Inflaton fragmentation in E-models of cosmological $\alpha$-attractors

Cosmological $\alpha$-attractors are observationally favored due to the asymptotic flatness of the potential. Since its flatness induces the negative pressure even after inflation, the coherent oscillation of the inflaton field could fragment into quasi-stable localized objects called I-balls (or "oscillons"). We investigated the possibility of I-ball formation in E-models of $\alpha$-attractors. Using linear analysis and the lattice simulations, we find that for $\alpha\lesssim10^{-3}$, the inflaton feels the negative pressure long enough and actually fragments into I-balls.