A Bell experiment during inflation: probing quantum entanglement in tensor fluctuations through correlations of primordial scalar curvature perturbations

Abstract We propose a method that provides an observational signature of the quantum origin of primordial fluctuations generated during inflation. The method gives a prescription for testing a Bell inequality constructed exclusively from the standard scalar and tensor perturbations of minimal single-field inflation. We consider an inflationary spacetime populated by pairs of gravitons entangled in their polarization states. Third-order interactions between two scalars and one graviton transfer polarization information to the scalar sector through the product of spatial derivatives of scalars with the tensor polarization factors. Rather than performing the full multidimensional momentum integrations, we isolate and compute the tensor polarization structure of the primordial scalar eight-point correlation function. This eight-point correlation function factorizes into the product of four scalar two-point functions associated with opposite (mirrored) momentum configurations in Fourier space. This factorization falls from the fact that the two gravitons are spatially well-separated within the cosmological horizon of inflation, replicating the setup of standard Bell experiments. Through this interactions, we track how non-local correlations between both gravitons from polarization entanglement are imprinted on the scalar sector. We show that, for specific configurations of the scalar momenta after the end of inflation (detailed in the text), this observable can be used to construct a Bell-violating quantity in a way that matches the well-known Clauser-Horne-Shimony-Holt inequality definition. In principle, this offers a route to probe the quantum nature of primordial fluctuations through observables accessible today.