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

Inflation with very small tensor-to-scalar ratio