  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.
