Infrared dynamics of massive scalars from the complementary series in de Sitter space

Abstract: We continue a previous study about the infrared loop effects in the $D$-dimensional de Sitter space for a real scalar $\phi^4$ theory from the complementary series whose bare mass belongs to the interval $\frac{\sqrt{3}}{4}\, \left(D-1\right) < m \leq \frac{D-1}{2}$, in units of the Hubble scale. The lower bound comes from the appearance of discrete states in the mass spectrum of the theory when that bound is violated, causing large IR loop effects in the vertices. We derive an equation which allows to perform a self--consistent resummation of the leading IR contributions from all loops to the two-point correlation functions in an expanding Poincar\'{e} patch of the de Sitter manifold. The resummation can be done for density perturbations of the Bunch--Davies state which violate the de Sitter isometry. There exist solutions having a singular (exploding) behavior and therefore the backreaction can change the de Sitter geometry.