Symmetry nonrestoration at high temperature in little Higgs models

A detailed study of the high temperature dynamics of the scalar sector of little Higgs scenarios, proposed to stabilize the electroweak scale, shows that the electroweak gauge symmetry remains broken even at temperatures much larger than the electroweak scale. Although we give explicit results for a particular modification of the littlest Higgs model, we expect that the main features are generic. As a spin-off, we introduce a novel way of dealing with scalar fluctuations in nonlinear sigma models, which might be of interest for phenomenological applications.