Inflationary α-attractor models with singular derivative of potential

Abstract

Abstract A generalization of inflationary α-attractor models (polynomial α-attractor) was recently proposed by Kallosh and Linde, in which the potential involves logarithmic functions of the inflaton so that the derivative of the potential but not potential itself has a singularity. We find that the models can lead to viable inflationary observables even without the pole in the kinetic term. Also, the generalization with a pole order other than two does not significantly change the functional form of the potential. This allows a systematic analysis of the predictions of this class of models. Our models predict larger spectral index ns and tensor-to-scalar ratio r than in the polynomial α-attractor: typically, ns around 0.97–0.98 and r observable by LiteBIRD. Taking advantage of the relatively large ns , we discuss the modification of the potential to produce primordial black holes as the whole dark matter and gravitational waves induced by curvature perturbations detectable by LISA and BBO/DECIGO, while keeping ns in agreement with the Planck/BICEP/Keck data.