标题： 常数滚动和非高斯尾部的对数对偶性视角 显示英文标题

标题： Constant roll and non-Gaussian tail in light of logarithmic duality

摘要： 常数滚动（CR）暴胀模型中的曲率扰动根据文献[1]中发现的对数对偶性，按照$\delta N$形式体系进行了解释。 我们确认决定CR条件是否稳定的临界值$\beta:=\ddot{\varphi}/(H\dot{\varphi})=-3/2$可以理解为场方程的吸引子解和非吸引子解相互交换的点。 对于吸引子解占主导的情况，CR模型中的曲率扰动由高斯随机场的一个简单对数映射给出，其概率密度函数的尾部行为取决于$\beta$的取值，可以表现为指数尾（即单指数衰减）或类似Gumbel分布的尾部（即双指数衰减）。 这种尾部行为对于例如原始黑洞丰度的估计非常重要。 显示英文摘要

摘要： The curvature perturbation in a model of constant-roll (CR) inflation is interpreted in view of the logarithmic duality discovered in Ref. [1] according to the $\delta N$ formalism. We confirm that the critical value $\beta:=\ddot{\varphi}/(H\dot{\varphi})=-3/2$ determining whether the CR condition is stable or not is understood as the point at which the dual solutions, i.e., the attractor and non-attractor solutions of the field equation, are interchanged. For the attractor-solution domination, the curvature perturbation in the CR model is given by a simple logarithmic mapping of a Gaussian random field, which can realise both the exponential tail (i.e., the single exponential decay) and the Gumbel-distribution-like tail (i.e., the double exponential decay) of the probability density function, depending on the value of $\beta$. Such a tail behaviour is important for, e.g., the estimation of the primordial black hole abundance.