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Non-minimal unimodular inflation revisited: Swampland diagnostics and CMB constraints

Saeed Noori Gashti, Mohammad Reza Alipour, Mohammad Ali S. Afshar, Behnam Pourhassan, İzzet Sakallı and Phongpichit Channuie

Published
Source
OpenAlex
Published in
arXiv (Cornell University)
DOI
10.48550/arxiv.2610.27991
Original
Read it at the publisher
Topics
Statistical Mechanics

Abstract

We study non-minimal unimodular inflation in the Einstein frame; the effective potential takes the form $U(φ)=U_0(1+ξφ^2/\mpl^2)^{-2}$. We consider the canonical field map and the inflationary observables directly from the Einstein-frame action. The exact potential slow-roll parameters, the leading scalar running, the scalar-amplitude normalization, the e-fold relation, and the end-of-inflation condition are obtained analytically. The model has a nontrivial structural tension: an $ε_V=1$ exit requires $ξ>1/2$, whereas the near-origin slow-roll regime requires $ξ\ll1$ and gives $n_s\simeq1-8ξ$. We next test three distinct swampland diagnostics. The further-refined de Sitter conjecture (FRDSSC) introduces the independent conjectural parameters $a$, $b$, and $q$, while the scalar weak gravity conjecture (SWGC) and its strong form (SSWGC) contain no analogous tunable conjecture parameter in the single-field realization adopted here. All three criteria are evaluated using the canonically normalized Einstein-frame scalar. Analytic limits show that the SWGC is violated at the stationary point for every nonzero $ξ$, whereas the SSWGC at that point requires $ξ\gtrsim0.0643$. In the large-field limit both scalar weak-gravity diagnostics reduce to the same threshold $ξ\ge0.1$. Numerical scans then show that the observationally relevant ACT/P-ACT region does not satisfy either scalar weak-gravity criterion, while the FRDSSC can be satisfied for $a$ close to unity. Consequently, the minimal model can reproduce acceptable $(n_s,r)$ at isolated field values, but this does not constitute a complete 50-60 e-fold inflationary history or simultaneous satisfaction of all three conjectures.

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