  In this paper we study the perturbation theory of the recently proposed
Regularized Lovelock Gravity, on the curved 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.
