On the oscillations of the inflaton field of the simplest $\alpha$-attractor T-model

In this work, we consider homogeneous oscillations of the inflaton field after inflation. In particular, we obtain an analytical result for the (average) equation of state for the oscillating inflaton field for the simplest $\alpha$-attractor T-model. We also study the post-inflationary evolution before inflaton decay. It is possible that during inflaton field oscillation, the (average) equation of state is that of a cosmological constant. This leads to the phenomenon of oscillating inflation. However, we show that the duration of oscillating inflation is very limited.