deletions | additions       diff --git a/cosmology.tex b/cosmology.tex  index 8e6b428..d573b65 100644  --- a/cosmology.tex  +++ b/cosmology.tex 
...
\begin{equation}  \begin{split}  \frac{d x}{d t} = &=  \frac{1}{a} \\ 1 + z = &=  \frac{\lambda_0}{\lambda} = \frac{\omega_0}{\omega} = \frac{a(t_0 )}{a(t_e )} \end{split}  \end{equation}