New formulas for the Hubble constant in a Euclidean static universe

Abstract

It is shown that the Hubble constant can be derived from the standard luminosity function of galaxies as well as from a new luminosity function as deduced from the mass-luminosity relationship for galaxies. An analytical expression for the Hubble constant can be found from the maximum number of galaxies (in a given solid angle and flux) as a function of the redshift. A second analytical definition of the Hubble constant can be found from the redshift averaged over a given solid angle and flux. The analysis of two luminosity functions for galaxies brings to four the new definitions of the Hubble constant. The equation that regulates the Malmquist bias for galaxies is derived and as a consequence it is possible to extract a complete sample. The application of these new formulae to the data of the two-degree Field Galaxy Redshift Survey provides a Hubble constant of $( 65.26 \pm 8.22 ) \mathrm{\ km\ s}^{-1}\mathrm{\ Mpc}^{-1}$ for a redshift lower than 0.042. All the results are deduced in a Euclidean universe because the concept of space-time curvature is not necessary as well as in a static universe because two mechanisms for the redshift of galaxies alternative to the Doppler effect are invoked.