Consistent Asymptotic Scalar Wavefunction in de Sitter Space

The approximate late conformal time wavefunction for self-interacting scalar quantum fields in de Sitter space is computed. It dominates for conformal times much larger than a certain critical value, $\eta=\eta_{\text{crit}}$ which depends on the dimension and on other characteristics of the matter fields. Its self-consistency (i.e., whether the back reaction is consistent with the de Sitter symmetry) is analyzed.