  We investigate infra-red dynamics of the non-linear sigma model in de Sitter
space. In the presence of minimally coupled massless scalar fields, the de
Sitter symmetry is dynamically broken and physical constants become time
dependent. We find that the coupling constant of the non-linear sigma model
becomes time dependent. The power counting arguments of the infra-red
logarithms indicate that the cosmological constant also acquires time
dependence. We find that such infra-red logarithms cancel out in a perturbative
investigation up to the two loop level. We further demonstrate a
non-perturbative non-renormalization of the cosmological constant in the large
$N$ limit of the non-linear sigma model.
