Constant-roll inflation with non-minimally derivative coupling

We investigate the constant-roll inflation with non-minimally kinetic coupling to the Einstein tensor. With the slow-roll parameter being a constant, we calculate the power spectra for scalar and tensor perturbations, and derive the expressions for the scalar spectral tilt ns, the tensor spectral tilt nT, and the tensor-to-scalar ratio r. We find that the expressions for ns are different with different ordering of taking the derivative of the scalar power spectrum with respect to the scale k and the horizon crossing condition csk = aH in the constant-roll inflation, the consistency relation r = − 8nT does not hold if ∣ηϕ∣ is not small, and the duality of the tensor-to-scalar ratio between the slow-roll inflation and ultra-slow-roll inflation does not exist in inflationary models with non-minimally derivative coupling. The result offers a fresh perspective on the understanding of the inflationary models with non-minimally derivative coupling and is helpful for the production of scalar induced gravitational waves in the framework of ultra-slow-roll inflation with non-minimally derivative coupling.