Universal Non-Gaussian Signatures from Transient Instabilities

Abstract: We identify universal signatures in the bispectrum arising from a transient tachyonic instability of entropic fluctuations during inflation, a phenomenon that naturally arises in hyperbolic field-space geometries. We perform exact numerical calculations directly at the level of fluctuations, without relying on a specific background model, and distinguish two cases. In the light case, with masses around the Hubble scale, our results provide the first-ever computation of the bispectrum due to such tachyonic instabilities. We find a universal magnification of the folded configuration, together with the known non-analytic scaling in the squeezed limit. As an illustrative example, we compute and analyse the bispectrum in angular inflation, demonstrating compatibility with current limits. In the heavy case, with masses well above the Hubble scale, the bispectrum exhibits a distinctive correlation between enhanced folded configurations and a `tachyonic resonance' in mildly squeezed limits, with the resonance scale set by the strength of the instability. While the main qualitative features are reproduced, we show that there exists no UV matching for which a single-field effective description, obtained by integrating out the entropic modes, accurately captures the bispectrum for all kinematic configurations. To facilitate observational applications, we introduce simple bispectrum shape templates suitable for current and forthcoming cosmological surveys. Our model-independent results allow for constraining non-standard inflationary attractors characterised by strongly non-geodesic motion.

• The paper demonstrates that transient tachyonic instabilities in multi-field inflation produce universal, non-Gaussian bispectrum signatures using detailed numerical and analytical methods.
• It distinguishes between light and heavy entropic regimes, revealing folded-enhancement, squeezed-limit non-analyticity, and tachyonic resonances in different configurations.
• The study illustrates the limitations of single-field EFT approaches and emphasizes the need for full multi-field computations to accurately capture inflationary dynamics.

Universal Non-Gaussian Signatures from Transient Instabilities

Introduction and Motivation

The paper "Universal Non-Gaussian Signatures from Transient Instabilities" (2604.01035) investigates universal features in the inflationary bispectrum originating from transient tachyonic instabilities of entropic fluctuations. These phenomena generically occur in multi-field inflation with negatively curved (hyperbolic) field-space geometries, characteristic of $\alpha$-attractor models and string-motivated scenarios. The analysis proceeds at the level of fluctuations, eschewing detailed background model dependence and thereby identifying robust, model-independent phenomenology.

In scenarios with strongly non-geodesic inflationary trajectories—quantified by a large dimensionless turn rate $\eta_\perp$—the entropic mode acquires a transient tachyonic effective mass. This instability magnifies isocurvature fluctuations, which in turn generate distinctive, non-trivial signatures in the inflationary bispectrum, potentially within observational reach. The paper methodically distinguishes between two regimes: a light entropic sector with mass $\sim H$, and a heavy regime with entropic mass $m_\sigma \gg H$, discussing their consequences for bispectrum shapes.

Multi-field Fluctuations and Transient Tachyonic Instabilities

In multi-field inflation, the dynamics of fluctuations transverse to the background trajectory are especially sensitive to field-space geometry. The Lagrangian under consideration is a nonlinear sigma model of $N$ scalars with internal metric $G_{IJ}$, minimally coupled to gravity. Focusing on two-field systems, curvature ($\zeta$) and isocurvature ($\sigma$) modes naturally arise as projections of field fluctuations onto tangent and normal directions, respectively.

The crucial parameter is the turn rate $\eta_\perp$, arising from the bending of the inflationary trajectory. Large $\eta_\perp$ leads to a negative bare entropic mass squared: $\eta_\perp$0 where $\eta_\perp$1 is the field-space Ricci scalar and $\eta_\perp$2 denotes the second derivative of the potential along the normal direction. Negative $\eta_\perp$3 engenders a brief tachyonic instability—a transient period during which isocurvature modes grow before decaying safely on super-horizon scales. This scenario is natural for negatively curved field-space manifolds.

Bispectrum Signatures: Universal Features

Employing exact numerical methods (CosmoFlow), the authors compute scale-invariant bispectrum shapes for the dominant cubic operators. They analyze three key cubic interactions:

• $\eta_\perp$4
• $\eta_\perp$5
• $\eta_\perp$6

Bispectra are characterized by $\eta_\perp$7, normalized to unity in the equilateral limit.

Figure 1: Dimensionless bispectrum shapes $\eta_\perp$8, normalized in the equilateral configuration, across all kinematic regimes for exemplar interactions and varying instability strengths.

A detailed investigation reveals several robust, universal signatures:

1. Folded-enhanced Bispectrum: All considered cubic operators yield bispectrum shapes with enhancement in the folded configuration ($\eta_\perp$9), relative to equilateral. This enhancement is directly connected to the period of tachyonic growth in the entropic sector, associated with an excited non-Bunch-Davies initial state.
2. Squeezed-limit Non-analytics (Cosmological Collider Signal): In the squeezed limit ($\sim H$0), the bispectrum displays the expected non-analytic scaling:

$\sim H$1

with $\sim H$2. The index $\sim H$3 encodes the strength of the instability (and thus the turn rate and entropic mass).

Figure 2: Isosceles slices of $\sim H$4 as $\sim H$5 is varied from folded to squeezed limits, illuminating the scaling transitions and resonance features for various cubic couplings and $\sim H$6 values.

1. Tachyonic Resonance: For $\sim H$7, a pronounced resonance arises in mildly squeezed configurations ($\sim H$8), whose position and amplitude are directly controlled by the strength of the tachyonic instability. This effect has no analog in standard single-field effective field theory (EFT) with real speed of sound.

   Figure 3: For large $\sim H$9, exact multi-field calculations reveal a pronounced resonance in the bispectrum in the mildly squeezed limit.

Breakdown of Single-field EFT and Kinematic-dependent UV Matching

In the heavy entropic regime, the system can be recast as a single-field EFT with imaginary speed of sound, reproducing several—but not all—multi-field features. Quantitatively, the paper demonstrates that no kinematic-independent UV matching exists for the EFT parameter $m_\sigma \gg H$0 (the cut-off for the validity of the single-field description) that reproduces the bispectrum in all kinematic settings. Specifically, while equilateral configurations can be matched by appropriate scaling, folded and squeezed configurations require kinematic-dependent rescalings. Accordingly, genuine multi-field computations are indispensable for robust predictions when entropic fields are sufficiently heavy or when backgrounds are complex.

Figure 4: Comparison of bispectrum shapes in equilateral and folded regimes, contrasting exact multi-field and single-field EFT results, which highlights mismatches and the necessity for kinematic-dependent UV matching.

Non-geodesic Shape Templates

To facilitate direct application to data analyses, the paper introduces robust template families for non-geodesic bispectrum shapes. These templates capture all salient features: folded enhancement/suppression, squeezed-limit scaling, and (when heavy) the tachyonic resonance.

Figure 5: Exemplary non-geodesic shape templates $m_\sigma \gg H$1 showing both folded-enhanced and folded-suppressed behaviors for light ($m_\sigma \gg H$2) and heavy ($m_\sigma \gg H$3) entropic masses.

Shape correlations are quantitatively assessed, demonstrating that non-geodesic templates are largely distinct from standard equilateral, orthogonal, or flattened shapes, especially as the instability strength increases.

Figure 6: Shape correlations between $m_\sigma \gg H$4 and standard templates as a function of instability strength $m_\sigma \gg H$5.

Angular Inflation as Realization and Observational Compatibility

As a concrete model, the authors assess angular inflation in hyperbolic field space—a setting natural in $m_\sigma \gg H$6-attractor supergravity constructions—where the inflationary trajectory becomes single-field-like but resides predominantly in the angular direction due to geometric effects.

The paper derives a universal, model-independent bound for when a transient tachyonic instability will arise, demonstrating that the phenomenon is generic in hyperbolic geometries for moderate field-space curvature and modest potential mass scales.

The spectral tilt $m_\sigma \gg H$7 and the viability of the model within current CMB constraints are mapped in detail. There exists parameter space where significant non-Gaussian signatures coexist with compatibility to present data. The resulting bispectrum for benchmark parameters is computed numerically.

Figure 7: Example background trajectories for angular inflation with $m_\sigma \gg H$8 and $m_\sigma \gg H$9, evidencing the angular attractor.

Figure 8: CMB spectral tilt $N$0 in the $N$1 plane, demonstrating observational viability for a non-trivial region.

Figure 9: Bispectrum shape for angular inflation, showing all predicted universal features: enhanced/suppressed folded limit, and power-law squeezed limit.

SUGRA Embedding

A complete embedding in $N$2 supergravity is outlined, demonstrating that the field-space geometry and potential structure required for the universal signatures can be realized in UV-complete frameworks, such as in $N$3-attractor constructions with a Poincaré disk Kähler geometry and appropriate superpotential/explicit symmetry breaking.

Implications and Prospective Developments

The results underscore that non-geodesic background motion in multi-field inflation, especially in hyperbolic field-space, imprints robust and observable signatures in non-Gaussian statistics. Detection of the characteristic bispectrum shape template—particularly simultaneous observation of both the folded enhancement and tachyonic resonance—would constitute strong evidence for high-dimensional inflation with large turn rates and transient instability episodes.

These findings imply that single-field templates may be insufficient for forthcoming data analyses and motivate updates to bispectrum estimators to directly probe these non-geodesic shape templates.

A key theoretical implication is that multi-field effects are not always reducible to effective single-field parameterizations; their signatures may only be captured by direct computation of interacting multi-field fluctuations, reinforcing the phenomenological motivation for precise multi-field Boltzmann solvers in CMB/LSS pipelines.

The authors highlight extensions to larger $N$4-field scenarios, where even more intricate signatures, including torsion, complicated target-space geometries, and a superposition of cosmological collider resonances, are expected. This will be especially pertinent for string-motivated N-flation and related scenarios.

Conclusion

This work identifies and characterizes universal, non-analytic bispectrum signatures arising from transient tachyonic instabilities of entropic fluctuations in multi-field inflation with hyperbolic field-space geometry. The distinctive combination of enhanced folded-limit bispectrum, characteristic squeezed limit scaling, and tachyonic resonance provide model-independent probes of non-geodesic inflationary dynamics. The results have immediate implications for both the interpretation of upcoming non-Gaussianity constraints and the future direction of theoretical inflationary model-building. Precise multi-field, fluctuation-level calculations are indispensable, and future observational discoveries of the signal structure described herein could provide compelling evidence for high-dimensional field dynamics during the inflationary epoch.