S10. A Newtonian Homogeneous Expanding Universe - SOLUTIONS

Exercise 10.1.1

Answer

\[\begin{equation*}
\begin{aligned}
d = a\ell \quad \Longrightarrow \quad \ell = \frac{d}{a}
\end{aligned}
\end{equation*}\]

Substituting for \(\ell\) in \(v = \dot a \ell\), we get

\[\begin{equation*}
\begin{aligned}
v = \frac{\dot a}{a}d
\end{aligned}
\end{equation*}\]

Now substituting in \(\dot a/a = H\), we get

\[\begin{equation*}
\begin{aligned}
v = H d
\end{aligned}
\end{equation*}\]