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arXiv · 1705.00730

Exact Geodesic Distances in FLRW Spacetimes

William J. Cunningham·David Rideout·James Halverson·Dmitri Krioukov
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Abstract

Geodesics are used in a wide array of applications in cosmology and astrophysics. However, it is not a trivial task to efficiently calculate exact geodesic distances in an arbitrary spacetime. We show that in spatially flat (3+1)-dimensional Friedmann-Lemaitre-Robertson-Walker (FLRW) spacetimes, it is possible to integrate the second-order geodesic differential equations, and derive a general method for finding both timelike and spacelike distances given initial-value or boundary-value constraints. In flat spacetimes with either dark energy or matter, whether dust, radiation, or a stiff fluid, we find an exact closed-form solution for geodesic distances. In spacetimes with a mixture of dark energy and matter, including spacetimes used to model our physical universe, there exists no closed-form solution, but we provide a fast numerical method to compute geodesics. A general method is also described for determining the geodesic connectedness of an FLRW manifold, provided only its scale factor.

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William J. Cunningham, David Rideout, James Halverson, Dmitri Krioukov. 2017-05-01. Exact Geodesic Distances in FLRW Spacetimes. https://doi.org/10.1103/physrevd.96.103538

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