Extra-natural production of superheavy Kaluza-Klein particles

TL;DR

This work shows that gauge potentials along compact dimensions can drive inflation (extra-natural inflation) in a 5D QED framework and that time-dependent backgrounds generate electric fields along the extra dimension, triggering Schwinger-like production of KK modes. By performing a KK decomposition of scalars and spinors in this time-dependent background, the authors demonstrate that multiple charged fields deform the one-loop potential into a multi-natural form compatible with current CMB constraints, while generically inducing KK-Schwinger production of KK states. They provide analytic estimates and numerical results for KK mode production (notably $n=1$ with $q=5$) during and after inflation, compute the resulting energy densities, and discuss the cosmological fate of these superheavy KK particles, including stringent relic-density constraints and the potential for KK modes to serve as dark matter under certain conditions. They also show that KK production persists even if the Wilson line modulus is a spectator field (misalignment scenario), indicating that KK-Schwinger production is a robust outcome whenever light gauge potentials along compact dimensions are present, and outline avenues for UV completion and extensions to broader higher-dimensional setups.

Abstract

Gauge fields in extra compact dimensions can drive inflation in the four-dimensional (4D) non-compact spacetime, a scenario known as extra-natural inflation. A time-dependent gauge field configuration generates the electric field along the compact dimension, enabling the production of Kaluza-Klein (KK) particles charged under the field via the Schwinger effect. We construct the extra-natural inflation model within a five-dimensional (5D) quantum electrodynamics (QED) framework coupled to gravity including matter fields that generate the inflationary one-loop effective potential. In general, multiple charged fields can exist, and we show that KK particle production occurs under these conditions. Since KK momentum is conserved, the produced KK particles may become superheavy dark matter or dominate the universe, depending on the model parameters. Furthermore, we show that even when the gauge field acts not as the inflaton but as a spectator field, its post-inflationary oscillations, initiated when the Hubble friction becomes negligible, can also generate superheavy KK modes. This suggests that KK particle production is a generic outcome when gauge potentials along compact dimensions are light.

Figures (18)

• Figure 1: The effective potential of the radion and the Wilson line modulus $(\varphi,\vartheta)$. The potential looks flat along $\vartheta$ due to the hierarchy of the effective mass of $(\varphi,\vartheta)$. During inflation driven by $\vartheta$, the radion $\varphi$ can be effectively treated as a constant.
• Figure 2: The potential of $\vartheta$ with a fixed $\varphi$ at the bottom.
• Figure 3: The time evolution of $\vartheta$.
• Figure 4: The time evolution of the scale factor.
• Figure 5: The scalar spectral index $n_s$ as the function of the corresponding e-foloding number $N_*$ of the horizon exit.