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The Age of the Universe and the Cosmological Constant Determined from Cosmic Microwave Background Anisotropy Measurements

L. Knox, N. Christensen, C. Skordis

TL;DR

The paper uses a Bayesian, MCMC-based analysis of a flat adiabatic CDM model to extract the Universe's expansion age from CMB anisotropies, exploiting a strong correlation between the age $t_0$ and the acoustic scale $\\theta_s$. By employing a fast $C_\ell$ calculation (DASh) and combining multiple CMB datasets with an offset log-normal likelihood, it finds $t_0 = 14.0 \\pm 0.5$ Gyr under the assumption $\\Omega_{tot}=1$, with $h$ and $\\Omega_\Lambda$ poorly constrained by the CMB alone. Imposing an external $H_0$ prior or a lower bound on $h$ yields a robust lower limit $\\Omega_\Lambda > 0.4$ (95% C.L.), providing independent evidence for dark energy. The analysis demonstrates the power of CMB data to constrain cosmic age via the acoustic scale and anticipates substantial improvements from future missions like MAP/Planck.

Abstract

If Omega_tot = 1 and structure formed from adiabatic initial conditions then the age of the Universe, as constrained by measurements of the cosmic microwave background (CMB), is t_0=14.0 +/- 0.5 Gyr. The uncertainty is surprisingly small given that CMB data alone constrain neither h nor Omega_Lambda significantly. It is due to the tight (and accidental) correlation, in these models, of the age with the angle subtended by the sound horizon on the last--scattering surface and thus with the well-determined acoustic peak locations. If we assume either the HST Key Project result h = 0.72 \pm .08 or simply that h > 0.55, we find Omega_Lambda > 0.4 at 95% confidence--another argument for dark energy, independent of supernovae observations. Our analysis is greatly simplified by the Monte Carlo Markov chain approach to Bayesian inference combined with a fast method for calculating angular power spectra.

The Age of the Universe and the Cosmological Constant Determined from Cosmic Microwave Background Anisotropy Measurements

TL;DR

The paper uses a Bayesian, MCMC-based analysis of a flat adiabatic CDM model to extract the Universe's expansion age from CMB anisotropies, exploiting a strong correlation between the age and the acoustic scale . By employing a fast calculation (DASh) and combining multiple CMB datasets with an offset log-normal likelihood, it finds Gyr under the assumption , with and poorly constrained by the CMB alone. Imposing an external prior or a lower bound on yields a robust lower limit (95% C.L.), providing independent evidence for dark energy. The analysis demonstrates the power of CMB data to constrain cosmic age via the acoustic scale and anticipates substantial improvements from future missions like MAP/Planck.

Abstract

If Omega_tot = 1 and structure formed from adiabatic initial conditions then the age of the Universe, as constrained by measurements of the cosmic microwave background (CMB), is t_0=14.0 +/- 0.5 Gyr. The uncertainty is surprisingly small given that CMB data alone constrain neither h nor Omega_Lambda significantly. It is due to the tight (and accidental) correlation, in these models, of the age with the angle subtended by the sound horizon on the last--scattering surface and thus with the well-determined acoustic peak locations. If we assume either the HST Key Project result h = 0.72 \pm .08 or simply that h > 0.55, we find Omega_Lambda > 0.4 at 95% confidence--another argument for dark energy, independent of supernovae observations. Our analysis is greatly simplified by the Monte Carlo Markov chain approach to Bayesian inference combined with a fast method for calculating angular power spectra.

Paper Structure

This paper contains 7 sections, 4 equations, 2 figures, 1 table.

Table of Contents

  1. Introduction
  2. Method
  3. Generating the Chain
  4. $C_l$ Calculation
  5. Likelihood Calculation
  6. Results
  7. Discussion

Figures (2)

  • Figure 1: The posterior probability density of $\Omega_\Lambda$ (lowest panel) and contours of equal probability density in the $\Omega_\Lambda$, $t_0$ plane (lower middle panel), $\Omega_\Lambda$, $\theta_s$ plane (upper middle panel) and $\Omega_\Lambda$, $h$ plane (top panel). Contour levels are at $e^{-6.17/2}$, $e^{-2.3/2}$ and 0.95 of maximum. The lowest panel curves are for $h > 0.4$ (solid) and $h = .72 \pm .08$ (dashed). Top panel dotted lines are at constant $t_0$.
  • Figure 2: The posterior probability density of the age of the Universe (lower panel) and contours of equal probability density (as in Figure 1) in the $\theta_s$, $t_0$ plane (upper panel). The lower panel curves are for $h > 0.4$ (solid) and $h = .72 \pm .08$.