Above, $d\Omega^2= d\theta^2+\sin^2\theta\, d\phi^2$, and $r, \theta, \phi$ are comoving coordinates, while $k =0$ for spacially flat universe and $k \pm1$ for positively/negatively curved universe. We defined the comoving distance $\chi$ and proper distance $D_p$ and showed that, for a spatially flat universe, $D_p(t)= a(t)\,\chi$.
Above, $d\Omega^2= d\theta^2+\sin^2\theta\, d\phi^2$, and $r, \theta, \phi$ are comoving coordinates, while $k =0$ for spacially flat universe
and $k =\pm1$ for positively/negatively curved universe. We defined the comoving distance $\chi$ and proper distance $D_p$ and showed that,
for a spatially flat universe, $D_p(t)= a(t)\,\chi$.
\subsubsection{Problems:}
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@@ -19,7 +20,7 @@ Can this be used as a way to constrain the spatial curvature of the universe?
What assumptions are required for this?
\item Define the angular diameter distance $D_A$ and the luminosity distance $D_L$.