Boundary conditions of the RGE flow in the noncommutative geometry approach to particle physics and cosmology

TL;DR

This paper explores how small changes in boundary conditions at unification significantly affect the renormalization group flow in a noncommutative geometry model, impacting particle physics and cosmology predictions.

Contribution

It demonstrates the sensitive dependence of RG flow on initial conditions and identifies specific initial conditions that satisfy geometric constraints while remaining consistent with low-energy observations.

Findings

RG flow is highly sensitive to initial boundary conditions.

Certain modified maximal mixing conditions satisfy geometric constraints.

Chosen initial conditions can produce realistic low-energy predictions.

Abstract

We investigate the effect of varying boundary conditions on the renormalization group flow in a recently developed noncommutative geometry model of particle physics and cosmology. We first show that there is a sensitive dependence on the initial conditions at unification, so that, varying a parameter even slightly can be shown to have drastic effects on the running of the model parameters. We compare the running in the case of the default and the maximal mixing conditions at unification. We then exhibit explicitly a particular choice of initial conditions at the unification scale, in the form of modified maximal mixing conditions, which have the property that they satisfy all the geometric constraints imposed by the noncommutative geometry of the model at unification, and at the same time, after running them down to lower energies with the renormalization group flow, they still agree in order of magnitude with the predictions at the electroweak scale.