标题： 宇宙膨胀的预测由亚历山大·弗里德曼提出以及粒子产生在宇宙学中的影响 显示英文标题

标题： Prediction of the Expansion of the Universe made by Alexander Friedmann and the Effect of Particle Creation in Cosmology

摘要： 这篇综述致力于纪念亚历山大·弗里德曼关于宇宙膨胀预测的百年，介绍了他在1922年和1924年获得的结果，以及这些结果后续发展的概要。 特别关注了数学的作用，这使得弗里德曼能够彻底偏离将我们的宇宙视为静态系统的传统做法。 在讨论宇宙膨胀中粒子产生效应的同时，也探讨了之前研究的由外部电场引起的真空对产生现象。 给出了不同宇宙演化阶段产生的标量和旋量粒子的数量，并指出粒子产生效应在暴胀期后形成相对论性等离子体和冷暗物质中的可能作用。 强调了通过引入宇宙膨胀的概念，弗里德曼对理解我们周围世界所做出的贡献，与托勒密、哥白尼和牛顿在前几个时代所做的贡献相一致。 显示英文摘要

摘要： This review devoted to the centenary of Alexander Friedmann's prediction of the Universe expansion presents the results obtained by him in 1922 and 1924 and the sketch of their further developments. Special attention is paid to the role of mathematics which enabled Friedmann to perform a radical departure from the conventional practice of considering our Universe as a static system. The effect of particle creation in expanding Universe is discussed concurrently with the earlier investigated phenomenon of pair creation from vacuum by external electric field. The numbers of scalar and spinor particles created at different stages of the Universe evolution are presented, and the possible role of the effect of creation of particles in the formation of relativistic plasma and cold dark matter after the inflationary period is noted. It is stressed that by introducing the concept of expanding Universe Friedmann made a contribution to understanding of the world around us compatible to those made by Ptolemy, Copernicus, and Newton in previous epochs.