Microwave Background Constraints on Cosmological Parameters

TL;DR

This paper evaluates how accurately future CMB experiments MAP and Planck can reconstruct cosmological parameters, using high-accuracy spectral calculations and Fisher information for both temperature and polarization data. It shows that polarization substantially improves constraints and helps break degeneracies, particularly in τ_ri and the tensor sector, while some combinations (e.g., Ω_b h^2, Ω_m h^2, Ω_m h^3) are tightly constrained even with temperature data alone. It also assesses the role of priors and gravitational lensing, validating the Gaussian assumption near the maximum and showing that external astronomical priors are crucial to fully disentangle parameter degeneracies. The results inform mission design and illustrate how combining CMB with other probes can yield robust cosmological parameter determinations and test inflationary predictions via the gravity-wave signal.

Abstract

We use a high-accuracy computational code to investigate the precision with which cosmological parameters could be reconstructed by future cosmic microwave background (CMB) experiments, in particular the two satellite missions MAP and Planck Surveyor (COBRAS/SAMBA). We identify several parameter combinations that could be determined with a few percent accuracy with MAP and the Planck Surveyor, as well as some degeneracies among the parameters that cannot be accurately resolved with the temperature data alone. These degeneracies can be broken by other astronomical measurements. Polarization measurments can significantly enhance the science return of both missions by allowing accurate determination of cosmological parameters, by enabling the detection of gravity waves and by probing the ionization history of the universe. We also address the question of how gaussian the likelihood function is around the maximum and whether gravitational lensing changes the constraints.

Figures (10)

• Figure 1: MAP confidence contours (68% and 95%) for models in the six parameter space (a) and seven parameter space with $T/S$ added as a free parameter (b). Parameters are normalized to their value in the underlying model denoted with an asterisk.
• Figure 2: Confidence contours $(68\%\ \& \ 95\%)$ in the $C_2^{(S)}-\tau_{ri}$ plane for models in the six parameter space described in the text with (dotted lines) or without (solid lines) polarization information.
• Figure 3: Power spectra of (a) temperature and (b) polarization for two models that will be degenerate for MAP if only temperature information is used. The model with $\Omega_\Lambda=0.6$ is the result of the minimization relative to the sCDM for models constrained to have $\Omega_\Lambda=0.6$. Polarization helps to break this degeneracy.
• Figure 4: Hubble diagram for Type Ia supernovae (a) and CDM linear power spectra (b) for sCDM and the $\Omega_\Lambda=0.6$ model described in the text.
• Figure 5: Confidence contours $(68\%\ \& \ 95\%)$ in the (a) $\Omega_b-h$ plane and (b) $\Omega_m-h$ plane for models in the seven parameter space described in the text with or without using polarization information.