Decoherence of Inflationary Perturbations due to Gravity

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In order for quantum fluctuations during inflation to be converted to classical stochastic perturbations, they must couple to an environment which produces decoherence. Gravity introduces inevitable nonlinearities or mode couplings. We study their contribution to quantum-to-classical behavior during inflation. Working in the Schrodinger picture, we evolve the wavefunctional for scalar fluctuations, accounting for minimal gravitational nonlinearities. The reduced density matrix for a given mode is then found by integrating out shorter-scale modes. We find that the nonlinearities produce growing phase oscillations in the wavefunctional, which decohere the single-mode reduced density matrix into a diagonal mixed state. However, the weakness of the coupling delays decoherence until the mode is much longer than the Hubble scale environment modes. In summary, the gravitational coupling of long and short scales is sufficient to produce a mixed state of classical perturbations during inflation.