Abstract
We investigate the constant-roll inflation with non-minimally kinetic coupling to the Einstein tensor.With the slow-roll parameter ηφ=-(φ)/(H(φ))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.
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