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

C. Pallis

Abstract

We review two types of fractional Kaehler potentials $K$ which reduce, along the inflationary path, to the form $N/(1-φ^{q_{\rm M}})^{p}$ with $q_{\rm M}=1$ or $2$ and $0.1\leq p\leq10$. Their coexistence, within a non-linear sigma model, with chaotic inflationary potentials of the form $φ^n$ (where $n=2$ or $4$) determines, independently from $q_{\rm M}$ 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.

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

Abstract

We review two types of fractional Kaehler potentials which reduce, along the inflationary path, to the form with or and . Their coexistence, within a non-linear sigma model, with chaotic inflationary potentials of the form (where or ) determines, independently from and , a class of -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 's above with a shift symmetry. Although inflation is attained for subplanckian inflaton values, the tensor-to-scalar ratio obtained for certain values can be possibly observable in the near future.
Paper Structure (6 sections, 42 equations, 4 figures, 1 table)

This paper contains 6 sections, 42 equations, 4 figures, 1 table.

Table of Contents

  1. Introduction
  2. Non-SUSY Framework
  3. SUGRA Framework
  4. Inflation Analysis
  5. Numerical Results
  6. Conclusions

Figures (4)

  • Figure 1: (a) Canonically normalized inflaton $\widehat{\phi}$ as a function of $\phi$ for E$_p$MI, $N=0.1$ and $p=2$ (solid line) or $p=1$ (dashed line); (b) inflationary potential $V_{\rm I}$ for E$_p$MI, $(n,p,N)=(2,2,0.1)$ as a function of $\phi$ (black line) and $\widehat{\phi}$ (gray line). Values corresponding to $\phi_\star$, $\phi_{\rm f}$, $\widehat{\phi}_\star$ and $\widehat{\phi}_{\rm f}$ are also depicted in both panels.
  • Figure 2: Allowed curves, as determined by Eq. (5.1), in the $n_{\rm s}-r$ plane for E$_p$MI ( a) and T$_p$MI ( b) with $n=2$, 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 also shown by the dark [light] shaded contours in the background.
  • Figure 3: The same as in Fig. 2 but for $n=4$.
  • Figure 4: Allowed (shaded for T$_p$MI and hatched for E$_p$MI) regions, as determined by Eq. (1.3) and (5.1), in the $p-N$ plane for $n=2$ ( a) or $n=4$ ( b). The conventions adopted for the boundary lines are also shown.