# On the Expected Production of Gravitational Waves During Preheating

## TL;DR

This paper presents a full quantum in-in formalism approach to predict gravitational wave production during preheating, highlighting differences from classical simulation methods and extending applicability to low resonance parameters.

## Contribution

It introduces a quantum field theoretic method for calculating gravitational waves during preheating, addressing divergences and comparing with traditional simulation-based predictions.

## Key findings

- Quantum approach agrees with simulations at high resonance
- Method remains valid at low resonance where simulations fail
- Addresses divergences through regularization and renormalization

## Abstract

The existing predictions of the energy density of gravitational waves produced during preheating mostly rely on computer simulations in which the matter field inhomogeneities essentially behave classically. In this article we follow instead a full quantum treatment of the process within the $in$-$in$ formalism. We use this approach to determine the expected density of the produced gravitational waves and numerically estimate its value in a simple scalar field model, neglecting backreaction. Particular attention is devoted to the regularization and renormalization of the divergences that appear in the in-in formalism. We also address how our approach compares with the conventional calculations used in the literature, and what elements could be missed in the conventional analyses of gravitational wave production that rely on numerical simulations. In the cases in which parametric resonance is effective, our results agree with the predictions expected from numerical simulations, as anticipated. At sufficiently low values of the resonance parameter, however, numerical simulations fail, while our approach remains applicable.