0
$\begingroup$

enter image description here

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.

$\endgroup$
3
  • $\begingroup$ 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
1
$\begingroup$

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

https://en.wikipedia.org/wiki/Friedmann_equations#Detailed_derivation

$H(t) = H_0 = 1.$

Therefore

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

Therefore

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

Therefore

$a = const$ 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.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.