We have obtained a generalization of the hydrodynamic theory of vacuum in the context of general relativity. While retaining the Lagrangian character of general relativity, the new theory provides a natural alternative to the view that the singularity is inevitable in general relativity and the theory of a hot Universe. We show that the macroscopic source-sink motion as a whole of ordinary (dark) matter that emerges during the production of particles out of the vacuum can be a new source of gravitational vacuum polarization (determining the variability of the cosmological term in general relativity). We have removed the well-known problems of the cosmological constant by refining the physical nature of dark energy associated precisely with this hydrodynamically initiated variability of the vacuum energy density. A new exact solution of the modified general relativity equations that contains no free (fitting) parameter additional to those available in general relativity has been obtained. It corresponds to the continuous and metric-affecting production of ultralight dark matter particles (with mass m_0 = (?/c~2) radical sign (12ρ_0k) ≈ 3 × 10~(-66) g, k is the gravitational constant) out of the vacuum, with its density ρ_0, constant during the exponential expansion of a spatially flat Universe, being retained. This solution is shown to be stable in the regime of cosmological expansion in the time interval -∞ < t < t_(max), when t = 0 corresponds to the present epoch and t_(max) = 2/3H_0cΩ_(0m) ≈ 38 × 10~9 yr at Ω_(0m) = ρ_0/ρ_c ≈ 0.28 (H_0 is the Hubble constant, ρ_c is the critical density). For t > t_(max), the solution becomes exponentially unstable and characterizes the inverse process of dark matter particle absorption by the vacuum in the regime of contraction of the Universe. We consider the admissibility of the fact that scalar massive photon pairs can be these dark matter particles. Good quantitative agreement of this exact solution with the cosmological observations of SnIa, SDSS-BAO, and the decrease in the acceleration of the expansion of the Universe has been obtained.
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