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Inflation with very small tensor-to-scalar ratio

We have investigated inflation models that predict a very small value of the tensor-to-scalar ratio, $r$. The spectral index $n_s$, and the tensor-to-scalar ratio $r$, are strictly constrained by the Planck data. $n_s$ and $r$ are sensitive to the shape and magnitude of the inflaton potential, respectively.The constraints by the Planck 2018 data combined with other cosmological observations are compared with the predictions from the inflation models regarding $n_s$ and $r$. Furthermore, we discuss the comparison of future tensor-to-scalar ratio data with predictions from the inflation models with a focus on part of the quantum fluctuation origin.