Quantum field theory, gravity and cosmology in a fractal universe

TL;DR

This paper introduces a fractal spacetime model for quantum field theory and gravity, achieving power-counting renormalizability with a Lorentz covariant action, and explores its implications for cosmology and the early universe.

Contribution

It presents a novel fractal spacetime framework for quantum fields and gravity, incorporating a Stieltjes measure and analyzing classical and quantum properties.

Findings

Spacetime flows from Hausdorff dimension 2 in the UV to D in the IR.

The scalar field exhibits a continuum of massive modes.

Ultraviolet cosmological solutions suggest early universe implications.

Abstract

We propose a model for a power-counting renormalizable field theory living in a fractal spacetime. The action is Lorentz covariant and equipped with a Stieltjes measure. The system flows, even in a classical sense, from an ultraviolet regime where spacetime has Hausdorff dimension 2 to an infrared limit coinciding with a standard $D$-dimensional field theory. We discuss the properties of a scalar field model at classical and quantum level. Classically, the field lives on a fractal which exchanges energy-momentum with the bulk of integer topological dimension D. Although an observer experiences dissipation, the total energy-momentum is conserved. The field spectrum is a continuum of massive modes. The gravitational sector and Einstein equations are discussed in detail, also on cosmological backgrounds. We find ultraviolet cosmological solutions and comment on their implications for the early universe.