Cosmological Correlators Using Tensor Networks

We develop a nonperturbative tensor-network framework for computing cosmological correlators in de Sitter space and use it to test the proposal that suitably defined in-in correlators can be obtained from an in-out formalism by gluing the expanding and contracting Poincar\'e patches. Focusing on interacting $1+1$-dimensional $\phi^4$ theory, we formulate finite-time lattice observables using Matrix Product State (MPS) techniques and analyze the regulator subtleties associated with the singular behavior near the patching surface. Within this regulated framework, we find controlled nonperturbative evidence for the proposed relation between in-in and in-out correlators in several examples. We also find suggestive evidence that the perturbative obstructions present for sufficiently light fields can be softened nonperturbatively, albeit in a regime of substantially larger entanglement. A central outcome of our analysis is an entanglement-based picture of the computation: for in-in evolution the entanglement remains modest and can decrease toward late times, whereas in the patched in-out set-up it grows significantly after the gluing slice. Thus, although the in-out formalism is perturbatively economical, the in-in formulation is numerically more favorable. We briefly discuss how the same strategy extends to low-angular-momentum sectors in $3+1$ dimensions, and why regimes of rapid entanglement growth may eventually motivate quantum-computing implementations.