非奇异宇宙的理想气体自相似模型

Self-similarity model of nonsingular perfect gas universe

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=-1),计算出标准宇宙模型的坐标空间膨胀率HF与哈勃常数H0的比值随z的增加而显著减小,该结果对应于高红移超新星的"宇宙加速膨胀"效应.

The present paper investigates the dimensionless dynamical continuity equation of perfect gas motion in gravitational field. Based on Ⅱ 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 HF 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.