Volume 6: Pages 567-571, 1993

The Cosmological Constant in Einstein's Field Equations and the Vacuum Density

Harry Hafner ¹

¹Physics Department, Hofstra University, Hempstead, New York 11550 U.S.A.

The present note is divided into two parts. In the first part we define the vacuum as the lowest energy of a physical system; then it can be regarded as a physical medium. According to the previous definition, the vacuum has to have a stress energy different from zero. In such a case it does not matter if we work in general coordinates, since no frame of reference is singled out. In order to connect the vacuum density (ρ_vac) and the cosmological constant Λ, which was introduced by Einstein as a mathematical device to construct a static cosmological model of the universe, Λ is considered to be a constant of nature and is currently used in cosmology, despite the fact that the initial purpose for which it was introduced has been discontinued. Using quantum statistics, we calculate the number of photons per cubic centimeter at the background radiation of 2.7 K. In the second part we provide a possible explanation of a well‐known paradox regarding Einstein's field equations with the cosmological constant and the Minkowski space‐time.

Keywords: cosmological constant, vacuum density, quantum statistics, background radiation

Received: June 16, 1992; Published Online: December 15, 2008