The maximum value of a occurs when the integral diverges, which is when
26
27
So
28
equals
29
As the maximum occurs at exactly halfway through the lifetime of a close universe, it's total lifetime is
30
31
Now we need to find a value for H_0 that means its evolution matches with the matter-dominated era of the LCDM model.
32
As the scale factor goes to zero, the integrand goes to
33
34
Similiarly for the LCDM model (ignoring the radiation-dominated era) the integrand goes to
35
36
Using
37
38
the integral below converges to the early LCDM universe
39
40
Moving the constant outside the integral we find that:
41
equals
42
Which gives us
43
equals
44
45
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