# de Sitter spacetime with a Becchi-Rouet-Stora quartet

## TL;DR

This paper develops a topological model with BRS symmetry for de Sitter spacetime, deriving perturbation actions and correlation functions, offering a novel quantum field theory perspective in de Sitter space.

## Contribution

It introduces a BRS-invariant topological model for de Sitter spacetime and constructs its cosmological perturbation theory, preserving BRS symmetry at second order.

## Key findings

- Derived second order action for perturbations maintaining BRS symmetry.
- Calculated two-point correlation functions for curvature and isocurvature perturbations.
- Provided a new quantum field theory framework for de Sitter spacetime.

## 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 a Becchi-Rouet-Stora(BRS) quartet terms which are regarded as a 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.