THE COSMOLOGICAL CONSTANT IN EINSTEIN FIELD-EQUATIONS AND THE VACUUM DENSITY

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 (rho(vac)) and the cosmological constant LAMBDA, which was introduced by Einstein as a mathematical device to construct a static cosmological model of the universe, LAMBDA 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.