Emergence of time in power-counting renormalizable Riemannian theory of gravity

TL;DR

This paper proposes a novel approach where gravity is fundamentally Riemannian without time, and Lorentzian structure emerges at large scales, with a renormalizable theory at short distances.

Contribution

It introduces a Riemannian gravity model that explains the emergence of time and Lorentzian geometry at macroscopic scales, ensuring renormalizability at microscopic scales.

Findings

Time and Lorentzian structure emerge at large distances.

The theory is power-counting renormalizable at short distances.

Gravity is described without a fundamental notion of time.

Abstract

We suggest a new scenario of gravitation in which gravity at the fundamental level is described by a Riemannian (i.e. locally Euclidean) theory without the notion of time. The Lorentzian metric structure and the notion of time emerge as effective properties at long distances. On the other hand, at short distances, higher derivative terms compatible with the Riemannian diffeomorphism become important and the system is described by a power-counting renormalizable Riemannian theory.