Cosmology weele 1
Chapter 2 Dodelson
First we need some basic GR
First of all, the metric
\[
d s^{2}=g_{\mu \nu} d x^{\mu} d x^{\nu} \quad \mu, \nu \in 0,1,2,3
\]
which defines clistance between spacetime points.
In special velativity the metric tensor guv is
\[
g_{\mu \nu}=\eta_{\mu \nu}=\left[\begin{array}{llll}
-1 & & & \\
& 1 & 1 & \\
& & 1 & 1
\end{array}\right]
\]
So that \( d s^{2}=-d t^{2}+d \bar{x}^{2} \)
(this also provides the well known result that photons move on null geodesics
\[
c s^{2}=\left.0\right|_{m=0}
\]
In general \( d s^{2}<0 \) means "timelike", i.e. points which can be reached while noving with \( |v|<c \).
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