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Two-Point Metric Perturbations in de Sitter

In this chapter we derive the full two-point quantum metric perturbations on a de Sitter background including one-loop corrections from conformal fields. We do the calculation using the CTP effective action with the 1/N expansion, and select an asymptotic initial state by a suitable prescription that defines the vacuum of the interacting theory. The decomposition of the metric perturbations into scalar, vector and tensor perturbations is reviewed, and the effective action is given in terms of that decomposition. We first compute the two-point function of the tensor perturbations, which are dynamical degrees of freedom. The relation with the intrinsic and induced fluctuations of stochastic gravity is discussed. We then compute the two-point metric perturbations for the scalar and vector modes, which are constrained degrees of freedom. The result for the full two-point metric perturbations is invariant under spatial rotations and translations as well as under a simultaneous rescaling of the spatial and conformal time coordinates. Finally, our results are extended to general conformal field theories, even strongly interacting ones, by deriving the effective action for a general conformal field theory.