First part of the cosmology paper

Signed-off-by: Riccardo Finotello <riccardo.finotello@gmail.com>

sec/part1/introduction.tex

@@ -85,11 +85,11 @@ implies
   - \frac{1}{2 \pi \ap}
   \infinfint{\tau}
   \finiteint{\sigma}{0}{\sigma}
-  \sqrt{\dX \cdot \dX - \pX \cdot \pX}
+  \sqrt{\dotX \cdot \dotX - \pX \cdot \pX}
   =
   S_{NG}[X],
 \end{equation}
-where $S_{NG}[X]$ is the Nambu--Goto action for the classical string, $\dX = \ipd{\tau} X$ and $\pX = \ipd{\sigma} X$.
+where $S_{NG}[X]$ is the Nambu--Goto action for the classical string, $\dotX = \ipd{\tau} X$ and $\pX = \ipd{\sigma} X$.
 
 The symmetries of $S_P[\gamma, X]$ are the keys to the success of the string theory framework~\cite{Polchinski:1998:StringTheoryIntroduction}.
 Specifically~\eqref{eq:conf:polyakov} displays symmetries under: