Removing the Cosmological Bound on the Axion Scale via Confinement During Inflation

Abstract

We implement the scenario of early relaxation of the axion via a high scale confinement within $SU(5)$ grand unified theory and study an epoch of strong QCD in inflationary cosmology. We consider scenarios in which, during inflation, the $SU(5)$ is either entirely or partially in the confining phase. This generates an early potential for the axion and dilutes its energy density removing any cosmological upper bound on the decay constant. We show that a phase of strong QCD can be realized by at least two mechanisms: 1) A direct coupling between the inflaton and the gauge fields and/or 2) by restoration of the $SU(5)$ symmetry during the inflationary epoch. In the latter case, strong coupling is already achieved via the RG running of the $SU(5)$ gauge coupling. We show that the mechanism works for all known realizations of the invisible axion idea: Peccei-Quinn (PQ) type formulations in which the anomalous global symmetry is realized via additional scalars (DFSZ) or heavy fermions (KSVZ) as well as the two-form gauge axion formulation based entirely on the QCD gauge redundancy without any anomalous global symmetry. Even if the expectation value of the PQ scalar vanishes during inflation, the axion is a well defined degree of freedom represented by the phase of the fermion 't Hooft determinant. For the DFSZ case, this phase is composed out of a condensate of the ordinary quarks, amounting to an early universe version of the $η'$-meson. In all considered scenarios, the present day axion can be a viable dark matter candidate for an arbitrarily large value of the decay constant.

Figures (5)

• Figure 1: A diagrammatic representation of the 't Hooft vertex in the KSVZ-like model. The fundamental ($\mathbf 5$) and anti-fundamental $\bar{\mathbf 5}$ fermions each contribute one zero mode in the instanton background, whereas the fermion in the antisymmetric $\mathbf 10$ contributes three.
• Figure 2: A diagrammatic representation of the dressing of the 't Hooft vertex by the exchange of a virtual Higgs.
• Figure 3: A Feynman diagram contributing to the tadpole for $\Phi$.
• Figure 4: A diagrammatic representation of the 't Hooft vertex in the minimal $SU(5)$ theory. The fermion in the anti-fundamental $\bar{\mathbf{5}}$ representation contributes one zero mode and the fermion in the antisymmetric $\mathbf{10}$ representation contributes three-zero modes, leading to the form \ref{['detTU5']}.
• Figure 5: A diagram that gives rise to the tadpole contribution for $\Phi$.