Testing the arrow of time at the cosmo collider

TL;DR

We address whether a Lee–Wick ghost with reversed arrow of time can leave observable imprints in cosmological collider signals during inflation. Using the Schwinger–Keldysh formalism and its de Sitter extension, we show that ghost exchange yields opposite-sign non-Gaussianities and a distinctive absence of non-local oscillations in cosmological correlators, with Boltzmann-unsuppressed local oscillations in the tri-/bi-spectrum and possible infrared enhancements depending on operator dimension. A key technical result is that ghost seed integrals lack the non-local oscillations characteristic of on-shell production, replacing them with local $\cos(\mu\ln(r_1/r_2))$ terms, while the influence of a finite decay rate $|\Gamma|$ can regulate acausal effects by shifting effective operator dimensions. The work clarifies how a ghost in a de Sitter background should be treated and motivates exploration of ghostly sectors in gravity and non-Bunch–Davies initial states as potential extensions.

Abstract

Normal particles carry a microscopic arrow of causality. Lee-Wick ghosts carry the reversed arrow, mediating characteristic collider signals in flat space: opposite-sign scattering amplitudes that violate positivity bounds; acausality on time scales set by their negative decay rate. During inflation, the corresponding cosmo-collider ghost signals are: opposite-sign non-Gaussianities; Boltzmann-unsuppressed local oscillatory signals without their non-local counterparts; IR-enhanced bi-spectrum and power spectrum, depending on the dimension of the interaction operator, which decreases if the ghost decay rate is comparable to the Hubble rate.

Figures (3)

• Figure 1: Resonant $s$-channel production of a normal particle with decay width $\Gamma>0$ (left) and of a ghost with $\Gamma<0$ (right).
• Figure 2: The momentum configuration of a 4-point correlator.
• Figure 3: Sample seed functions ${\cal I}(r_1, r_2)$ for a normal particle and for a ghost. The left panel shows the result at fixed $r_2$. The right panel displays the ghost $\overleftarrow{\cal I}(r_1,r_2)$ in the upper side, and the normal $\overrightarrow{\cal I}(r_2, r_1)$ in the lower side. Regions of positive (negative) ${\cal I}$ are shaded in red (blue). The different shapes reflect the absence of non-local effects in the ghost case, understood analytically in the in the $\mu\gg1$ limit, eq. (\ref{['eq:Ighost']}). The ghost seed integral is logarithmically divergent at $r_2\to 1$.