Basic geometric and kinematic features of the Standard Cosmological Model
D. Nagirner,1 and S. Jorstad 1,2 1
Astronomy Department, St. Petersburg State University, Universitetskij Pr. 28, Petrodvorets, 198504 St. Petersburg, Russia 2 Boston University, 725 Commonwealth Ave., Boston, MA, 02215, USA
arXiv:1706.00895v1 [gr-qc] 3 Jun 2017
Abstract
In this paper we calculate quantitative characteristics of basic geometric and kinematic properties of the Standard Cosmological Model (ΛCDM). Using equations of Friedman uniform cosmological models we derive equations characterizing a ΛCDM, which describes the most appropriate real universe. The equations take into account the effects of radiation and ultrarelativistic neutrinos. We show that the universe at very early and late stages can be described to sufficient accuracy by simple formulas. We derive moments when densities of gravitational components of the universe become equal, when they contribute equally to the gravitational force, when the accelerating expansion of space starts, and several others. The distance to the expanding spherical horizon and its acceleration are determined. Terms of the horizon, second inflation, and second horizon are explained. The remote future of the universe and the opportunity in principle of connection with extraterrestrial civilizations are discussed. 1
Introduction
Let’s list the questions that reveal the essence of the model. What is equal the Hubble distance? At what distance from us is the horizon? What is the speed of expansion at the horizon? What is the rate of expansion of the horizon? What is the acceleration at the Hubble distance and on the horizon? When did acceleration start, at what redshift? What will happen to the universe in the distant future? What is the second inflation and second horizon? To what distances, in principle, can a signal reach extraterrestrial civilizations? From what distances will they be able to answer? This paper provides answers to the questions posed above and describes quantitative characteristics of the cosmological model, which is called Standard. Based on this model, the anisotropy of the relic radiation was quite accurately reproduced, and primary nucleosynthesis and formation of large-scale structure of the universe were calculated, as described in well-known monographs [1, 2, 3, 4, 5]. However, we do not touch on these and other physical problems of the history of the universe, limiting ourselves to geometric and kinematic studies of the Standard model. We begin with a brief exposition of the general theory of homogeneous cosmological models.
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5 Conclusion
Therefore, our paper gives a quantitative description of geometric and kinematic properties of the model, which is now considered as the most adequate model of the existing universe.