Complex Inflaton Potentials with Nonminimal Coupling: Robust Inflation and Geometric Reheating

TL;DR

This paper explores a complex scalar field with nonminimal coupling driving inflation, demonstrating robustness of inflationary predictions and a novel geometric reheating mechanism via non-Hermitian effects.

Contribution

It introduces a non-Hermitian complex scalar field model for inflation, showing compatibility with observations and a new reheating process driven by imaginary sector dynamics.

Findings

Inflation duration mainly controlled by nonminimal coupling ζ

Spectral index n_s approximately 0.968-0.971

Tensor-to-scalar ratio r less than 10^{-3}

Abstract

We investigate an inflationary scenario driven by a complex scalar field nonminimally coupled to gravity and subject to a non-symmetric complex potential. The real part of the potential controls the cosmological background and realizes a plateau-type inflation compatible with $\alpha$-attractor $\mathrm{T}$-models, while the imaginary part acts as an effective non-Hermitian deformation encoding dissipative effects. Working in the Jordan frame and imposing ghost-free conditions on the effective Planck mass, we derive the background equations and define a complex equation-of-state parameter whose real part governs the expansion and whose imaginary part quantifies departures from conservative dynamics. Numerical integration shows that the duration of inflation is primarily controlled by the nonminimal coupling $\zeta$, whereas the complex asymmetry parameter $\Delta\varepsilon$ has a negligible impact on the real background: the real energy density and pressure vary by less than $10^{-5}$ as $\Delta\varepsilon$ is scanned over its allowed range. Mapping the two-field dynamics to an effective single-field description in the Einstein frame, we obtain a spectral index $n_s\simeq 0.968-0.971$ and a tensor-to-scalar ratio $r<10^{-3}$, fully consistent with Planck 2018 bounds. We introduce a relevance parameter and show that non-Hermitian effects remain strongly suppressed during slow roll but grow to $\mathcal{O}(1)$ near the end of inflation, triggering an efficient reheating phase without additional fields or {\it ad hoc} friction terms. In this sense, the imaginary sector behaves as an effective $\mathcal{PT}$-symmetric channel for energy transfer, providing a geometrical mechanism for inflation and its exit within a non-Hermitian scalar-tensor framework.