Einstein Universe under Deconstruction: the case with degenerate fermions

TL;DR

This paper investigates static Einstein universe solutions within a graph-based induced gravity framework, utilizing the graph Laplacian spectrum to control UV divergences and analyze fermion degenerate pressure effects.

Contribution

It introduces a novel approach using graph spectra to study Einstein universe solutions in induced gravity, controlling UV divergences at one-loop level.

Findings

Static solutions supported by fermion degenerate pressure identified.

Spectrum distribution function effectively manages UV divergences.

Framework links graph theory with gravitational solutions.

Abstract

We study self-consistent static solutions for an Einstein universe in a graph-based induced gravity. In the generalization of the deconstruction model based on the graph, the eigenvalues of the graph Laplacian and the adjacent matrix gives the mass spectrum the particles. Thus we can easily control UV divergences at one-loop level in such a model. We use the calculation method with the spectrum distribution function of the graph and search for the static solution supported by the degenerate pressure of the fermion (at zero temperature). The report is based on arXiv:1110.5697.