1. May 8, 2004

meteor

cos the Friedmann equation is:
$$H^{2}= \frac{8*pi*G*rho}{3}-\frac{k*c^{2}}{R^{2}}$$
but the concordance model says that k=0, so we can eliminate the last term of the equation
then we isolate rho, the density of energy:
$$rho=\frac{3*H^{2}}{8*pi*G}$$
but however, the formula for the critical energy density is
$$rho_{crit}=\frac{3*H^2*c^2}{8*pi*G}$$
but the concordance model says that rho=rhocrit
but you see that the 2 formulae are not equal, there's an extra c2 in the formula for rhocrit

I can't figure where is the mistake

Last edited: May 8, 2004
2. May 8, 2004

Stingray

rho is mass density. rho_crit is energy density (as you wrote it). Mass and energy have different units, and you use c^2 to convert between them.

Most people like to use units such that c=1, and then energy and mass are interchangable. This convention is so common that books are sometimes careless about distinguishing the two.

Last edited: May 8, 2004
3. May 8, 2004

meteor

Here's jeff, and I think that he is a knowledgeable person, and says that rho includes all kinds of energy, not only mass

Last edited: May 8, 2004
4. May 8, 2004

Stingray

That's true. I was being a little sloppy myself. rho includes everything, but the way you wrote it, it has units of mass/volume, whereas rho_crit has units of energy/volume. Wherever you're quoting rho_crit from has a slightly different form for Friedmann's equation than you do, so their answer is different by c^2. This is just a convention. You can choose either mass units or energy units for rho as long as H works out as 1/time in the end.

5. May 19, 2004

Chronos

use the conversion c^2=m/e