Distribution of Mass and Energy in Five General Cosmic Models

Distributions of the universe horizon distance and universe horizon volume were investigated in the light of five general cosmic models which were constructed in a previous study. Both distributions increase so slowly up to t ≈ 21.5444 Myr, then they start raising very fast up to t ≈ 60 Gyr. Afterwards, they increase again very slowly until t ≈ 124 Gyr. Distributions of mass of radiation, matter and dark energy within the horizon volume of the universe were also studied in the five general cosmic models. The masses of both radiation and matter decrease gradually with time while the mass of dark energy increases. The mass of radiation prevailed in the early universe up to t ≈ 34627.5 55916.2 yr, where it becomes equal to the mass of matter. Then the mass of matter dominated until t ≈ 9.4525 10.0632 Gyr, where it becomes equal to the mass of dark energy. Thenceforward, the mass of dark energy prevails the universe. The cosmic space becomes approximately matter empty in the so far future of the universe.


Introduction
In a previous study [1] the distribution of density parameters of radiation, matter and dark energy were investigated in details in five general cosmic models.Hence, it would be interesting to study the distributions of equivalent mass of radiation, mass of matter and equivalent mass of dark energy within the horizon volume of the universe in the general models.
Therefore, it is necessary to start this study by investigating the distributions of the horizon distance and horizon volume of the universe in the general models at different time intervals depending on the bases discussed in [2].Description of methodology is given in Section 2 while algorithm would be illustrated in Section 3. Results and discussion are presented in Section 4. Conclusion is shown in Section 5.

Methodology
We have seen in [2] that the horizon distance and horizon volume of the universe at the present time are respectively ( ) ( ) ( ) ( ) where c H are all defined as in [1].Thus the horizon distance of the universe at any given time is Consequently the change in the horizon distance of the universe in the time interval between two instants of scale factors 1 2 , a a is written as The horizon volume of the universe at any given time is It is also obvious from [2] that the total density of the universe is given by ( ) ( ) , Ω .

. 8π
Hence, the total mass within the horizon volume of the universe at any given time is expressed as The mass of matter The cosmic time is given by Equation ( 16) in [1] as Thus the time interval between two instants with scale factors 1 2 , a a during the universe expansion is ex- pressed as ( )

Algorithm
In determination of the distributions of  11), ( 7), (8), ( 9), (10), (6), (5), ( 12), (13), ( 14) and (15) respectively.viii) Continue the general DO loop.Table 1 shows the universe horizon distances in the general models at special times.These times are the time of radiation-matter mass equivalence rm t , the time of matter-dark energy mass equivalence Λ m t , the present time 13.7 0.2 Gyr  Afterwards, the two distributions diverge from each other.However, the distribution of the total mass coincides on the distribution of matter from the time 857695.9yr t ≈ onwards.The distribution of mass and energy within the universe horizon volume of the universe in any general model in the range 0.5 -50 Gyr t = is displayed in Figure 3(b).It is obvious that the distributions of matter and radiation decrease gradually with time and the former lies above the later.The distribution of dark energy increases with time and intersects with the distribution of matter at 9.4525 -10.0632Gyr t = as illustrated in Table 5.The distribution of the total mass coincides on the distribution of the matter up to 4.5714 Gyr t = , then they diverge from each other.Furthermore, the distribution of the total mass coincides on the distribution of the dark energy from 18.2857 Gyr t = onwards.Masses of radiation, matter and dark energy within the universe horizon volume in the general models at the present time are illustrated in Table 6.
The distribution of mass and energy within the universe horizon volume in any general model in the range      3(c).Again the distribution of both matter mass and radiation mass decrease with time and the former is higher than the later.The distributions of dark energy mass and total mass coincide on each other.Masses of radiation, matter and dark energy within the universe horizon volume in the general models at n t are given in Table 7. Table 8 shows the equivalent number of the Coma-like clusters to the mass of matter within the universe horizon volume ( ) COMA N t in the general models at the special times Λ , , and rm m o n t t t t .It is obvious that this content of matter strongly decreases with time such that the cosmic space becomes almost matter empty in the far future of the universe.

Conclusion
In this article distributions of the universe horizon distance and universe horizon volume were determined in the five general cosmic models which were established previously.The two distributions were found increasing slowly up to 21.5444 Myr t ≈ , hence they raise appreciably fast up to 60 Gyr t = , then they increase again so slowly until 124 Gyr t = . Distributions of mass of radiation, matter and dark energy within the universe horizon volume were also investigated in the five general models.The masses of radiation and matter are decreasing with time although the mass of dark energy is increasing.The mass of radiation was dominant in the early  where it becomes equivalent to the mass of matter.Afterwards, the mass of matter prevailed until 9.4525 -10.0632Gyr, t = where it becomes equal to the mass of dark energy.From this time onwards the mass of dark energy dominates the universe.The cosmic space gets approximately matter empty in the very remote future of the universe.

Figure 1 .
Figure 1.The distribution of the universe horizon distance in the general cosmic models (a) up to t = 0.5 Gyr; (b) in the range t = 0.5 -50 Gyr; (c) in the range t = 50 -124 Gyr.
The results illustrated in Figures1(a)-(c) are supported by those displayed in Figures2(a)-(c) which show the distributions of the universe horizon volume in the general models in the ranges up to t = 0.5 Gyr, t = 0.5 -50 Gyr and t = 50 -124 Gyr respectively.

Figure 2 .
Figure 2. The distribution of the universe horizon volume in the general cosmic models (a) up to t = 0.5 Gyr; (b) in the range t = 0.5 -50 Gyr; (c) in the range t = 50 -124 Gyr.

Figure 3 .
Figure 3.The distribution of mass and energy within the universe horizon volume in any general cosmic model (a) up to t = 0.5 Gyr; (b) in the range t = 0.5 -50 Gyr; (c) in the range t = 50 -124 Gyr.

Table 2
presents the universe horizon volumes in the general models at the special times

Table 3 .
On the other hand, the distribution of dark energy increases gradually until it intersects with the radiation distribution at the time

Table 1 .
Horizon distances of the universe in the general cosmic models at special times.

Table 2 .
Horizon volumes of the universe in the general cosmic models at special times.

Table 3 .
Cosmic times at which = within the universe horizon volume in the general cosmic models.rmt ( )  ( ) Λ Log M M

Table 4 .
Cosmic times at which

Table 5 .
Cosmic times at which

Table 6 .
Masses of radiation, matter and dark energy within the universe horizon volume in the general cosmic models at Model()

Table 7 .
Masses of radiation, matter and dark energy within the universe horizon volume in the general cosmic models at

Table 8 .
Equivalent number of the Coma-like clusters to the mass of matter within the universe horizon volume in the general cosmic models at special times.