# Non-smooth gravity and parity violation

## TL;DR

This paper proposes a modified theory of gravity allowing non-smooth metrics, which introduces new physics including an extra scalar invariant and a massless spin-1 field, potentially violating P and CP symmetries.

## Contribution

It extends general relativity by relaxing metric smoothness, revealing new invariants and fields, and exploring symmetry violations with experimental implications.

## Key findings

- Introduction of a new scalar curvature invariant
- Discovery of an additional massless spin-1 field
- Potential P and CP symmetry violations at leading order

## Abstract

A conservative extension of general relativity is proposed by alleviating the differentiability of the metric and allowing for non-smooth solutions. We show that these metrics break some symmetries of the Riemann tensor, yielding a new scalar curvature invariant besides the usual Ricci scalar. To first order in the curvature, this adds a new piece of information to the action, containing interesting and unexplored physics. The spectrum of the theory reveals the presence of an additional massless spin-1 field apart from the massless spin-2 graviton. We argue that this new contribution violates P and CP symmetries at leading order in the curvature and we discuss the possibility of observing these effects in existing experiments.