Current cosmological constraints from a 10 parameter CMB analysis

TL;DR

This paper develops a practical framework to constrain a 10-parameter CDM cosmology from CMB data by combining scalar and tensor spectra and leveraging a four-step pipeline plus interpolation to explore ~30 million models. It addresses key systematics, including calibration errors and closed geometries, and demonstrates that current CMB data constrain spatial curvature and CDM density, with a positive cosmological constant favored when external priors are included. The method reveals that the CMB alone supports flat or mildly curved geometries and that SN1a data reinforce a nonzero $\Omega_\Lambda$, while calibration and modeling refinements remain crucial for robust inferences. Overall, the work provides a robust, scalable approach for multi-parameter cosmology with the potential for improvements as data quality improves.

Abstract

We compute the constraints on a ``standard'' 10 parameter cold dark matter (CDM) model from the most recent CMB and data and other observations, exploring 30 million discrete models and two continuous parameters. Our parameters are the densities of CDM, baryons, neutrinos, vacuum energy and curvature, the reionization optical depth, and the normalization and tilt for both scalar and tensor fluctuations. Our strongest constraints are on spatial curvature, -0.24 < Omega_k < 0.38, and CDM density, h^2 Omega_cdm <0.3, both at 95%. Including SN 1a constraints gives a positive cosmological constant at high significance. We explore the robustness of our results to various assumptions. We find that three different data subsets give qualitatively consistent constraints. Some of the technical issues that have the largest impact are the inclusion of calibration errors, closed models, gravity waves, reionization, nucleosynthesis constraints and 10-dimensional likelihood interpolation.

Figures (11)

• Figure 1: The analysis of a large CMB data set is conveniently broken down into four steps: mapmaking, foreground removal, power spectrum extraction and parameter estimation.
• Figure 2: The band power measurements used.
• Figure 3: Marginalization method comparison. $\chi^2$ is plotted as a function of $\Omega_\Lambda$ when maximizing over all other parameters with no priors. The squares show the result of using multidimensional spline interpolation when maximizing and the crosses show the result of simply picking the smallest $\chi^2$-value in the model grid. Note that a seemingly small error of unity in $\chi^2$ changes the likelihood by a factor of 1.6.
• Figure 4: The best fit model is shown for the case of no prior (solid red/dark grey) and with the priors $h=0.65\pm 0.07$, $h^2\Omega_{\rm b}=0.02$ and $\tau=r=0$ (solid green/light grey). The dotted lines show the decomposition of the former curve into scalar and tensor fluctuations. The model parameters are listed in Table 2. Although all 65 measurements were used in the fits, they have been averaged into 14 bands in this plot to avoid cluttering. The band powers whose central $\ell$-value fell into any given band were average with minimum-variance weighting, and their corresponding window functions were averaged as well. This binning was used only in this plot, not in our analysis.
• Figure 5: The marginalized likelihood is shown for six individual parameters using all 65 band power measurements and priors only from nucleosynthesis ($h^2\Omega_{\rm b}=0.02$) and the Hubble parameter ($h=0.65\pm 0.07$). The $2\sigma$ limits (see Table 2) are roughly where the curves cross the horizontal lines.