# Exact non-linear equations for cosmological perturbations

## TL;DR

This paper derives a comprehensive set of exact, gauge-ready, non-linear equations for all three types of cosmological perturbations in a flat universe, applicable to various gauges and backgrounds.

## Contribution

It provides the first complete, gauge-ready formulation of non-linear equations for scalar, vector, and tensor cosmological perturbations.

## Key findings

- Equations are fully non-linear and exact.
- Applicable to any gauge choice.
- Can be used for flat, expanding, or Minkowski backgrounds.

## Abstract

We present a complete set of exact and fully non-linear equations describing all three types of cosmological perturbations -- scalar, vector and tensor perturbations. We derive the equations in a thoroughly gauge-ready manner, so that any spatial and temporal gauge conditions can be employed. The equations are completely general without any physical restriction except that we assume a flat homogeneous and isotropic universe as a background. We also comment briefly on the application of our formulation to the non-expanding Minkowski background.