The Upper Limit on the Minimum Mass of Relic Neutrinos, Allowing for the Equivalence of Their Gravitational Density with the Density of Dark Energy

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Abstract

A cloud of relativistic material particles is considered, the gravitational interaction between which can be neglected when determining their motion. In proper frame the isotropic Schwarzschild metric defines the field of each particle. The active gravitational mass of the cloud is obtained by applying Lorentz transformations to this metric and using the superposition principle. It is found for the region where the cloud can be considered as a point body. This result is used to estimate the upper limit of a neutrino mass sufficient for gravitational density of relic neutrinos to be close to the density of dark energy.

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