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 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, xi, theta, phi) can be established. A perfect gas universe solution can be worked out, in which there is a constant density rho, 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 H-0 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.