In this talk, we present whether the new ekpyrotic scenario can be
embedded into ten-dimensional supergravity. We use that the scalar
potential obtained from flux compactifications of type II supergravity
with sources has a universal scaling with respect to the dilaton and
the volume mode. Similar to the investigation of inflationary models,
we find very strong constraints ruling out ekpyrosis from analyzing
the fast-roll conditions. We conclude that flux compactifications tend
to provide potentials that are neither too flat and positive
(inflation) nor too steep and negative (ekpyrosis).
We also discuss the swampland conjecture, which has recently been
attracting attention in string theory and gravity theory, relates to
the slow-roll condition of inflation. First, we will briefly explain
the reason why we focus on the swampland conjecture to investigate the
dynamics of inflation. Next, we discuss the behavior of the scalar
field describing the evolution of the inflationary scenario from the
viewpoint of the swampland conjecture. Finally, we present the
implications of energy conditions on cosmological compactification
solutions of the higher-dimensional Einstein field equations, and show
the relation between the slow-roll condition in the inflationary
scenario and the swampland criterion.