ACT-Inspired Kaehler-Based Inflationary Attractors

TL;DR

This work addresses the tension between conventional E- and T-model inflation and recent ACT data by introducing two attractor variants, E_pMI and T_pMI, built from two families of pole-like Kähler potentials $K_{lM}$ that yield a kinetic term with the pole structure $N/f_M^p$, where $f_M=1-\phi^{q_M}$, $q_E=1$, $q_T=2$. Coupled to chaotic potentials $V_I\propto \phi^n$ ($n=2,4$), these models form $(N,p)$-attractors with $n_s$ and $r$ primarily governed by $N$ and $p$ and remarkably independent of $n$ and $q_M$ at leading order, while allowing sub-Planckian inflaton values and predicting an r that grows with $N$. The authors provide non-SUSY and SUGRA embeddings, stabilize auxiliary fields via shift-symmetric Kähler constructions, and show that radiative corrections can be controlled by a judicious choice of the RG scale $Q$ to preserve inflationary predictions. Numerical analyses demonstrate broad compatibility with ACT-LB-BK18 and identify favorable regions in the $(p,N)$ plane, with $n_s$ rising with $p$ and $r$ potentially within reach of upcoming observations. Overall, the paper establishes a robust, testable class of attractor models that reconcile current CMB data with sub-Planckian field excursions and offer clear experimental targets.

Abstract

We develop a new class of cosmological attractors which are compatible with the recent ACT results. They are based on two types of fractional Kaehler potentials, K, for a gauge-singlet inflaton phi which reduce, along the inflationary path, to the form N/(1-phi^qM)^p with qM=1, 2 and 0.1< p<10. The combination of these K's with the chaotic potentials phi^n (where n=2, 4) within a non-linear sigma model leads to inflationary observables which are consistent with the current data and largely independent from qM and n. Endowing these K's with a shift symmetry we also offer a supergravity realization of our models introducing two chiral superfields and a monomial superpotential, linear with respect to the inflaton-accompanying field. The attainment of inflation with subplanckian inflaton values and the large values for the tensor-to-scalar ratio, which increases with N, are two additional attractive features of our proposal.

Figures (4)

• Figure 1: Canonically normalized inflaton $\widehat{\phi}$ as a function of $\phi$ for E$_p$MI (left panel) or T$_p$MI (right panel). We employ $K=K_{\rm 1E}$ and $K_{\rm 1T}$ (gray lines) or $K=K_{\rm 2E}$ and $K_{\rm 2T}$ (light gray lines) for BPs of tab1 A$_{\rm E}$ and A$_{\rm T}$ (solid lines) or B$_{\rm E}$ and B$_{\rm T}$ (dashed lines).
• Figure 2: Inflationary potential $V_{\rm I}$ for E$_p$MI and BP A$_{\rm E}$ (left panel) or T$_p$MI and BP B$_{\rm T}$ (right panel) -- the BPs are defined in tab1 -- as a function of $\phi$ (black lines) for $\phi>0$ and $\widehat{\phi}$ for $\widehat{\phi}>0$ and $K=K_{\rm 1M}$ (gray lines) or $K=K_{\rm 2M}$ (light gray lines) with $\rm M=\rm E$ and $\rm T$. Values corresponding to $\phi_\star$, $\phi_{\rm f}$, $\widehat{\phi}$ and $\widehat{\phi}_{\rm f}$ are also depicted.
• Figure 3: Allowed curves in the $n_{\rm s}-r$ plane for E$_p$MI (upper plots) and T$_p$MI (lower plots) with $n=2$ (left panels) or $4$ (right panels), various $p$ values -- shown in the legends -- and $N$ values indicated on the curves. The marginalized joint $68\%$ [$95\%$] c.l. regions from P-ACT-LB-BK18 data are depicted by the dark [light] shaded contours.
• Figure 4: Allowed (shaded for T$_p$MI and hatched for E$_p$MI) regions as determined by Eqs. (\ref{['data']}) and (\ref{['Prob']}) in the $p-N$ plane for $n=2$ (left panel) or $n=4$ (right panel). The conventions adopted for the boundary lines are also shown.