We describe the dynamics of strongly coupled field theories in de Sitter
spacetime using the holographic gauge/gravity duality. The main motivation for
this is to explore the possibility of dynamical phase transitions during
cosmological evolution. Specifically, we study two classes of theories: (i)
conformal field theories on de Sitter in the static patch which are maintained
in equilibrium at temperatures that may differ from the de Sitter temperature
and (ii) confining gauge theories on de Sitter spacetime. In the former case we
show the such states make sense from the holographic viewpoint in that they
have regular bulk gravity solutions. In the latter situation we add to the
evidence for a confinement/deconfinement transition for a large N planar gauge
theory as the cosmological acceleration is increased past a critical value. For
the field theories we study, the critical acceleration corresponds to a de
Sitter temperature which is less than the Minkowski space deconfinement
transition temperature by a factor of the spacetime dimension.Comment: 35 pages, LaTeX, 4 figures, v2: refs adde
