Solving Friedmann Equation for Cosmology

[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)

 

[cristo]

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 [itex]\LaTeX[/itex] feature.

 

[foranlogan5]

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

 

[cristo]

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.

 

[foranlogan5]

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

 

[George Jones]

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

I s either [itex]\rho_m[/itex] or [itex]\rho_\Lambda[/itex] a function of [itex]a[/itex]? In order to do the integral, explicit functional forms must be used.

 

[foranlogan5]

could you further that point george,i don't quite understand what you are saying?

 

[George Jones]

could you further that point george,i don't quite understand what you are saying?

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 [itex]a[/itex].