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.

Figures (10)

• Figure 1: Dimensionless bispectrum shapes $S(k_1, k_2, k_3)$, normalized to unity in the equilateral configuration $k_1=k_2=k_3$, in the entire kinematic configurations, induced by the interactions $(\partial_\mu \zeta)^2\sigma$ for $\lambda=1$ ( left panel), $\dot{\zeta}\sigma^2$ for $\lambda=5$ ( middle panel), and $\sigma^3$ for $\lambda=10$ ( right panel).
• Figure 2: Slices of the dimensionless bispectrum shapes $S(k_1, k_2, k_3)$ in the isosceles configuration $k_2=k_3$ from the folded limit $k_1/k_3=2$ to the squeezed limit $k_1/k_3\to0$, for each interactions given in Eq. \ref{['eq: cubic interactions']}, for $\lambda=1$ ( upper panel), $\lambda=5$ ( middle panel) and $\lambda=10$ ( lower panel). We have normalized the shapes to unity in the equilateral configuration, represented by the vertical gray line. The typical power-law scaling $S\sim (k_1/k_3)^{1/2-\nu_\lambda}$ for the light entropic field is represented by the gray dashed line. We show the non-geodesic shape templates $S^{\rm ng}_\pm$, defined in \ref{['eq: light hyperbolic template']} and \ref{['eq: heavy hyperbolic template']}, in black dashed and dotted lines. The dotted $S_-^{\rm ng}$ curve reproduces the shape predicted by angular inflation, see Sec. \ref{['subsec: bispectrum shape']}.
• Figure 3: Dimensionless bispectrum shapes $S(k_1, k_2, k_3)$ in the isosceles configuration $k_2=k_3$ from the folded limit $k_1/k_3=2$ to the squeezed limit $k_1/k_3\to0$, fixing $\lambda=10$, from the exact multi-field calculation (blue) and as predicted by the single-field EFT (red). The UV matching of the parameter $\lambda\to x$ is done by fitting the bispectrum amplitude at the isosceles folded configuration. For illustrative purposes, we have chosen the interaction $\dot{\zeta}\sigma^2$ which reduces to $\dot{\zeta}^3$ in the effective description. Notice that fitting the effective parameter $x$ at the tachyonic resonance peak would result in mismatch for its location and the amplitude in the folded contribution would be overestimated.
• Figure 4: Dimensionless bispectrum shape functions in the equilateral $k_1=k_2=k_3=k$ ( upper panel) and isosceles folded $k_1=2k_2=2k_3=k$ ( lower panel) for all considered interactions, as predicted by the multi-field theory (solid line) and the modified single-field EFT (dashed line). Notice that we have rescaled the single-field EFT prediction as in \ref{['eq: empirical scaling']}, including the factor from integrating out the heavy field and the additional empirical factor $f(\{k_i\})/\lambda$ in the folded configuration only, which comes from a kinematic-dependent UV matching.
• Figure 5: Schematic illustration of the interplay between three modes $k_1<k_2<k_3$ as function of time (in $e$-folds). The leading single-field EFT contribution correlates the longest decaying$k_1$ mode with two growing modes $k_2$ and $k_3$. The single-field EFT regime of validity $x$ is to be fitted to the data or determined by UV matching. The transient tachyonic instability described by this effective theory lasts $\approx \log(x)$ (which can differ from $\log(\lambda)$), and inevitably misses part of the evolution in case of different momenta.