Weighing the Universe with the Cosmic Microwave Background

TL;DR

This work evaluates the precision with which Ω can be determined by a CMB map as a function of sky coverage, pixel noise, and beam size.

Abstract

Variations in $Ω$, the total density of the Universe, leave a clear and distinctive imprint on the power spectrum of temperature fluctuations in the cosmic microwave background (CMB). This signature is virtually independent of other cosmological parameters or details of particular cosmological models. We evaluate the precision with which $Ω$ can be determined by a CMB map as a function of sky coverage, pixel noise, and beam size. For example, assuming only that the primordial density perturbations were adiabatic and with no prior information on the values of any other cosmological parameters, a full-sky CMB map at $0.5^\circ$ angular resolution and a noise level of $15\,μ{\rm K}$ per pixel can determine $Ω$ with a variance of 5\%. If all other cosmological parameters are fixed, $Ω$ can be measured to better than 1\%.

Figures (2)

• Figure 1: The variance on $\Omega$ that can be obtained with a full-sky mapping experiment as a function of the beam width $\theta_{\rm fwhm}$ for noise levels $w^{-1}=2\times10^{-15}$, $9\times10^{-15}$, and $4\times10^{-14}$ (from lower to upper curves). The underlying model is "standard CDM." The solid curves are the sensitivities attainable with no prior assumptions about the values of any of the other cosmological parameters. The dotted curves are the sensitivities that would be attainable assuming that all other cosmological parameters, except the normalization, were fixed. The results for a mapping experiment which covers only a fraction $f_{\rm sky}$ of the sky can be obtained by replacing $w \rightarrow w f_{\rm sky}$ and scaling by $f_{\rm sky}^{-1/2}$ [c.f., Eq. (2)].
• Figure 2: Same as Fig. 1, except for a reionized model with $\tau=0.5$.