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

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.