【摘要】 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^-1<D^1/2α₂₀^-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_f为高维相结束时的总熵与温度;S₀,T₀为进入迅变阶段前的总熵和温度;α₂₀和α_2f分别为迅变前后的额外空间的标度因子;D为额外空间的维数。本文采用=c=k_B=G=1的普朗克单位制。更多还原

【Abstract】 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 St 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 ).更多还原