Expansion of positively and negatively curved universe

[Apashanka]

From the friedmann equation H²=8πGρ/3-k/a²,
1=ρ/(3H²/8πG)-k/a²H²
1=ρ/ρ_c-k/adot²
adot=+-√[k/(ρ/ρ_c-1)]
It is therefore if expansion/contraction is taking place ,
Positively curved space will have ρ>ρ_c
And negatively curved will have ρ<ρ_c
Is it the case??

 

[PeterDonis]

It is therefore if expansion/contraction is taking place ,
Positively curved space will have ρ>ρ_c
And negatively curved will have ρ<ρ_c
Is it the case??

Sort of. But the version of the Friedmann equation you keep on trying to use, in multiple threads now, is not suitable for answering this question.

Here is the equation you insist on trying to use (btw, it would be a good idea to learn how to use the PF LaTeX feature):

$$
\dot{a} = \pm \sqrt{\frac{k}{\frac{\rho}{\rho_c} - 1}}
$$

The first problem is that this equation gives incorrect information for $\dot{a} = 0$.

The second problem (which came up in a previous thread) is that this equation doesn't work for $k = 0$.

So I really don't understand why you keep on insisting on this form of the equation, when it has these problems.

 

[Apashanka]

Sort of. But the version of the Friedmann equation you keep on trying to use, in multiple threads now, is not suitable for answering this question.

Here is the equation you insist on trying to use (btw, it would be a good idea to learn how to use the PF LaTeX feature):

$$
\dot{a} = \pm \sqrt{\frac{k}{\frac{\rho}{\rho_c} - 1}}
$$

The first problem is that this equation gives incorrect information for $\dot{a} = 0$.

The second problem (which came up in a previous thread) is that this equation doesn't work for $k = 0$.

So I really don't understand why you keep on insisting on this form of the equation, when it has these problems.

Thanks