  We study the dynamics of light quantum scalar fields in de Sitter space on
superhorizon scales. We compute the self-energy of an O(N) symmetric theory at
next-to-leading order in a 1/N expansion in the regime of superhorizon momenta,
and we obtain an exact analytical solution of the corresponding Dyson-Schwinger
equations for the two-point correlator. This amounts to resumming the infinite
series of nonlocal self-energy insertions, which typically generate spurious
infrared and/or secular divergences. The potentially large de Sitter logarithms
resum into well-behaved power laws from which we extract the field strength and
mass renormalization. The nonperturbative 1/N expansion allows us to discuss
the case of vanishing and negative tree-level square mass, which both
correspond to strongly coupled effective theories in the infrared.
