A note on loop resummation in de Sitter spacetime with the wavefunction of the universe approach

TL;DR

This paper investigates how loop corrections in de Sitter spacetime, computed via the wavefunction of the universe approach, reintroduce IR divergences, aligning with known correlator behaviors and requiring potential renormalization.

Contribution

It demonstrates that loop corrections are IR finite in the wavefunction stage but reintroduce IR divergences in the correlator stage, clarifying the renormalization process.

Findings

Loop integrals in the wavefunction stage are IR finite.

IR divergences reappear in the correlator calculation.

Renormalization of the potential aligns results with other methods.

Abstract

We analyze the computation of $n$-point correlation functions in de Sitter spacetime, including loop corrections, using the wavefunction of the universe approach. This method consists of two stages employing distinct Feynman rules. First, one must compute the wavefunction coefficients using interactions as vertices. Then, in the second stage, one computes correlation functions using wavefunction coefficients as vertices. For massless fields, loop corrections in the first stage are free of infrared (IR) divergences, which leads to the question of how this matches the well-known IR behavior of correlators obtained via other methods. By considering a scalar field with an arbitrary potential, we compute $n$-point correlation functions to first order in the potential but to all orders in loops. We find that, although loop integrals in the first stage are indeed IR convergent, the second procedure reintroduces the IR divergence. We discuss how this induces renormalization of the interaction potential such that the final result combining both steps exactly matches the form of $n$-point functions previously calculated with other methods.