Can the Baryon Number Density and the Cosmological Constant be interrelated?

TL;DR

This paper proposes a toy model linking the cosmological constant and baryon number density through scalar field dynamics, but it requires fine-tuning and does not establish a direct relation.

Contribution

It combines mechanisms from Dimopoulos, Susskind, and Yoshimura to explore a potential connection between baryon density and the cosmological constant.

Findings

Model fails to directly relate the two quantities without fine-tuning

Scalar field dynamics can generate a small positive cosmological constant

The approach highlights challenges in linking baryon number and dark energy

Abstract

A toy model is proposed in which the cosmological constant and the baryon number density of the universe are interrelated. The model combines the mechanism of Dimopoulos and Susskind in which the baryon number density of the universe is generated by the time-dependence of the phase of a complex scalar field, i.e. its `angular momentum' in the two-dimensinal complex field space, with that of Yoshimura in which the `centrifugal force' due the `angular momentum' pushes the vacuum expectation value of the scalar field out of a negative potential minimum and provides a small but positive cosmological constant. Unfortunately, our model fails to relate the smallness of the two numbers directly, requiring a fine-tuning of the negative potential minimum.