  Instabilities of two dimensional (1+1) de Sitter space induced by interacting
fields are studied. As for the case of flat Minkowski space, several
interacting fermion models can be translated into free boson ones and vice
versa. It is found that interacting fermion theories do not lead to any
instabilities, while the interacting bosonic sine-Gordon model does lead to a
breakdown of de Sitter symmetry and to the vanishing of the vacuum expectation
value of the S matrix.
