标题： 对数对偶性下的恒定滚动和非高斯尾部 显示英文标题

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

摘要： 在常滚动（CR）暴胀模型中的曲率扰动根据参考文献[1]中发现的对数对偶性，按照$\delta N$形式进行解释。我们确认决定CR条件是否稳定的临界值$\beta:=\ddot{\varphi}/(H\dot{\varphi})=-3/2$被理解为双解，即场方程的吸引子解和非吸引子解相互交换的点。对于吸引子解的主导情况，CR模型中的曲率扰动由高斯随机场的简单对数映射给出，这可以根据$\beta$的值实现概率密度函数的指数尾部（即单指数衰减）和Gumbel分布类似的尾部（即双指数衰减）。这种尾部行为对于原初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.