高维宇宙中标量粒子的非热分布和总熵的增加

本文讨论了宇宙处于高维相时无质量标量粒子气的非热分布、能密度以及增加的熵。从迅变阶段粒子数分布不变的假定出发,在初始温度β₀^-11/2α₂₀^-1的近似下,计算得高维相结束时的总熵与初始总嫡之比S_f/S₀与T₀α₂₀/T_fα_2f同量级。S_f,T 关键词：

NON-THEPMAL DISTRIBUTION AND TOTAL ENTROPY INCREASE OF SCALAR PARTICLE GAS IN THE MULTI-DIMENSIONAL UNIVERSE

In this paper, we discuss the non-thermal distribution, the energy density and entropy increase of a massless particle gas in the Multi-dimensional phase of universe. Starting from the assumption that the distribution of particle number be invariant during the inflation, and in the approximate condition that the initial temperature T₀ = β₀^-1 < D^1/2a₂₀^-1 (D is the dimension of the extra space and a₂₀ is the scale of the extra space befor inflation), we calculate the ratio of the total entropy S_t at the ending of the Multi-dimensional phase to the corresponding quantity S₀ in the initial stage, which has the same order of magnitude as the ratio of T₀a₂₀ to T_fa_2f (T_f is the temperature just as the universe enters the ordinary phase and a_2f is the stable scale of the extra space. Planck unit, h =c = k_B=G= 1, is used throughout ).