A Bell Experiment in an Entangled Universe

Abstract

We propose a possible quantum signature of the early Universe that could lead to observational imprints of the quantum nature of the inflationary period. Graviton production from the presence of a classical, coherent state of the inflaton scalar field results in entangled states in the gravitons' polarizations. At horizon crossing, interactions between the gravitons and (lower scale) inflatons, together with the gathering of ``which-path information'' from the cosmological horizon, perform the required Bell experiments leading to a definitive measure, which can be imprinted in the scalar correlation four-point function. This is because of a non-trivial effect due to the derivatives on two scalar fluctuations, and it provides a fingerprint that depends on the polarization of the graviton that Alice and/or Bob measured in their patch. We hint how this signature could be measured in the high-order correlation function of galaxies, in particular on the halo bias and the intrinsic alignment.

Figures (4)

• Figure 1: Set up for a Bell inequality violating experiment. The comoving time flows from left to right ($\eta=0$ represents the end of inflation), and spacial dimensions are drawn vertically. The entangled 2-state $\ket{\Psi}$ has components at two spatially-separate locations 1 (top) and 2 (bottom). Two different results of the measurement of observables $A$ and $B$ can be obtained, each dependent on the choice of the local variables $\theta_1$ and $\theta_2$, respectively. This choice is dependent on the interaction of the state with its local environment, it can be seen as a dependence on the measuring apparatus. The possible imprinting of the entanglement of state $\ket{\Psi}$ is represented by the dashed-line box. These results, together with the choices of $\theta_i$, are transmitted through classical channels (black arrows) to a final observer after inflation has finished.
• Figure 2: Graviton exchange of four inflatons Bellomo_2018. Process of imprinting at horizon crossing. The graviton is entangled with its partner, as described in the text. Note that the graviton on the diagram is in fact the two soft gravitons. The dependence in $P$ stretches the fact that this process will depend on the polarization of the graviton, as described in the text.
• Figure 3: Imprinting of non-local correlations between halos $A$ and $B$. The left figure represents the first and last term of equation \ref{['eq: S for correlation functions']} (terms $AB$ and $A'B'$), while the right figure represents the second and third terms ($A'B$ and $AB'$). The cosmological horizon is labeled as $H_\Lambda^{-1}$. The process is interpreted as follows. The 2-state wave function $\ket{\Psi}$ propagates to both halos, as gravitons propagate in approximately opposite directions towards halos A and B, respectively. Each wavy line represents the exchange of a low energy graviton between inflatons (straight lines) at different locations in each halo (subhalos without and with "prime"). The GE occurs at a time before horizon crossing of the gravitons, which imprints the non-local effects of entanglement in polarizations. At a later time, the inflatons (whose correlation carries the imprinting) become super-horizon.
• Figure 4: Schematic representation of the whole process described in this work, from the perspective of the evolution of physical scales $\lambda_\text{ph}$ during inflation as a function of the scale factor ($a_f$ denotes the end of inflation, $a_\text{eq}$ the matter-radiation equality, and $a_0$ the scale factor today). $H_\Lambda^{-1}$ denotes the physical Hubble horizon during inflation (constant part) and during the usual Hubble expansion (growing part). $k_D$ corresponds to the tensor modes that will undergo GE with the scalar modes before decoherence (around the time of horizon crossing $k_D|\eta|\sim 1$). $k_\text{obs}$ corresponds to the scalar modes in which we aim to find correlations as a prove of non-local nature (thus quantumness) of inflation. If we are looking at intrinsic alignment between halos, $k_\text{obs}\gtrsim 1$$\text{Mpc}^{-1}$, so that horizon exit occurs in the last e-folds of inflation, and is observable at the appropriate scale today.