# The general gravitational Lagrangian with deformed covariance

## TL;DR

This paper derives a generalized gravitational Lagrangian incorporating all orders of curvature, accounting for deformed covariance constraints predicted by loop quantum cosmology, revealing complex deformation functions with potential discontinuities.

## Contribution

It provides a comprehensive derivation of the gravitational Lagrangian under deformed covariance, extending classical theory to include quantum-inspired modifications.

## Key findings

- Deformation functions satisfy a non-linear fluid mechanics equation.
- Deformation functions can exhibit discontinuities.
- The derived Lagrangian generalizes classical gravity to all curvature orders.

## Abstract

We derive the gravitational Lagrangian to all orders of curvature when the canonical constraint algebra is deformed by a phase space function as predicted by some studies into loop quantum cosmology. The deformation function seems to be required to satisfy a non-linear equation usually found in fluid mechanics, and can form discontinuities quite generally.