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This is from p.120 of Ta-Pei Cheng's Relativity, Gravitation and Cosmology. I cannot understand the way the book calculated the age of the empty universe. The velocity $v$ of expansion is proportional to the distance $d$. That means the expansion velocity has not been constant. But why does the book conclude the age of universe from simply dividing the distance $d$ from the velocity of the current moment? Is there something that I am missing? I need help.

  • $\begingroup$ It is a limit estimation $\endgroup$
    – Alchimista
    Jan 13 '18 at 10:53
  • $\begingroup$ What does that mean? $\endgroup$
    – Keith
    Jan 13 '18 at 14:27
  • $\begingroup$ That it is just an estimate that indeed does not fit to observations. They clearly state that in an empty universe H is supposed to be constant in time $\endgroup$
    – Alchimista
    Jan 13 '18 at 14:29

An empty universe never changes. Also, its value of $H_0$ never changes, and using the Friedmann equation


$H(t) = H_0 = 1.$


$(1/a) (da/dt) = 1,$ and $da/dt = a.$


$dt = da/a$, and $t = ln(a) + const.$


$a = const$ x $e^t.$

Therefore the age is not determinable, since there is no way to choose one value for the constant in preference to another.


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