(3)       The age of the universe

The outmost layer was expanded from   a₀  to  a  in time  t_e ,  its equation is

or

                                                                                                                   (10)

Now put   L=constant,   upon solving this differential equation we obtain

The  t_e  is the minimum of expansion age from  Z=0   to  Z=2.3   because   
L=constant.   Substituting the value of cosmic parameter (Table 1), we get 
t_e>18.6×10⁹  years

Upon solving equation (10) or formula (14) can be written as

using   a₀=ma  to find    

thus

Assuming   m=0.4   to be starting point of time, i.e.  t=0, we obtain 
age curve in Fig.3.

Initial velocity of outmost layer equals zero to be impossible. If there
 was Initial velocity about thousands of kilometer, this corresponded to the
 beginning of repulsion expansion from  m=0.98.
    

                         Fig.5 Age curve

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[note]

put  L=constant

When

a=a0,

,

thus

Substituting  a₀=μa ,  we  get