We study the infrared divergences arising from gravitational loops in the standard cosmological perturbation theory. We provide a simple solution to the problem at all orders of cosmological perturbation theory by redefining the perturbation theory in terms of a local observer. We propose to reformulate the standard perturbations in the in-in formalism, and obtain an infrared safe perturbation theory. Our results do not depend on any infrared cutoffs or similar parameters. We then present an explicit example of graviton one-loop corrections, and briefly discuss non-gaussianities.Comment: 18 pages plus bibliography; improved presentation of the new redefined perturbation theory centred on locality; improved discussion and comparison with other approaches in the literature based for example on redefinition of the background or the gauge transformations, showing in a clearer way the differences between such approaches and our
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