We reconsider linear perturbations around general Friedmann-Lemaitre-Robertson-Walker (FLRW) cosmological backgrounds. Exploiting gauge freedom involving only time reparametrizations, we write down classical background solutions analytically, for an arbitrary number of fluid components. We then show that the time evolution of scalar and tensor adiabatic perturbations are governed by Schrödinger-like differential equations of generalized Heun type. After recovering known analytic results for a single-component fluid, we discuss more general situations with two and three different fluid components, with special attention to the combination of radiation, matter and vacuum energy, which is supposed to describe the ΛCDM model. The evolution of linear perturbations of a flat ΛCDM universe is described by a two-transient model, where the transitions from radiation to matter and matter to vacuum energy are governed by a Heun equation and a Hypergeometric equation, respectively. We discuss an analytic approach to the study of the general case, involving generalized Heun equations, that makes use of (quantum) Seiberg-Witten curves for 𝒩 = 2 supersymmetric gauge theories and has proven to be very effective in the analysis of Black-Hole, fuzzball and ECO perturbations.

中文翻译：

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规范论遇上宇宙学


我们重新考虑了围绕一般 Friedmann-Lemaitre-Robertson-Walker （FLRW） 宇宙学背景的线性扰动。利用仅涉及时间重新参数化的厚度自由度，我们分析写下了任意数量的流体成分的经典背景解。然后，我们表明标量和张量绝热扰动的时间演化由广义 Heun 类型的类似薛定谔的微分方程控制。在恢复了单组分流体的已知解析结果后，我们讨论了两种和三种不同流体成分的更一般情况，特别注意辐射、物质和真空能的组合，这应该描述 ΛCDM 模型。平面 ΛCDM 宇宙的线性扰动演化由双瞬态模型描述，其中从辐射到物质和物质到真空能的转变分别由 Heun 方程和超几何方程控制。我们讨论了一种研究一般情况的分析方法，涉及广义 Heun 方程，该方法使用 N = 2 超对称规范理论的（量子）Seiberg-Witten 曲线，并已被证明在分析黑洞、模糊球和 ECO 扰动方面非常有效。