We assume that the noncommutativity starts to be visible continuously from a scale $Lambda_{NC}$. According to this assumption, a two-loop effective action is derived for noncommutative $phi^{4}$ and $phi^{3}$ theories from a Wilsonian point of view.
We show that these effective theories are free of UV/IR mixing phenomena. We also investigate the positivity constraint on coefficients of higher dimension operators present in the effective theory. This constraint makes the low energy theory to be UV completion of a full theory. Finally, we discuss noncommutativity and extra dimensions. In our effective theories formulated on noncommutative extra dimensions, if the campactification scale $Lambda_{c}$ is less than the scale $Lambda_{NC}$, the theory will not suffer from UV/IR mixing.
We investigate the generation of large scale magnetic fields in the universe from quantum fluctuations produced in the inflationary stage. By coupling these quantum fluctuations to the dilaton field and Ricci scalar, we show that the magnetic fields
with the strength observed today can be produced. We consider two situations: First, the evolution of dilaton ends at the onset of the reheating stage. Second, the dilaton continues its evolution after reheating and then decays. In both cases, we come back to the usual Maxwell equations after inflation and then calculate present magnetic fields.
