Review article / Journal of Physical Science Successes, 1980, t. 130, vol. 4, s. 55914. The article provides general expressions for the concentration of elementary particles in a hot expanding world, limits on the number of types of light particles are given, and restrictions on the masses of light weakly interacting particles and heavy stable particles are obtained. Limitations on masses of heavy stable neutral leptons with standard weak interaction. are discussed Astrophysical limitations on mass and lifetime for unstable leptons. are given. The consequences of the strong degeneration of neutrino gas, t. are discussed e. the presence of a significant lepton charge in the universe. The possibility of solving the problem of hidden mass of galaxies is briefly discussed. Limitations on the properties of various hypothetical particles that can be obtained from astrophysics are discussed The consequences of models of elementary particles with spontaneously broken symmetry for cosmology near the singularity . are considered. Various hypotheses of the occurrence of an observed excess of baryons over antibaryons in the Universe are discussed