We show that the consistent application of the rules of quantum mechanics to cosmological systems inevitably results in the so-called multiverse states in which neither the background spacetime nor the inhomogeneous perturbation are in definite states. We study the multiverse states as perturbations to the usually employed so-called Born-Oppenheimer states that are products of a wave function of the background and a wave function of the perturbation. The obtained corrections involve integrals over virtual backgrounds that represent the effect of quantum background fluctuations on the perturbation state. They resemble loop corrections in quantum field theory. This approach demonstrates the inevitable existence of very specific non-Gaussian features in primordial fluctuations. We express the resulting non-Gaussian perturbation as a nonlinear function of the Gaussian perturbation obtained within the Born-Oppenheimer approximation, and compute its trispectrum, to show that the multiverse scenario leads to testable and distinct signatures in cosmological perturbations. Our approach applies both to inflationary and alternative cosmologies.

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• Cosmology
• Quantum cosmology