http://arxiv.org/abs/1705.00730
Geodesics are used in a wide array of applications in cosmology and astrophysics. However, it is not a trivial task to efficiently calculate exact geodesics distances in an arbitrary spacetime. We show that in spatially flat $(3+1)$-dimensional Friedmann-Lema\^itre-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.
W. Cunningham, D. Rideout, J. Halverson, et. al.
Wed, 3 May 17
7/60
Comments: 11 pages, 2 figures