Flat space analog for the quantum origin of structure

The analytic structure of non-Gaussian correlators in inflationary cosmologies has recently been proposed as a test of the quantum origin of structure in the Universe. To further understand this proposal, we explore the analogous equal-time in-in correlators in flat space and show they exhibit the same features as their cosmological counterparts. The quantum vacuum is uniquely identified by in-in correlators with a total energy pole and no additional poles at physical momenta. We tie this behavior directly to the S-matrix and show that poles at physical momenta always arise from scattering of particles present in the initial state. We relate these flat-space in-in correlators to the probability amplitude for exciting multiple Unruh-de Witt detectors. Localizing the detectors in spacetime, through the uncertainty principle, provides the energy and momentum needed to excite the vacuum and explains the connection to cosmological particle production. In addition, the entanglement of these detectors provides a probe of the entangled state of the underlying field and connects the properties of the correlators to the range of entanglement of the detectors.

Figure 1

Illustration of the difference between non-Gaussian in-in correlations of $\varphi$ for quantum vacuum fluctuations (left) and classical fluctuations (right). Measuring quantum fluctuations of $\varphi$ at three spacelike separated points corresponds to the creation of three particles from the vacuum, producing a total energy pole in the correlator. In contrast, classical fluctuations only occur in a state containing particles. Any local classical process that produces a total energy pole will also cause particles in the initial state to decay, producing additional three-point correlations with poles at physical momenta.

Figure 2

Entanglement between detector in region $A$, located at $\overrightarrow{x}$, and two detectors in $B$, located at ${\overrightarrow{y}}_1$ and ${\overrightarrow{y}}_2$, produced by the three-point interaction ${\mathcal{H}}_{\mathrm{int}}=\mu {\varphi }^3$. Time runs in the vertical direction such that the correlation between detectors on the equal time surface is due to interactions in the past.