Generalized Galileons: All scalar models whose curved background extensions maintain second-order field equations and stress tensors

TL;DR

This paper generalizes flat-space scalar field models to curved backgrounds, ensuring second-order equations and stress tensors, thus preserving their mathematical properties across all dimensions.

Contribution

It provides a systematic method to extend all flat-space second-order scalar models to curved backgrounds while maintaining their key second-order features.

Findings

All extended models preserve second-order equations.

Stress tensors are restored to second order.

The method applies uniformly across all dimensions.

Abstract

We extend to curved backgrounds all flat-space scalar field models that obey purely second-order equations, while maintaining their second-order dependence on both field and metric. This extension simultaneously restores to second order the, originally higher derivative, stress tensors as well. The process is transparent and uniform for all dimensions.