Non-linear sigma model in de Sitter space

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.