  We study the time development of strongly coupled ${\cal N}=4$ supersymmetric
Yang Mills (SYM) theory on cosmological Friedmann-Robertson-Walker (FRW)
backgrounds via the AdS/CFT correspondence. We implement the cosmological
background as a boundary metric fulfilling the Friedmann equation with a
four-dimensional cosmological constant and a dark radiation term. We analyze
the dual bulk solution of the type IIB supergravity and find that the
time-dependence of the FRW background strongly influences the dynamical
properties of the SYM theory. We in particular find a phase transition between
a confined and a deconfined phase. We also argue that some cosmological
solutions could be related to the inflationary scenario.
