The particle and event horizons are widely known and studied concepts, but
the study of their properties, in particular their evolution, have only been
done so far considering a single state equation in a decelerating universe.
This paper is the first of two where we study this problem from a general point
of view. Specifically, this paper is devoted to the study of the evolution of
these cosmological horizons in an accelerated universe with two state
equations, cosmological constant and dust. We have obtained closed-form
expressions for the horizons, which have allowed us to compute their velocities
in terms of their respective recession velocities that generalize the previous
results for one state equation only. With the equations of state considered, it
is proved that both velocities remain always positive.Comment: 12 pages, 8 figures. This is an author-created, un-copyedited version
of an article accepted for publication in Journal of Cosmology and
Astroparticle Physics. New versions have been submitted to update the
bibliography and corrected/clarify some non essential topic
