Semiclassical analysis of pair creation in de Sitter space

We study a massive scalar field theory in de Sitter space. Using a worldline instanton approach, we calculate the pair creation probability in the weak-field limit. In addition to the exponential factor, we derive the pre-exponential factor. In this method, the pair creation probability for an odd-dimensional space vanishes. We find the leading contribution to the two-point correlator in the φ³ theory.