_{1}

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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.

In a previous study [

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 [

We have seen in [

where

Consequently the change in the horizon distance of the universe in the time interval between two instants of scale factors

The horizon volume of the universe at any given time is

It is also obvious from [

where

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 [

Thus the time interval between two instants with scale factors

In determination of the distributions of

i) Set

ii) Compute

iii) Start general DO loop

iv)

v) Calculate new value of cosmic time t numerically using(16-b), where

vi) Determinate new value of the universe horizon distance

vii) Obtain the corresponding values of

viii) Continue the general DO loop.

The distribution of the universe horizon distance in the general models up to

The results illustrated in Figures 1(a)-(c) are supported by those displayed in Figures 2(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.

The distribution of mass and energy within the universe horizon volume of the universe in any general model up to

The distribution of mass and energy within the universe horizon volume of the universe in any general model in the range

The distribution of mass and energy within the universe horizon volume in any general model in the range

Model | ||||
---|---|---|---|---|

A | 118.1520 | 12.7667 | 14.2969 | 19.0103 |

B | 112.1480 | 12.7586 | 14.1588 | 18.9849 |

C | 118.0740 | 12.7812 | 14.2780 | 19.0274 |

D | 98.0130 | 12.3367 | 13.8666 | 18.3062 |

E | 94.3170 | 12.4269 | 13.8070 | 18.4510 |

Model | ||||
---|---|---|---|---|

A | 13820.0 | 17.4322 | 24.4819 | 57.5555 |

B | 11820.0 | 17.3990 | 23.7792 | 57.3248 |

C | 13790.0 | 17.4916 | 24.3849 | 57.7111 |

D | 7890.0 | 15.7295 | 22.3372 | 51.3939 |

E | 7030.0 | 16.0772 | 22.0504 | 52.6234 |

Model | |||
---|---|---|---|

A | 55.9162 | 28.2526 | 18.1498 |

B | 49.6665 | 28.2876 | 18.0712 |

C | 55.8428 | 28.2529 | 18.1562 |

D | 38.4783 | 28.3338 | 17.9566 |

E | 34.6275 | 28.3753 | 17.8515 |

Model | |||
---|---|---|---|

A | 0.5839 | 23.0153 | 25.5410 |

B | 0.5736 | 22.9834 | 25.5375 |

C | 0.5808 | 23.0202 | 25.5445 |

D | 0.5166 | 22.9407 | 25.5350 |

E | 0.5259 | 22.8906 | 25.5216 |

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

Model | |||
---|---|---|---|

A | 9.4650 | 24.2507 | 20.8831 |

B | 9.6930 | 24.2393 | 20.8339 |

C | 9.4525 | 24.2594 | 20.8937 |

D | 9.6289 | 24.2564 | 20.7974 |

E | 10.0632 | 24.2109 | 20.7030 |

Model | |||
---|---|---|---|

A | 20.4531 | 23.9625 | 24.3973 |

B | 20.4324 | 23.9683 | 24.3785 |

C | 20.4570 | 23.9663 | 24.4086 |

D | 20.4035 | 23.9954 | 24.3981 |

E | 20.3684 | 23.9921 | 24.3328 |

Model | |||
---|---|---|---|

A | 8.8400 | 15.3480 | 24.7694 |

B | 8.9797 | 15.4781 | 24.7571 |

C | 8.7546 | 15.2847 | 24.7779 |

D | 8.1326 | 14.8863 | 24.7706 |

E | 8.8615 | 15.4585 | 24.7258 |

Model | ||||
---|---|---|---|---|

A | 1.1142 | |||

B | 1.5034 | |||

C | 0.9631 | |||

D | 0.3848 | |||

E | 1.4370 |

universe up to