De Sitter spacetime with a Becchi–Rouet–Stora quartet

Abstract

We generalize the topological model recently proposed and investigate the cosmological perturbations of the model. The model has an exact de Sitter background solution associated with the Becchi–Rouet–Stora (BRS) quartet terms which are regarded as the Lagrangian density of the topological field theory. The de Sitter solution can be selected without spontaneously breaking the BRS symmetry, and be interpreted as a gauge fixing of de Sitter spacetime. The BRS symmetry is preserved for the perturbations around the de Sitter background before we solve the constraints of general relativity. We derive action to the second-order of the perturbations and confirm that even after solving the constraints, we have the BRS symmetry at least for the second-order action. We construct the cosmological perturbation theory involving the BRS sector, and obtain the two-point correlation functions for the curvature perturbation and the isocurvature perturbations which compose the BRS sector. Our result gives a new description for de Sitter spacetime and the quantum field theory in de Sitter spacetime.