We apply the gradient expansion approximation to the light-cone gauge, obtaining a separate universe picture at non-linear order in perturbation theory within this framework. Thereafter, we use it to generalize the \(\delta \mathcal {N}\) formalism in terms of light-cone perturbations. As a consistency check, we demonstrate the conservation of the gauge invariant curvature perturbation on uniform density hypersurface \(\zeta \) at the completely non-linear level. The approach studied provides a self-consistent framework to connect at non-linear level quantities from the primordial universe, such as \(\zeta \), written in terms of the light-cone parameters, to late time observables.

我们将梯度展开近似应用于光锥规范，在此框架内获得微扰理论中非线性阶的单独宇宙图景。此后，我们用它来概括光锥扰动的\(\delta \mathcal {N}\)形式主义。作为一致性检查，我们证明了在完全非线性水平上均匀密度超曲面\(\zeta \)上规范不变曲率扰动的守恒性。研究的方法提供了一个自洽的框架，可以在非线性水平上将原始宇宙中的量（例如用光锥参数编写的\(\zeta \) ）与晚期可观测值连接起来。