Fractality in Cosmic Topology Models with Spectral Action Gravity

TL;DR

This paper explores how cosmic topology and fractal structures influence spectral action gravity models, affecting inflationary power spectra and gravitational waves, and providing potential observational signatures.

Contribution

It introduces a framework linking cosmic topology and fractality within spectral action gravity, highlighting their combined effects on inflation and gravitational waves.

Findings

Topology constrains fractal structures in spacetime.

Fractal corrections to spectral action differentiate cosmic topologies.

Effects are detectable in inflationary power spectra and gravitational waves.

Abstract

We consider cosmological models based on the spectral action formulation of (modified) gravity. We analyze the coupled effects, in this model, of the presence of nontrivial cosmic topology and of fractality in the large scale structure of spacetime. We show that the topology constrains the possible fractal structures, and in turn the correction terms to the spectral action due to fractality distinguish the various cosmic topology candidates, with effects detectable in a slow-roll inflation scenario, through the power spectra of the scalar and tensor fluctuations. We also discuss explicit effects of the presence of fractal structures on the gravitational waves equations.