On the estimation of the current value of the cosmological constant

Abstract

We advance the viewpoint that only relevant modes of the vacuum fluctuations, namely, with wavelengths conditioned by the size, homogeneity, geometry and topology of the Universe, do contribute into the cosmological constant. A formula is derived which relates the cosmological constant with the size of the Universe and the three fundamental constants: the velocity of light, Planck and Newton gravitational constants. Then the current value of the cosmological constant remarkably agrees with the value indicated by distant supernovae observations, i.e. is of the order of the critical density. Thus the cosmological constant had to be smaller than the matter density in the past and will be bigger in the future.