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For solutions to equations (5) in the form of monochromatic waves

u

t

(

p

) =

u

t

(

p

)

0

exp(

ikpa

0

ωt

);

u

l

(

p

) =

u

l

(

p

)

0

exp(

ikpa

0

ωt

)

, p

= 0

,

1

,

2

, . . . ,

the following dispersion laws of the respective waves can be derived:

ω

2

t

= 4

γ

t

m

sin

2

ka

0

2

= 4

c

2

0

a

2

0

sin

2

ka

0

2

;

c

2

0

=

γ

t

m

a

2

0

;

ω

l

= 0; (

γ

l

= 0)

.

For small wave vectors

k

for transverse acoustic waves of the physical

vacuum the dispersion law can be approximated by the dispersion

relationship known in the theory of relativity for transverse electromagnetic

waves in vacuum:

ω

t

=

с

0

k

, where

с

0

=

с

t

is a velocity of transverse

electromagnetic waves (velocity of light) in vacuum. With respect to the

longitudinal acoustic waves, the initial phase of the physical vacuum

(praphase) turned out to be non-stable (

ω

l

= 0

). Cooling of the Universe

resulted in structural phase transformation and formation of superstructure

with period

a a

0

(

а

10

15

cm, Fig. 5,

b

). The dispersion law for

transverse acoustic waves in the initial (high-temperature) phase of physical

vacuum (praphase) is presented in Fig. 6,

a

.

Motion equations for translational longitudinal oscillations of the

clusters in a new (low-temperature) phase take the following form:

M

¨

u

l

(

p

) =

γ

0

u

l

(

p

)

γ

l

[2

u

l

(

p

)

u

l

(

p

1)

u

l

(

p

+ 1)] ;

p

= 0

,

1

,

2

, . . .

;

γ

l

<

0

, γ

0

>

0

.

A solution to equations (6) in the form of planar monochromatic waves

results in the dispersion law for longitudinal optical electromagnetic waves

(Fig. 6,

b

).

ω

2

l

=

ω

2

0

4

c

2

a

2

sin

2

ka

2

;

ω

2

0

=

γ

0

M

;

c

2

a

2

=

γ

l

M

.

(5)

Fig. 6. Dispersion laws for transverse acoustic waves in the initial phase of physical

vacuum (praphase) (

a

) and longitudinal acoustic and optical waves in vacuum after

superstructural phase transformation (

b

)

42

ISSN 1812-3368. Herald of the BMSTU. Series “Natural Sciences”. 2015. No. 1