In this paper we study the perturbation theory of the recently proposed Regularized Lovelock Gravity (Glavan and Lin, 2020), on the curved Friedmann–Lemaître–Robertson–Walker (FLRW) space–time. We provide the first order perturbation equations both in the scalar and tensor sector in the presence of an additional minimally coupled scalar field. A general expression for the velocity of gravitational waves at the generic order is inferred. Moreover, we apply the results on the study of slow-roll inflation on flat FLRW background, at second order in the Regularized Lovelock Gravity, i.e. in the presence of the Gauss–Bonnet correction only. We derive the power spectra of scalar and tensor perturbations, and provide the equations for the inflation observable quantities: the spectral indices and the tensor-to-scalar spectra ratio.

在本文中，我们研究了弯曲的Friedmann-Lemaître-Robertson-Walker（FLRW）时空上最近提出的正则化Lovelock重力的摄动理论（Glavan和Lin，2020年）。在存在额外的最小耦合标量场的情况下，我们在标量和张量扇区中均提供一阶摄动方程。推断出一般次序下的重力波速度的一般表达式。此外，我们将结果应用在FLRW平坦背景下的慢滚动通气研究中，在正则Lovelock重力中处于二阶，即仅在存在高斯-贝内校正的情况下。我们推导了标量和张量摄动的功率谱，并提供了可观察到的通货膨胀量的方程式：光谱指数和张量与标量的光谱比。