Abstract
The thesis explains the effect of cosmic vacuum of gravitational field on properties of scalar field equation. In the space-time plane, the scalar field equation has periodic solution φx,y,z,t=Acos (kx±ωt). Consideration the cosmic vacuum of gravitational field (using De Sitter metric in its synchronization time) the equation of scalar field will have accurate solution in form of Beseel function. By using the asymptotic representation, the periodic solution (t→±∞) will vanish. The scalar field equation when t→+∞ will decrease regularly, and when t→-∞ it will increasing fluctuate.
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