailing $\Lambda$CDM model of cosmology. The precision limitations posed by cosmic variance illustrate the robustness of this model, while the constraints on parameters imply additional dark energy properties remain aligned with a cosmological constant ($w = -1$).

Practically, the research marks a benchmark in cosmological analysis by demonstrating the utility of combining multiple observational data streams. The mutual consistency reinforces the accuracy of the datasets and enhances confidence in their derived parameters.

Future Speculations

The paper underscores unresolved questions about the nature of dark matter, dark energy, and the exact physics governing inflation. While the precision of current datasets like WMAP offers robust insights, upcoming missions such as the European Space Agency's Planck mission were anticipated to extend our understanding by targeting the same frequency spectrum more finely and constraining parameters even further.

In conclusion, the nine-year WMAP observations provide pivotal constraints on cosmological parameters, offering substantial insights and setting a foundational framework for future explorations in cosmology. The amalgamation of high-quality data and robust theoretical frameworks signifies a symbolic transition into a precision-driven era in understanding the universe's physical makeup and evolutionary history. This paper effectively crowns a productive era of CMB observations while setting the stage for subsequent missions to build upon its legacy.