We extend our investigation on a possible de Sitter symmetry breaking
mechanism in non-linear sigma models. The scale invariance of the quantum
fluctuations could make the cosmological constant time dependent signaling the
de Sitter symmetry breaking. To understand such a symmetry breaking mechanism,
we investigate the energy-momentum tensor. We show that the leading infra-red
logarithms cancel to all orders in perturbation theory in a generic non-linear
sigma model. When the target space is an N sphere, the de Sitter symmetry is
preserved in the large N limit. For a less symmetric target space, the
infra-red logarithms appear at the three loop level. However there is a counter
term to precisely cancel it. The leading infra-red logarithms do not cancel for
higher derivative interactions. We investigate such a model in which the
infra-red logarithms first appear at the three loop level. A nonperturbative
investigation in the large N limit shows that they eventually grow as large as
the one loop effect.Comment: 39page
