Update cosmology.tex, $k=\pm 1$, FRW -> FLRW

tutorials/cosmology.tex

-
 \subsection{Background cosmology}
 \subsection{Background cosmology}
 
 
-The Friedmann-Robertson-Walker (FRW) metric is
+The Friedmann-Lema\^{\i}tre-Robertson-Walker (FLRW) metric is
 \begin{equation}
 \begin{equation}
 ds^2 = -c^2 dt^2 + a^2(t)\left[\frac{dr^2}{1-kr^2} + r^2 \, d\Omega^2 \right]. 
 ds^2 = -c^2 dt^2 + a^2(t)\left[\frac{dr^2}{1-kr^2} + r^2 \, d\Omega^2 \right]. 
 \end{equation}
 \end{equation}
-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 $k \pm 1$ 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 $k = \pm 1$ 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:}
 \subsubsection{Problems:}
 
 
@@ -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? 
 What assumptions are required for this? 
 
 
 \item Define the angular diameter distance $D_A$ and the luminosity distance $D_L$.
 \item Define the angular diameter distance $D_A$ and the luminosity distance $D_L$.
-Show that in any FRW universe,
+Show that in any FLRW universe,
 \[
 \[
 D_L = (1+z)^2 D_A.
 D_L = (1+z)^2 D_A.
 \]
 \]