Spectral interaction between universes

TL;DR

This paper develops a perturbative approach to model the direct spectral interaction between two four-dimensional geometries, providing explicit potential formulas and comparing them to bimetric gravity models.

Contribution

It introduces a spectral interaction formula based on the spectral action principle, expanding the potential up to third order around flat vacua.

Findings

Derived explicit third-order interaction potential

Expressed interaction as polynomials of metric invariants

Compared spectral interaction model with bimetric gravity

Abstract

We derive a perturbative formula for the direct interaction between two four-dimensional geometries. Based on the spectral action principle we give an explicit potential up to the third order perturbation around the flat vacua. We present the leading terms of the interaction as polynomials of the invariants of the two metrics and compare the expansion to the models of bimetric gravity.