Induced gravitational waves for arbitrary higher orders: vertex rules and loop diagrams in cosmological perturbation theory

TL;DR

This paper introduces a vertex approach and diagrammatic method to efficiently compute higher-order induced gravitational waves in cosmology, simplifying complex calculations and revealing diagrammatic contributions to different wave types.

Contribution

The paper presents a novel vertex and diagrammatic framework for calculating arbitrary higher-order induced gravitational waves, avoiding complex perturbation calculations.

Findings

One-particle reducible diagrams affect tensor-scalar waves.

The vertex approach simplifies higher-order gravitational wave calculations.

Loop diagrams correspond to correlations between tree diagrams.

Abstract

Gravitational waves induced by primordial perturbations serve as crucial probes for studying the early universe, providing a significant window into potential new physics during cosmic evolution. Due to the potentially large amplitudes of primordial perturbations on small scales, the contributions of high-order cosmological perturbations are highly significant. We propose a vertex approach applicable to the study of induced gravitational waves for arbitrary higher orders. Using the vertex approach and tree diagrams, we can directly derive the explicit expressions of higher-order induced gravitational waves without involving the complex and lengthy calculations of higher-order cosmological perturbations. Correlations between different tree diagrams correspond to the loop diagrams of two-point correlation functions of induced gravitational waves. Our investigation reveals that one-particle reducible diagrams impact tensor-scalar induced gravitational waves while leaving scalar induced gravitational waves unaffected.