QFT in the flat chart of de Sitter space

TL;DR

This paper demonstrates that in the flat chart of de Sitter space, interacting quantum field theory correlators calculated via the in-in formalism are de Sitter invariant and identical to Euclidean correlators, providing an alternative proof of their equivalence.

Contribution

The paper provides a direct calculation proof that in-in and Euclidean correlators in de Sitter space are identical, confirming their invariance and correspondence.

Findings

Correlators are de Sitter invariant.

In-in and Euclidean correlators are identical.

Alternative proof of correlator equivalence.

Abstract

We study the correlators for interacting quantum field theory in the flat chart of de Sitter space at all orders in perturbation. The correlators are calculated in the in-in formalism which are often applied to the calculations in the cosmological perturbation. It is shown that these correlators are de Sitter invariant. They are compared with the correlators calculated based on the Euclidean field theory. We then find that these two correlators are identical. This correspondence has been already shown graph by graph but we give an alternative proof of it by direct calculation.