The effect of cosmic vacuum on the properties of scalar field

. 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 φ (x,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.


INTRODUCTION
The study of cosmic vacuum is one from import lines studying in modern cosmology. Cosmological observations shows presence cosmic vacuum in universe [2]. Vacuum create antigravitation field, which call for acceleration cosmological expansion. The detection of cosmic vacuum made substantial evolution on the modern's nature of universe.

THE DISCOVERY OF COSMIC VACUUM
In cosmological science occur developments that many specialists consider it revolution, thanks only three points in cosmology: a. In the universe dominates vacuum of energy density exceeds all the "usual" forms of cosmic matter together.
b. Antigravity governs the dynamics of the cosmological expansion.
c. Cosmological expansion is accelerating, and the space in four-dimensional space-time is static, because the time a static [2].
Discovery made by astronomer's observers, who have been studying distant supernovae.
Observers have data on only a few supernovae, but already it was enough to notice the cosmological effect of decrease in the apparent brightness with the distance [9]. More precisely, it is better to look not at a distance, but a redshift "as is usually done in the case of distant sources". It was found that the decrease in the average brightness is faster than that expected for the cosmological theory, which has recently been considered the standard [4].
The theory of the expanding universe was created by Friedman in 1922-1924 [1]. With the opening of the cosmological expansion all doubts in the introduction of the cosmological constant disappeared.
The geometry of Friedman's four-dimensional space describes the metric element Friedman's theory assumes that the distribution of matter is homogeneous in the universe. In his theory Friedman predicts the cosmological expansion in homogeneous and isotropic space must occur according linear law [6]: "in any moment the velocity distant source, which exist at distance R proportion to this distance".
Vacuum appear in cosmology with Einstein's cosmological constant. In the first role cosmological constant became how to explain anti-gravity. Einstein predicts in that way possible equilibrium gravity material's universe, and i.e. the universe itself stationary [12].

THE SCALAR FIELD
Scalar field explains particles with spin s=0 .Effective (pseudo)scalar field explains natural spinless mesons. Complex (pseudo)scalar field explains charge spinless mesons [11]. The difference between scalar and pseudo scalar conclude with transforming law for reflection even number of axial coordinate and appear just in form possibly interaction law with other fields [7].

THE EFFECT OF COSMIC VACUUM ON SOLUTION OF SCALAR FIELD EQUATION:
Scalar field equation in general form [6]: In the first we looking for solution this equation in the space-time plane with metric By using this metric, Eq. 6 written in form: Solution of Eq. 8: ( , , , ) = 1 ( − ) + 2 ( + ) , 1 2 − .

International Letters of Chemistry, Physics and Astronomy Vol. 61 59
This solution is periodic function. Now, we are looking for solution of Eq. 6 using De Sitter metric.
Now we study the asymptotic representation of solution Eq. 18 considering that expansion of university corresponds → ∞ и → 0 .

ILCPA Volume 61
Comeback to Eq. 16 we find: This function non-periodic, it is decrease regularly with time.
For → ∞ we find the following expression: Considering Eq. 21 we find: Therefore This function increase and fluctuate with time.
We can write it in another form "real part": Eq. 39 increase and fluctuate with time.

CONCLUSIONS:
In the space-time plane, the scalar field equation has periodic solution. In gravitational field for expansion of university for t→+∞ the solution of scalar field equation will decrease regularly or decreasing fluctuate according to sign of the difference