Redshift in Terms of k | General Relativity

[unscientific]

Hi, I have been studying general relativity using Hobson's lately, particularly about the FRW universe.

I know that for a matter universe with curvature,
$$H^2 = \left( \frac{\dot a}{a} \right)^2 = \frac{8\pi G}{3} \rho_m -\frac{kc^2}{a^2}$$
Another expression I came across is also
$$1 = \Omega_m + \Omega_k$$

I am thinking when the curvature dominates at late times what would the redshift be like.
When curvature dominates, the FRW equation is simply $\left( \frac{\dot a}{a} \right)^2 = \frac{8\pi G}{3} \rho_m -\frac{kc^2}{a^2}$.

I know that redshift is $1+z = \frac{1}{a}$. How do I find redshift in terms of $\Omega_k$?

 

[unscientific]

solved.