# Age of Universe (Liddles Modern Cosmology)

## Main Question or Discussion Point

Hi,
I am currently reading Liddles Introduction to Modern Cosmology (2nd Ed) and having trouble with problem 8.4, about the age of the universe with a cosmological constant.
The question asks to derive the formula for the age by first writing the Fridemann equation in such a model as
$\frac{da}{dt}$ = $H^{2}_{0}$ $[Ω_{0}a^{-1}$ + $\left(1-Ω_{0})a^{-2}\right]$

But i'm not sure how this step is found, so can't proceed any further. I would appreciate any help to get me started.

cepheid
Staff Emeritus
Gold Member
Welcome to PF hawker3! Hi,
I am currently reading Liddles Introduction to Modern Cosmology (2nd Ed) and having trouble with problem 8.4, about the age of the universe with a cosmological constant.
The question asks to derive the formula for the age by first writing the Fridemann equation in such a model as
$\frac{da}{dt}$ = $H^{2}_{0}$ $[Ω_{0}a^{-1}$ + $\left(1-Ω_{0})a^{-2}\right]$

But i'm not sure how this step is found, so can't proceed any further. I would appreciate any help to get me started.
I'd be happy to help you, but in order to do so, you need to tell me what form of the Friedmann equation you are starting with. Then I can give you suggestions on what manipulations to perform in order to get it into the form given above.

BillSaltLake
Gold Member
I'm having trouble finding a set of conditions in which the formula is correct. Look at the matter-only case for example: a $\propto$t2/3. Then the left side is $\propto$ t-1/3 whereas the 2 right side terms are $\propto$ t-2/3 and t-4/3.

cepheid
Staff Emeritus
I'm having trouble finding a set of conditions in which the formula is correct. Look at the matter-only case for example: a $\propto$t2/3. Then the left side is $\propto$ t-1/3 whereas the 2 right side terms are $\propto$ t-2/3 and t-4/3.