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How can a time-like trajectory be calculated using the Friedmann-Robertson-Walker metric?
Using the following FRW metric,
$$ds^2=-c^2dt^2+R^2(t)(d\chi^2+f(\chi)d\Omega)$$
and considering $d\Omega=0$ from now on, it is clear that for a light-like trajectory, the equation must read $ds^2=0$ ...
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