Solution

Past exam of the mathematics course of the University of Cambridge / 2018 / ii / Paper 1 / 37E / d / Solution

{c}

The geodesic with nonzero conserved spatial momentum reaches $t=-\infty$ after the finite past proper time
$$
\tau_-=-\frac1{2H}\log\frac{\sqrt{1+v_0^2}+1}{\sqrt{1+v_0^2}-1}.
$$
This is incompleteness of the expanding coordinate patch, whose geodesics extend smoothly in global <de Sitter spacetime>; it is not a curvature singularity.

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 Incoming links: Past incompleteness of the expanding flat slicing of de Sitter spacetime