Nonlinear sigma model in de Sitter space

We investigate infrared dynamics of the nonlinear 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 effective coupling constant of the nonlinear sigma model becomes time dependent. The power counting arguments of the infrared logarithms indicate that the effective cosmological constant also acquires time dependence. We find that such infrared logarithms cancel out in a perturbative investigation up to the two loop level. We further demonstrate a nonperturbative nonrenormalization of the cosmological constant in the large N limit of the nonlinear sigma model.