(1) cosmic radius
Suppose the universe isa spheroid. After the radius of the sphere became critical radius a0 , the universe began to expound under the action of repulsion, that is, repulsion expansion.
Because the number of QSOs remarkably decrease When Z > 2.3 (Fig 1) , we define the apparent radius of the outmost layer of the universe.
The a must be the apparent radius, for Z > 2.3 , QSOs are observed by us.
Fig.1 Space distribution of readshift
 S.osmer, Ap.J.,247,762-773(1981).