  We discuss the particle horizon problem in the framework of spatially
homogeneous and isotropic scalar cosmologies. To this purpose we consider a
Friedmann-Lemaitre-Robertson-Walker (FLRW) spacetime with possibly non-zero
spatial sectional curvature (and arbitrary dimension), and assume that the
content of the universe is a family of perfect fluids, plus a scalar field that
can be a quintessence or a phantom (depending on the sign of the kinetic part
in its action functional). We show that the occurrence of a particle horizon is
unavoidable if the field is a quintessence, the spatial curvature is
non-positive and the usual energy conditions are fulfilled by the perfect
fluids. As a partial converse, we present three solvable models where a phantom
is present in addition to a perfect fluid, and no particle horizon~appears.
