非奇异宇宙的理想气体自相似模型

通过引力作用下理想气体运动连续性方程的无量纲化，根据量纲理论Π定理，以尺度因子R(t)为物理量统一度量基准，发现了引力作用下理想气体宇宙模型的自相似性和一系列R(t)的解析解.基于R(t)，可建立对应的、具有非欧氏几何特性的均匀膨胀时空坐标系S(t，ξ，θ，φ)，并获得一个密度ρ为常数、速度u为零、压强p不为零的理想气体宇宙解.在这个解的形式中，光子红移量z所表现的是光子传播距离r，当红移量z较小时两者成正比(即哈勃定律).由均匀膨胀坐标系还可推导出Robertson-Walker度规(k= 关键词： 宇宙 自相似 哈勃定律

Self-similarity model of nonsingular perfect gas universe

The present paper investigates the dimensionless dynamical continuity equation of perfect gas motion in gravitational field. Based on Π axiom of dimensional theory， self-similarity of perfect gas universe with gravity and a series of exact solutions of R(t) are deduced. Based on R(t)，a non-Euclidean homogeneous space-time coordinate system S(t,ξ，θ，φ) can be established. A perfect gas universe solution can be worked out， in which there is a constant density ρ， the velocity u value being zero， and there is a nonzero pressure p. In this solution， the red shift z represents the propagating distance r. When z is much less than 1， it is proportional to r (Hubbles law). The Robertson-Walker (k=-1) metric of normal universe model is obtained from homogeneous expanding coordinates， and the ratio of expanding rate H_F to the Hubble constant H₀ decreases notably as the value of z rises. It corresponds to the “universal accelerated expansion” observed in the spectrum of a high-red-shift supernova.