 Timelike geodesic in the expanding flat slicing of de Sitter spacetime

ID: timelike-geodesic-in-the-expanding-flat-slicing-of-de-sitter-spacetime

For a timelike geodesic moving in the

x

direction with

t (0) = x (0) = 0

and

\overset{x}{˙} (0) = v_{0} > 0

e^{2 H t} \overset{x}{˙} = v_{0}

\dot{t} = 1 + v_{0}^{2} e^{- 2 H t} .

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