2026 Fibre Inflation axion-assisted primordial black-hole model study

Given: The source paper’s finite-field Type IIB Fibre Inflation ansatz, its specified P2 base parameters and axion data, the paper’s linear perturbation solver and its stated PBH-seeding criterion. Planck units and the authors’ conventions are retained.

Compactification-derived four-dimensional moduli EFT data: the actual draft statement specifies retained chiral coordinates, Kähler potential, superpotential, gauge-kinetic functions, Einstein-frame normalization, truncation range/cutoff and omitted KK, warped-throat, string and open-string modes. Its current Step 1 readiness record is missing. Its proof remains conditional on the O3/O7 chiral-coordinate and large-volume Kähler/gauge interfaces, whose item files exist outside the current run manifest without current Step 1 records, and on two $N=1$ suppliers with escalated Step 1 records.

Admissible nonperturbative sectors contributing to a moduli superpotential: the actual draft statement admits a semiclassical instanton term only with the two universal fermion modes, all additional modes absent/lifted/saturated, a nonzero holomorphic determinant, and gauge-invariant quantized axion charge; gaugino condensation separately requires its specified low-energy gauge dynamics. Its current Step 1 readiness record is missing and it depends on [F1].

Four-dimensional Einstein-frame multi-scalar cosmology EFT data: the four-dimensional scalar data declare the Einstein frame, fields, potential, units, cutoff, omitted modes and approximation domain, without asserting a global string realization.

Primordial scalar and tensor observables for inflation models: primordial scalar/tensor observables are defined for a specified perturbation model and pivot; likelihoods and observations are separate.

Periodic axion EFT data and sources: axion periods, kinetic matrix, canonical normalization, nonperturbative charge/action data and periodic potential are explicit; a monodromy branch is separate data.

Cicoli et al., arXiv:2607.27361v1, relevant passages in §§2–7, article pp. 3–24: §4 Eqs. (33)–(37) define the energy split and impose subdominant axion energy, while Fig. 5 and §5.2 describe temporary axion dominance of the field velocity. Figure 5 uses the Illustrative parameters of Table 3, not the Success parameters of Table 4. P2 has $(V_0,C_2,C_3,C_4,C_5,C_6)=(1.89\times {10}^{-9},0.5,0.2661400,7.00\times {10}^{-7},0.03911680,0.03575230)$ before the stated Success-point rescaling. In §5.1 the source writes ${\varphi }^I(x,t)={\varphi }^I(t)+\delta {\varphi }^I$ and defines $Q^I=\delta {\varphi }^I+({\dot{\varphi }}^I\mathrm{/}{H}_{\mathrm{H}\mathrm{u}\mathrm{b}})\psi$, where $H_{\mathrm{H}\mathrm{u}\mathrm{b}}=\dot{a}\mathrm{/}a$ and $\psi$ is the scalar spatial-metric perturbation on equal-time slices. For positive field-space metric $G_{IJ}$, it sets $\dot{\sigma }=(G_{IJ}{\dot{\varphi }}^I{\dot{\varphi }}^J{)}^{1\mathrm{/}2}$ and ${\widehat{\sigma }}^I={\dot{\varphi }}^I\mathrm{/}\dot{\sigma }$. Indices on $\widehat{\sigma }$ are lowered with $G$. For the three-field Success model, $I=1,2,3$ and the orthogonal projector is $P^I{}_J={\delta }^I{}_J-{\widehat{\sigma }}^I{\widehat{\sigma }}_J$. The source’s §5.1 Eqs. (5.3)–(5.6) define $Q_s^I=P^I{}_J{Q}^J$, $\mathcal{R}=H_{\mathrm{H}\mathrm{u}\mathrm{b}}{\widehat{\sigma }}_I{Q}^I\mathrm{/}\dot{\sigma }$ and $S^I=H_{\mathrm{H}\mathrm{u}\mathrm{b}}{Q}_s^I\mathrm{/}\dot{\sigma }$. There are two independent entropy components, since ${\widehat{\sigma }}_I{S}^I=0$; in a chosen $G$-orthonormal normal basis $e_a^I$, $a=1,2$, they are $S_a=G_{IJ}{e}_a^I{S}^J$. The later coupled equations for a single $S$ in §5.1 concern the separate two-field limit, not this whole three-field model. Table 5 labels its Success isocurvature output ${\beta }_{\mathrm{i}\mathrm{s}\mathrm{o}}=0.0001$ at $N_{\mathrm{C}\mathrm{M}\mathrm{B}}=53$. The inspected formalism and table do not specify how that scalar label aggregates the two entropy spectra or its normalization; it remains a source-reported solver label here, without identifying it with a single-$S$ power fraction or deriving an independent three-field isocurvature bound. Figure 1 and §3 use the number of e-folds before the end of inflation, with $N(t)=\log [a(t_{\mathrm{e}\mathrm{n}\mathrm{d}})\mathrm{/}a(t)]$; §3 evaluates the spectrum at $N=0$, while Tables 4–5 identify the CMB exit by $N_{\mathrm{C}\mathrm{M}\mathrm{B}}=53$. With its Fourier convention it defines ${\mathcal{P}}_{\mathcal{R}}(k,N)=k^3\mathrm{\mid }{\mathcal{R}}_k(N){\mathrm{\mid }}^2\mathrm{/}(2{\pi }^2)$ and evaluates the spectrum at the end of inflation. The Fourier modes are defined on the source’s flat FLRW slices; $\mathcal{R}$ is its comoving curvature perturbation and is not identified here with the uniform-density curvature $\zeta$ of [F4]. It uses ${\mathcal{P}}_{\mathcal{R}}(k_{\mathrm{P}\mathrm{B}\mathrm{H}})>{10}^{-3}$ as its adopted PBH-seeding criterion and converts $k_{\mathrm{P}\mathrm{B}\mathrm{H}}$ to a formation mass with $\gamma =0.2$ and $g_{\ast }=106.75$. Tables 4 and 5 give the Success parameters and outputs. These are model calculations; the threshold is not an observed event or universal PBH theorem.

The paper’s finite truncation, flux-dependent coefficients, initial conditions, spectator treatment, linear perturbations and reported numerical solver outputs are adopted only for this model study. No underlying compactification is assumed to exist unless separately constructed.