Bose–Fermi cancellation of cosmological Coleman–Weinberg potentials

Abstract

Cosmological Coleman–Weinberg potentials are induced when normal matter is coupled to the inflaton. It has long been known that the corrections from bosonic fields are positive whereas those from fermionic fields are negative. In flat space both take the form ±φ4 ln(φ), and they can be made to cancel by appropriately choosing the coupling constants. In an expanding Universe the bosonic and fermionic results no longer take the same form, although their large field limits do. We choose the coupling constants so that the large field limits cancel, and then follow the deviations which result as inflation progresses. Although the result is not satisfactory we discuss how adding scalars with various conformal couplings likely solves the problem.