From N- to (p,N)- Inflationary Attractors in view of ACT

Abstract

We review two types of fractional Kaehler potentials $K$ which reduce, along the inflationary path, to the form $N/(1-{\varphi }^{q_{\mathrm{M}}}{)}^p$ with $q_{\mathrm{M}}=1$ or $2$ and $0.1\le p\le 10$. Their coexistence, within a non-linear sigma model, with chaotic inflationary potentials of the form ${\varphi }^n$ (where $n=2$ or $4$) determines, independently from $q_{\mathrm{M}}$ and $n$, a class of $(p,N)$-inflationary attractors which leads to observables compatible with the ACT DR6. An implementation of these models in the context of supergravity can be also achieved by introducing two chiral superfields and a monomial superpotential, linear with respect to the inflaton-accompanying field, and supplementing the $K$'s above with a shift symmetry. Although inflation is attained for subplanckian inflaton values, the tensor-to-scalar ratio obtained for certain $N$ values can be possibly observable in the near future.

Comments: Prepared for the Proceedings of Workshop ''Tensions in Cosmology'' 2 - 8 September 2025 Corfu, Greece - Conference C25-09-02.1