We study whether the inflation is realized based on the radion gauge-Higgs potential obtained from the one-loop calculation in the 5-dimensional gravity coupled to a $U(1)$ gauge theory. We show that the gauge-Higgs can give rise to inflation in acco
rd with the astrophysical data and the radion plays a role in fixing the values of physical parameters. We clarify the reason why the radion dominated inflation and the hybrid inflation cannot occur in our framework.
There has been a proposal that infrared quantum effects of massless interacting field theories in de-Sitter space may provide time-dependent screening of the cosmological constant. As a concrete model of the proposal, we study the three loop correcti
ons to the energy-momentum tensor of massless $lambda phi^4$ theory in the background of classical Liouville gravity in $D=2$ dimensional de-Sitter space. We find that the cosmological constant is screened in sharp contrast to the massless $lambda phi^4$ theory in $D=4$ dimensions due to the sign difference between the cosmological constant of the Liouville gravity and that of the Einstein gravity. To argue for the robustness of our prediction, we introduce the concept of time-dependent infrared counter-terms and examine if they recover the de-Sitter invariance in the $lambda phi^4$ theory in comparison with the Sine-Gordon model where it was possible.
We propose gauge-Higgs unification in fuzzy extra dimensions as a possible solution to the Higgs naturalness problem. In our approach, the fuzzy extra dimensions are created spontaneously as a vacuum solution of certain four-dimensional gauge theory.
As an example, we construct a model which has a fuzzy torus as its vacuum. The Higgs field in our model is associated with the Wilson loop wrapped on the fuzzy torus. We show that the quadratic divergence in the mass of the Higgs field in the one-loop effective potential is absent. We then argue based on symmetries that the quantum corrections to the Higgs mass is suppressed including all loop contributions. We also consider a realization on the worldvolume theory of D3-branes probing $C^3/(Z_N times Z_N)$ orbifold with discrete torsion.
