Inflationary models that generalize the constant roll constraint

Recently a class of inflationary models satisfying the constant rate of roll constraint, \(\ddot{\phi}+(3+\alpha)H\dot{\phi}=0\), has been studied and compared with the latest cosmological observational data. We consider the broader class of constraints \( \ddot{\phi}+\frac{\alpha_1}{2}\dot{\phi}+\alpha_2 H\dot{\phi}=0\) and find an exact particular solution, without initial singularity, which is an attractor of the dynamics governed by a positive periodic potential \(V(\phi)=E+ F \cos (\Omega \phi )+G \cos (2 \Omega \phi )\). The spectral index \(n_s\) and the tensor to scalar ratio \(r\) are consistent with the recent observational data.