Can an Infinitely Long Object Fit in an Expanding Universe?

Abstract

Does space stretch its contents as the universe expands? Usually we say the answer is no - the stretching of space is not like the stretching of a rubber sheet that might drag things with it. In this paper we explore a potential counter example - namely we show that is is impossible to make an arbitrarily long object in an expanding universe, because it is impossible to hold the distant end of the object "stationary" with respect to us (as defined in the Friedmann-Lemaitre-Robertson-Walker metric). We show that this does not mean that expanding space has a force associated with it, rather, some fictitious forces arise due to our choice of reference frame. By choosing our usual time-slice (where all comoving observers agree on the age of the universe), we choose a global frame that does not correspond to the frame of any inertial observer. As a result, simple relativistic velocity transforms generate an apparent acceleration, even where no force exists. This effect is similar to the fictitious forces that arise in describing objects in rotating reference frames, as in the case of the Coriolis effect.