We construct a model of cosmological inflation and perturbation based on the higherdimensional gauge theory. The inflaton and curvaton are the scalar fields arising from the extra space components of the gauge field living in more than four dimensions. We take the six-dimensional (6D) Yang-Mills theory compactified on T 2 as a toy model, and apply the one-loop effective potential of the inflaton and the curvaton to the curvaton scenario. We have found that the curvaton is subdominant for the linear curvature perturbation, but that a significant non-Gaussianity and a sizable tensor to scalar ratio are generated. It is possible to set a twisted boundary condition associated with a global U (1) symmetry with the phase α for this fermion. Here we set α = 0.

We study the possibility that the Higgs and the inflaton are the same single field or cousins arising from the extra space components of some higher-dimensional gauge field. We take 5D supersymmetric gauge theory with a matter compactified on S 1 as a toy model and evaluate the one-loop contribution to the Higgs-inflaton potential. Our gauge-Higgs-inflaton unification picture applied to the gauge field of intermediate energy scale (∼ 10 13 GeV) can explain the observed inflation parameters without fine-tuning.

We examine integrability of self-dual Yang-Mills system in the Higgs phase, with taking simpler cases of vortices and domain walls. We show that the vortex equations and the domain-wall equations do not have Painlevé property. This fact suggests that these equations are not integrable. *