# Homework Help: Event Horizon of Universe

1. Jan 6, 2010

### Cheetox

1. The problem statement, all variables and given/known data
Compute the horizon of the universe as a function of $$\Omega$$m in a flat universe with both matter and a cosmological constant but no radiation.

2. Relevant equations

Event horizon distance
r = a(t)c $$\int_0^tcdt'/a(t')$$

3. The attempt at a solution

No idea how i'm going to be able to transform that integral into something I can do,

Using the FRW equation you can get H2 = $$\Lambda/ 3($$$$\Omega$$m -1)

possibly using H = (da/dt)/a thus dt = da/aH ?

and then if you do substitute for an integral in a would the limits be 0 to 1 as we set a = 1 at present or 0 to a?