We study the accelerated expansion of the Universe through its consequences
on a congruence of geodesics. We make use of the Raychaudhuri equation which
describes the evolution of the expansion rate for a congruence of timelike or
null geodesics. In particular, we focus on the space-time geometry contribution
to this equation. By straightforward calculation from the metric of a
Robertson-Walker cosmological model, it follows that in an accelerated
expanding Universe the space-time contribution to the Raychaudhuri equation is
positive for the fundamental congruence, favoring a non-focusing of the
congruence of geodesics. However, the accelerated expansion of the present
Universe does not imply a tendency of the fundamental congruence to diverge. It
is shown that this is in fact the case for certain congruences of timelike
geodesics without vorticity. Therefore, the focusing of geodesics remains
feasible in an accelerated expanding Universe. Furthermore, a negative
contribution to the Raychaudhuri equation from space-time geometry which is
usually interpreted as the manifestation of the attractive character of gravity
is restored in an accelerated expanding Robertson-Walker space-time at high
speeds.Comment: 11 pages, 2 figures. Final version changed to match published version
in JCAP. References updated. Conclusions unchange
