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It is shown that in Einstein’s theory and in the theory of gravity with Logunov constraints, there is a field-theoretical model of dark energy that is consistent with the observational data indicating that the Hubble value increases over time. In the developed model of dark energy, the isotropic energy dominant condition is violated. It solves the problem of the cosmological singularity and the singularity of “black holes”. The compact configuration of the scalar field can generate a flux of particles by the pairs of particles production mechanism from the vacuum by a field of barrier and in the process of transformation of thermal energy (Hawking radiation) and acceleration energy into radiation. The scalars can play the role of the so-called “black holes” with no singularity inside themselves.