Uniformly accelerated traveler in an FLRW universe

This paper introduces an analytical treatment of accelerated and geodesic motion within the framework of the Friedmann-Lema\^{\i}tre-Robertson-Walker (FLRW) spacetime. By employing conformal time transformations we manage to convert second order differential equations of motion in FLRW spacetime to first order equations in the conformally transformed spacetime. This allows us to derive a general analytical solution in closed-form for accelerated motion in spatially curved FLRW spacetime. We provide few examples of this general solution. The last part of our work focuses on the return journey for a traveler exploring a FLRW universe. We derive certain conditions for a de Sitter universe that have to be satisfied in order to achieve a return journey.