Amplifying the Cosmological Collider with Ghost Spectators

TL;DR

This work introduces a ghost condensate as a spectator during inflation, yielding a modified dispersion $\omega^2 \propto k^4$ that weakens Boltzmann suppression for heavy states and amplifies cosmological collider signals in the bispectrum and trispectrum. Using the in--in formalism, the authors derive the relevant propagators and seed functions, compute the trispectrum and bispectrum, and show that the enhancement grows with the exchange mass parameter $\mu$ and is controlled by the ghost scale ratio $\gamma=H/M$. They also formulate ghost-specific bootstrap equations with higher-derivative operators, revealing a modified singularity structure while preserving a residual conformal-like boundary constraint. The results broaden the cosmological collider program by linking de Sitter bootstrap and boostless approaches, suggesting that heavy-particle signatures could be accessible in upcoming cosmological surveys.

Abstract

Ghost inflation is a well-known framework in which cosmological fluctuations can generate enhanced primordial non-Gaussianity, typically of the equilateral type. In its original form, however, it is in tension with current observational constraints. Here we instead consider a setup in which a standard inflaton drives the background evolution, while excitations of a ghost condensate act as spectator fields that interact with the inflaton. This proposal fits naturally within the cosmological collider program: the exchanged particle has a modified dispersion relation, $ω\propto k^2$. We show that this ghost-inspired dynamics weakens the usual Boltzmann suppression, similarly to models with a very small effective sound speed, yielding an enhanced bispectrum signal relative to standard cosmological collider scenarios. At the same time, the horizon-crossing scale remains a free parameter of the theory. As a result, the model shares features of both the de Sitter bootstrap and boostless frameworks. Finally, we derive the differential equations governing cosmological correlators in the ghost-collider setup. Their structure reflects the quadratic momentum dependence of the dispersion relation and distinguishes this scenario from conventional relativistic cases.

Figures (5)

• Figure 1: Oscillatory contribution to the trispectrum in the collapsed limit, where $\kappa_{1} = u^{-1}$ and $\kappa_{2} = v^{-1}$. In the left panel, the black curve shows the full de Sitter result $\hat{\mathcal{I}}^{0,0}_{\mathrm{dS}}(\kappa_{1},\kappa_{2})$ for $\mu = 1$, while the blue curve shows the mixed seed $\hat{\mathcal{I}}^{0,0}_{\mathrm{mix}}(\kappa_{1},\kappa_{2})$ for the same value of $\mu$. For $\mu = 1$, both contributions have the same order of magnitude. As shown in the right panel, when the mass is increased to $\mu = 5$, the de Sitter seed must be multiplied by a factor of $10^{2}$ in order to be comparable to the mixed result. In this analysis we have fixed $v = 0.005$.
• Figure 2: Mixed seed function $\hat{\mathcal{I}}^{0,0}_{\mathrm{mix}}(\kappa_{1},\kappa_{2})$ for $\mu = 5$. The blue curve corresponds to $\gamma = 0.001$, and the black curve corresponds to $\gamma = 1 \cdot 10^{-6}$, where we also have set $v=0.005$. The amplitude does not change; this shows that the effect of $\gamma$ is to shift the phase, acting as an effective sound speed.
• Figure 3: This plot shows the role of the mass of the fields, as the mass increases the discrepancy between the amplitudes becomes even bigger. The oscillatory contribution to the bispectrum. On the left the comparison between the full dS case $F_{\text{dS}}$ and the mixed $F_{\text{mix}}$ for the exchange of a ghost in the bulk, for $\mu = 4$. In the right we have considered $\mu = 8$ and for both curves we set $\gamma = 0.001$.
• Figure 4: This plot shows the role of the gamma $\gamma$ in fields, as gamma changes the signal can be in phase or out of phase, reproducing an "effective" speed of sound. The oscillatory contribution to the bispectrum. On the left the comparison between the full dS case $F_{\text{dS}}$ and the mixed $F_{\text{mix}}$ for the exchange of a ghost in the bulk, for $\mu = 8$ and $\gamma = 15 \cdot 10^{-4}$. In the right we have considered $\gamma = 1 \cdot 10^{-6}$.
• Figure 5: Keldysh contour. The contour $C_{+}:-\infty(1 - i\xi)$ is represented by the green curve; it represents the contour of time-ordered operators. The contour $C_{-}:-\infty(1 + i\xi)$ is represented by the blue curve; it represents the contour of anti-time-ordered operators.