On the role of Bernoulli distribution in cosmology

Cosmological observations suggest that the transition scale to homogeneity is not smaller than' (200−300)h−1 Mpc (h is the Hubble parameter in units 100 km s−1 Mpc−1), and that in addition this transition scale seems to decrease with increasing redshift. Nevertheless, these claims are highly uncertain, and call for further observational tests allowing to verify the homogeneity even on scales' (400−1000)h−1 Mpc for different redshifts. The key ideas of such a test are presented. Simultaneous pencil beam surveys are proposed to be done, and then the randomness of observed objects should be verified by the so called ”Bernoulli test”. The method is in fact a generalization of the usual counts-in-cells analysis, where the Poisson distribution is substituted by the Bernoulli distribution. Hence, it is shown that this distribution may have a great importance in cosmology.