Multi-scale gravity and cosmology

TL;DR

This paper explores multi-scale, non-Riemannian spacetimes with fractal-like measures, revealing novel cosmological features such as bounce replacements for the big bang, reinterpretation of dark energy, and potential observable imprints in cosmological spectra.

Contribution

It introduces and analyzes three classes of multi-scale spacetimes with non-Riemannian structures, highlighting their implications for cosmology and potential observational signatures.

Findings

Big-bang singularity replaced by a bounce

Accelerating phases explained without scalar fields

Logarithmic oscillations in cosmological spectra

Abstract

The gravitational dynamics and cosmological implications of three classes of recently introduced multi-scale spacetimes (with, respectively, ordinary, weighted and q-derivatives) are discussed. These spacetimes are non-Riemannian: the metric structure is accompanied by an independent measure-differential structure with the characteristics of a multi-fractal, namely, different dimensionality at different scales and, at ultra-short distances, a discrete symmetry known as discrete scale invariance. Under this minimal paradigm, five general features arise: (a) the big-bang singularity can be replaced by a finite bounce, (b) the cosmological constant problem is reinterpreted, since accelerating phases can be mimicked by the change of geometry with the time scale, without invoking a slowly rolling scalar field, (c) the discreteness of geometry at Planckian scales can leave an observable imprint of logarithmic oscillations in cosmological spectra and (d) give rise to an alternative mechanism to inflation or (e) to a fully analytic model of cyclic mild inflation, where near scale invariance of the perturbation spectrum can be produced without strong acceleration. Various properties of the models and exact dynamical solutions are discussed. In particular, the multi-scale geometry with weighted derivatives is shown to be a Weyl integrable spacetime.