Investigation of Distribution of Mass and Energy in Closed Model of the Universe

The universe’s horizon distance and volume are constructed in the closed cosmic model. The universe horizon distance distribution increases constantly for t < tme and decreases for t > tme . However, the universe’s horizon volume shows a sudden reduction in the range t = 0.5 Gyr - tme due to the change of the universe space from flat to curved then closed in the interval 15.1261 Gyr t tme. On the other hand, this distribution exhibits an abrupt rise in the range t = tme - t* due to the change of the universe space from closed then curved to flat in the interval 39.3822 t 40.7521 Gyr. The distributions of mass of radiation, matter and dark energy within the horizon volume of the universe are also investigated. These distributions reveal similar noticeable changes as the universe’s horizon volume distribution for the same reasons. The mass of radiation dominates up to t = 53221.5 yr, then the mass of matter becomes larger. Afterwards, both distributions of radiation and matter decrease while the distribution of dark energy rises until t = 10.1007 Gyr, where the mass of dark energy prevails up to t = tme. Hence, the distribution of dark energy descends until t = 40.2892 Gyr, where the mass of matter becomes prominent again. At t = 53.6246 Gyr the masses of both matter and radiation become appreciably high such that the intercluster space will vanish and clusters of galaxies interfere with each other. Furthermore, not only the intergalactic medium will disappear, but also galaxies will collide and merge with each other to form extremely dense and close cosmological bodies. These very dense bodies will undergo further successive collisions and mergers under the action of central gravity, where the interstellar medium will vanish and the universe would develop to big crunch at tbc = 53.6251 Gyr. It is interesting to note that the horizon distance of the universe in the closed model at t = tme is in very good agreement with the maximum horizon distances in the five general cosmic models.