标题： 从超势能和全息理论的$δN$形式主义 显示英文标题

标题： $δN$ formalism from superpotential and holography

摘要： 我们考虑超势形式来描述标量场在膨胀期间的演化，并将其推广到包括非规范动能项的情况。我们通过一阶和二阶慢滚参数（它们不必很小）来表征背景演化的吸引子行为。我们发现超势有助于从梯度展开证明单独宇宙近似的合理性，并且在$\delta N$形式中计算吸引子解周围的原初扰动谱时也很有用。作为应用，我们考虑一类模型，在这类模型中，膨胀子场的背景轨迹是从乘积可分离的超势中导出的。从全息膨胀场景的角度来看，此类模型与边界理论中的变形共形场论相对偶，其中$D$个相互无关的变形算符。我们计算了原初绝热和熵宇宙学扰动的体积功率谱，并表明结果与使用对偶图景中的共形微扰理论得到的结果一致。 显示英文摘要

摘要： We consider the superpotential formalism to describe the evolution of scalar fields during inflation, generalizing it to include the case with non-canonical kinetic terms. We provide a characterization of the attractor behaviour of the background evolution in terms of first and second slow-roll parameters (which need not be small). We find that the superpotential is useful in justifying the separate universe approximation from the gradient expansion, and also in computing the spectra of primordial perturbations around attractor solutions in the $\delta N$ formalism. As an application, we consider a class of models where the background trajectories for the inflaton fields are derived from a product separable superpotential. In the perspective of the holographic inflation scenario, such models are dual to a deformed CFT boundary theory, with $D$ mutually uncorrelated deformation operators. We compute the bulk power spectra of primordial adiabatic and entropy cosmological perturbations, and show that the results agree with the ones obtained by using conformal perturbation theory in the dual picture.