Help with Friedman equations and density of energy

[Helpsearcher]

Hi there,

 

I really hope someone can help me with my stupid but urgent problem of understanding something crucial about the Friedman equations.

 

So; one of them looks like this (forget about the constants; it is about the principles):

 

change of the scale factor with time - density - cosmol. constant = -k (curvature term)


Then this is sometimes rewritten in terms of densities, which gives:

 

change of the scale factor with time - (density of matter + vacuum energy density) = -k (curvature term)

 

Now; here is what I do not get.

 

Generally the density of the vacuum (or equivalently the cosmol. constant) are treated just like the density of matter; so they have the same effect on the curvature, which somehow should be understandable as energy=matter and so both curve the spacetime.

But then, it is usually stated that the cosmol. constant, and so the vacuum energy density, are working against gravitation (repulsive).

However; I do not understand, how to see this in the equations above. I mean; both seem to have the same effect: energy=matter -> attraction (simplified).

 

Where is my error of thinking?

I really hope that someone here can enlighten me.

 

Thx

[Iggy]

Hi there,

 

I really hope someone can help me with my stupid but urgent problem of understanding something crucial about the Friedman equations.

 

So; one of them looks like this (forget about the constants; it is about the principles):

 

change of the scale factor with time - density - cosmol. constant = -k (curvature term)

 

 

Then this is sometimes rewritten in terms of densities, which gives:

 

change of the scale factor with time - (density of matter + vacuum energy density) = -k (curvature term)

 

 

Now; here is what I do not get.

 

Generally the density of the vacuum (or equivalently the cosmol. constant) are treated just like the density of matter; so they have the same effect on the curvature, which somehow should be understandable as energy=matter and so both curve the spacetime.

But then, it is usually stated that the cosmol. constant, and so the vacuum energy density, are working against gravitation (repulsive).

However; I do not understand, how to see this in the equations above. I mean; both seem to have the same effect: energy=matter -> attraction (simplified).

 

Where is my error of thinking?

I really hope that someone here can enlighten me.

 

Thx

The Friedmann acceleration equation is:

 

[math]\frac{\ddot{a}}{a} = - \frac{4 \pi G}{3} \left( \rho + \frac{3p}{c^2} \right) + \frac{\Lambda c^2}{3}[/math]

 

A positive density term, [math]\rho[/math] pushes [math]\ddot{a}[/math] in the negative direction meaning it decreases the expansion speed over time, A positive cosmological constant term, [math]\Lambda[/math], pushes [math]\ddot{a}[/math] in the positive direction -- increasing expansion speed over time.

 

A static universe would have [math]\dot{a} = \ddot{a} = 0[/math]. Assuming no (or very little) radiation pressure, that would make [math]\Lambda = 4 \pi G \rho[/math].

 

Is this the equation you're talking about?

[Helpsearcher]

Thx for the hint; ya....I missed the more important acceleration equation. Need to have a deeper a look on those together.