Metric affine gravity with dynamical chronology protection

TL;DR

This paper introduces a metric-affine gravity model that enforces stable causality through dynamical time generation, unifies mimetic gravity as a special case, and suggests chronology protection as a guiding principle for modified theories.

Contribution

It proposes a new toy model of metric-affine gravity that dynamically enforces causality and unifies mimetic gravity with a broader dark sector.

Findings

The model achieves stable causality via breaking of projective invariance.

Mimetic gravity is recovered as a special case of the model.

A broader dark sector naturally emerges from the model.

Abstract

Modified theories of gravity often introduce geometric structure beyond general relativity in order to address unresolved problems in the gravitational sector without invoking ad hoc matter fields. Mimetic gravity, for example, generates an effective cosmological dark sector by isolating the conformal mode of the metric, while Horava--Lifshitz gravity attains power-counting renormalizability by endowing spacetime with a preferred dynamical foliation. Although chronology protection was not the original motivation for either theory, both enforce it classically through stable causality. This suggests that chronology protection itself may be elevated from a derived property to a guiding principle for constructing modified gravitational theories, especially if its implementation at the quantum-gravitational level leaves infrared imprints in the effective action. Motivated by this possibility, we introduce a toy metric--affine gravity model that modifies only the geometric sector. The model realizes stable causality by dynamically generating a global time function via breaking of projective invariance. We further show that mimetic gravity is recovered as a special case, while a broader dark sector emerges naturally.