 Past incompleteness of the expanding flat slicing of de Sitter spacetime

ID: past-incompleteness-of-the-expanding-flat-slicing-of-de-sitter-spacetime

The geodesic with nonzero conserved spatial momentum reaches

t = - \infty

after the finite past proper time

τ_{-} = - \frac{1}{2 H} lo g \frac{1 + v _{0}^{2} + 1}{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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