Heavy Spinning Particles from Signs of Primordial Non-Gaussianities: Beyond the Positivity Bounds

TL;DR

The paper broadens the cosmological collider framework by proposing that the sign of a six-derivative inflaton operator, beta, can reveal the spins of heavy intermediate states beyond the universal positivity of the four-derivative term. By constructing a UV-amplitude basis and analyzing IR–UV connections under Froissart-Martin bounds, it shows beta>0 for intermediate scalars and beta<0 for higher-spin exchanges (with caveats in gravity and multi-particle states). Open string amplitudes illustrate a concrete UV completion where beta vanishes, while KK graviton analyses reveal subtleties that still allow beta as a potential spin-diagnostic with careful treatment. The work then translates these insights into de Sitter four-point functions and inflationary three-point functions, identifying distinct angular and high-energy signatures (equilateral vs folded configurations) that could help distinguish derivative-order contributions in primordial non-Gaussianities. Overall, the study provides a path to infer the spins of heavy particles at the inflation scale from signs and shapes of primordial non-Gaussianities, offering new observational handles in the cosmological collider program.

Abstract

Within the so-called cosmological collider program, imprints of new particles on primordial non-Gaussianities have been studied intensively. In particular, their non-analytic features in the soft limit provide a smoking gun for new particles at the inflation scale. While this approach is very powerful to probe particles of the mass near the Hubble scale, the signal is exponentially suppressed for heavy particles. In this paper, to enlarge the scope of the cosmological collider, we explore a new approach to probing spins of heavy particles from signs of Wilson coefficients of the inflaton effective action and the corresponding primordial non-Gaussianities. As a first step, we focus on the regime where the de Sitter conformal symmetry is weakly broken. It is well known that the leading order effective operator $(\partial_μφ\partial^μφ)^2$ is universally positive as a consequence of unitarity. In contrast, we find that the sign of the six derivative operator $(\nabla_μ\partial_νφ)^2(\partial_ρφ)^2$ is positive for intermediate heavy scalars, whereas it is negative for intermediate heavy spinning states. Therefore, under the assumption of tree-level UV completion, the sign can be used to probe spins of heavy particles generating the effective interaction. We also study phenomenology of primordial non-Gaussianities thereof.

Figures (4)

• Figure 1: Integration contour and analytic structure: The red lines represent branch cuts associated to multi-particle states generated by loops, whereas the red dots are single poles associated to single-particle states. The left panel is the integration contour used to read off the IR coefficients. By deforming it into the one on the right panel, we may clarify how the UV data is encoded into the IR coefficients.
• Figure 2: The coefficients of $s^2$ (blue) and $s^2 t$ (red) obtained after summing up over $n$ from $1$ to $n_{\rm max}$: As the positivity bound implies, each sector labeled by $n$ contributes to the $s^2$ coefficient positively. On the other hand, the $n=1$ sector gives a negative contribution to the $s^2t$ coefficient, which is canceled by positive contributions from $n\geq3$ to obtain a vanishing coefficient in the limit $n_{\rm max}\to\infty$ representing the open superstring amplitude.
• Figure 3: Equilateral configurations of four momenta
• Figure 4: Shape of $\mathcal{A}_{\rm 3pt}$(left) and $\mathcal{B}'_{\rm 3pt}$(right): Both of them have a peak at the equilateral configuration $k_1=k_2=k_3$, but the height at the folded configuration $k_1=k_2=k_3/2$ is different by a factor $\sim3$.