  We derive criteria for whether two cosmological events can have a shared
causal past or a shared causal future, assuming a
Friedmann-Lemaitre-Robertson-Walker universe with best-fit \Lambda CDM
cosmological parameters from the Planck satellite. We further derive criteria
for whether either cosmic event could have been in past causal contact with our
own worldline since the time of the hot "big bang", which we take to be the end
of early-universe inflation. We find that pairs of objects such as quasars on
opposite sides of the sky with redshifts z >= 3.65 have no shared causal past
with each other or with our past worldline. More complicated constraints apply
if the objects are at different redshifts from each other or appear at some
relative angle less than 180 degrees, as seen from Earth. We present examples
of observed quasar pairs that satisfy all, some, or none of the criteria for
past causal independence. Given dark energy and the recent accelerated
expansion, our observable universe has a finite conformal lifetime, and hence a
cosmic event horizon at current redshift z = 1.87. We thus constrain whether
pairs of cosmic events can signal each other's worldlines before the end of
time. Lastly, we generalize the criteria for shared past and future causal
domains for FLRW universes with nonzero spatial curvature.
