diff --git a/theory/Cosmology/coordinates.tex b/theory/Cosmology/coordinates.tex index 22d0da29330f850df7fc3bdb979b49c70670d96c..38a571aefea68fbe1bc7a8ebc3867109f1c4736e 100644 --- a/theory/Cosmology/coordinates.tex +++ b/theory/Cosmology/coordinates.tex @@ -35,7 +35,7 @@ respectively. Following \cite{Peebles1980} (ch.7), we introduce the gauge transformation $\Lag \rightarrow \Lag + \frac{d}{dt}\Psi$ with $\Psi \equiv \frac{1}{2}a\dot{a}\mathbf{r}_i^2$ and obtain \begin{align} - \Lag &= \frac{1}{2}m_ia^2 \dot{\mathbf{r}}_i^2 - + \Lag &= \frac{1}{2}m_ia^2 \dot{\mathbf{r}}_i'^2 - \frac{1}{\gamma-1}m_iA_i'\left(\frac{\rho_i'}{a^3}\right)^{\gamma-1} -\frac{\phi'}{a},\\ \phi' &= a\phi + \frac{1}{2}a^2\ddot{a}\mathbf{r}_i'^2,\nonumber