Constant-roll inflation with non-minimally derivative coupling

Abstract

We investigate the constant-roll inflation with non-minimally kinetic coupling to the Einstein tensor. With the slow-roll parameter ${\eta }_{\varphi }=-\ddot{\varphi }/(H\dot{\varphi })$ being a constant, we calculate the power spectra for scalar and tensor perturbations, and derive the expressions for the scalar spectral tilt $n_s$, the tensor spectral tilt $n_T$, and the tensor-to-scalar ratio $r$. We find that the expressions for $n_s$ 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 $c_{s}k=aH$ in the constant-roll inflation, the consistency relation $r=-8n_T$ does not hold if $|{\eta }_{\varphi }|$ 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.

8 pages, accepted by Communications in Theoretical Physics

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