Vacuum Energy Density Measured from Cosmological Data

Abstract

Within the $\Lambda$CDM cosmological model, the absolute value of Einstein's cosmological constant $\Lambda$, sometimes expressed as the gravitating mass-energy density $\rho_\Lambda$ of the physical vacuum, is a fundamental constant of nature, whose accurate measurement plays a central role in testing some proposed theories of quantum gravity. Several combinations of currently public cosmological data and an assumed flat $\Lambda$CDM cosmological model are used here to make a joint Bayesian inference on the combination of conventional parameters $\Omega_\Lambda h^2$ that corresponds to the absolute physical density $\rho_\Lambda$. In physical units, we obtain $\rho_\Lambda = \left(60.3\pm{1.3}\right)\times 10^{-31}{\rm g/cm^3}$, the most accurate constraint to date, with an absolute calibration of cosmological measurements based on CMB temperature. Significantly different values are obtained with calibrations that use a local distance scale, mainly connected to systematic differences in the value of the Hubble constant. It is suggested that future comprehensive cosmological parameter studies assuming the $\Lambda$CDM model include constraints on the vacuum density.