多场Gauss-Bonnet暴胀中的曲率与等曲率扰动
Curvature and Isocurvature Perturbations in multi-field Gauss-Bonnet inflation
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中文总结 AI 辅助
该研究针对多场Gauss-Bonnet暴胀模型，推导场扰动二次作用量并分解曲率与等曲率模，验证相关质量为零的结论，在两种极限下计算曲率功率谱，同时给出一阶耦合的张量功率谱与张标比。
中文摘要 AI 辅助
我们研究了标量场通过通用耦合函数$f(ϕ^a)$与Gauss-Bonnet项耦合的多场暴胀中的宇宙学扰动。我们推导了空间平坦规范下场扰动的完整二次作用量，发现除了对动能矩阵、梯度矩阵和质量矩阵的修正外，Gauss-Bonnet耦合还会诱导出一种在爱因斯坦引力中为零的反对称速度耦合。将场扰动分解为曲率模和等曲率模后，我们证明曲率扰动的有效质量与非导数混合质量恒等于零，即$\boldsymbol{\rm M}_{\boldsymbol{\rm R}}^2 = \boldsymbol{\rm M}_{\rm mix}^2 =0$，这一结果可由Weinberg绝热模得到验证。随后我们在两种极限下计算了曲率功率谱：第一种，当等曲率模较重时，可在所有尺度上将其积分掉，由此得到一种声速修正的曲率扰动有效单场理论；第二种，当耦合函数的梯度与背景轨迹对齐（$f_N =0$）时，导数混合消失，等曲率扰动向曲率扰动的超视界转移由转向率主导，且该转向率受到Gauss-Bonnet修正的影响。我们还给出了耦合一阶近似下的张量功率谱与张标比。
英文摘要
We study cosmological perturbations in multi-field inflation in which the scalar fields couple to the Gauss-Bonnet terms through a general coupling function $f(ϕ^a)$. We derive the complete quadratic action for the field perturbations in spatially flat gauge and find that, besides corrections to the kinetic, gradient and mass matrices, the Gauss-Bonnet coupling induces an antisymmetric velocity coupling that vanishes in Einstein gravity. Decomposing the field perturbations into curvature and isocurvature modes, we show that the effective mass of the curvature perturbation and the non-derivative mixing mass vanish identically, $\mathcal{M}_{\mathcal{R}}^2 = \mathcal{M}_{\rm mix}^2 =0$ which are justified by the Weinberg's adiabatic mode. We then compute the curvature power spectrum in two limits. First, when the isocurvature mode is heavy, it can be integrated over all scales. This yields an effective single-field theory of the curvature perturbation with a modified sound speed. Second, when the gradient of the coupling function is aligned with the background trajectory ($f_N =0$), the derivative mixings disappear and the superhorizon transfer of isocurvature into curvature perturbations is governed by the turn rate, which is modified by the Gauss-Bonnet corrections. We also present the tensor power spectrum and the tensor-to-scalar ratio at linear order in the coupling.
