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具有非最小耦合的复 inflaton 势：稳健的膨胀与几何再加热

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

Federal University of São Carlos（圣卡洛斯联邦大学）

S. D. Campos

发表信息：
JCAP 07, 097 (2026)
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AI总结：

本文提出了一种基于复标量场非最小耦合的膨胀模型，通过虚部编码耗散效应，实现稳健膨胀和几何再加热，其结果与普朗克2018界限一致。

摘要：

我们研究了一个由复标量场非最小耦合到引力并受非对称复势驱动的膨胀场景。势的实部控制宇宙背景并实现与 α-吸引子 T 模型相容的平台型膨胀，而虚部则作为有效的非厄米特变形，编码耗散效应。在乔丹框架下，并对有效普朗克质量施加无鬼条件，我们推导了背景方程并定义了一个复方程状态参数，其实部控制膨胀，虚部量化偏离保守动力学的程度。数值积分显示，膨胀的持续时间主要由非最小耦合 ζ 控制，而复不对称参数 Δε 对实背景的影响微乎其微：当 Δε 在允许范围内变化时，实能量密度和压力的变化小于 10^-5。将双场动力学映射到爱因斯坦框架下的有效单场描述，我们得到谱指数 ns ≈ 0.968-0.971 和张量-标量比 r < 10^-3，完全符合 2018 年普朗克界限。我们引入了一个相关性参数，并表明非厄米特效应在慢滚过程中仍被强烈抑制，但接近膨胀结束时增长到 O(1)，触发高效的再加热阶段，而无需额外场或 ad hoc 摩擦项。从这个意义上说，虚部行为如同一个有效的 PT 对称通道，为能量转移提供几何机制，在非厄米特标量-张量框架中实现膨胀及其退出。

英文摘要：

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 $α$-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 $ζ$, whereas the complex asymmetry parameter $Δ\varepsilon$ has a negligible impact on the real background: the real energy density and pressure vary by less than $10^{-5}$ as $Δ\varepsilon$ 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.

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