1. Dec 13, 2007

### foranlogan5

could anyone please help me with this coursework,i am soo confused with maths,thanks
1)

Start with friedmann equation for case for flat universe k=0 with mass density total p =p(m) + p(cosmo constant). how can i derive integral relating scale factor to time in form

$f(a)da =$(8piG/3)^(1/2) where \$=integral
then by using change of variable a to s
s = {(p(cos)/p(mo))x(a/a(o))^3}^(1/2)

and

Then another change of variable s to (THETA) = sinh^-1(s) should be able to calculate integral in A to obtain a relation for t = G(A) WHERE G(A) YOU DERIVE

where p(mo) is density matter at t =0 and a(o) is scale factor at time t=0
x=times
^3= to power of three
sinh(s)^-1 does not equal 1 /sinh(s)

2. Dec 13, 2007

### cristo

Staff Emeritus
Well, first you should write down the correct Friedmann equation.

Note that you need to show some work before we can help you here. Also, if you intend writing long mathematical expressions, it may be worth learning to use the board's $\LaTeX$ feature.

3. Dec 13, 2007

### foranlogan5

thanks cristo, friedmann H^2 = (8piG/3)p + (kc^2)/(a^2)
and i'll consider learning latex

4. Dec 13, 2007

### cristo

Staff Emeritus
Now, you are told that the space is flat, so that should make a change to your Friedmann equation. Write H in terms of the scale factor and its time derivative. You should be able to write rho_m and rho_lambda in terms of the scale factor also.

5. Dec 13, 2007

### foranlogan5

da/{ax(rho_m +rho_lamb)^1/2} = dt(8piG/3)^1/2
is that the answer to first part?
i think thats correct

6. Dec 13, 2007

### George Jones

Staff Emeritus
I s either $\rho_m$ or $\rho_\Lambda$ a function of $a$? In order to do the integral, explicit functional forms must be used.

7. Dec 13, 2007

### foranlogan5

could you further that point george,i dont quite understand what you are saying?

8. Dec 13, 2007

### George Jones

Staff Emeritus
As the universe expands, does the density of matter change? What about the energy density of the vacuum? If they do change, in what way? If they do change, you might want to write them in terms of their values now (look at your first post) and $a$.