A small cosmological constant from the modified Brans-Dicke theory - an interplay between different energy scales

TL;DR

This paper presents a modified Brans-Dicke model that naturally produces a small effective cosmological constant after symmetry breaking, without fine-tuning, by involving two distinct energy scales.

Contribution

It introduces a model with two energy scales, linking the Higgs VEV and a high scale for the Brans-Dicke field, to explain the small cosmological constant without fine-tuning.

Findings

Achieves the observed small cosmological constant scale

Avoids fine-tuning despite a large bare cosmological constant

Links energy scales to fundamental physics parameters

Abstract

In this paper we discuss a model in which the energy density, corresponding to the effective cosmological constant, after the $SU(2)\times U(1)$ symmetry breaking appears to be of the desired order of $10^{-48}\div 10^{-47} GeV^{4}$. The model contain two different energy scales, one of which is associated with the Higgs's vacuum expectation value. Another scale is of the order of $10^{21}GeV$ and defines the vacuum expectation value of the Brans-Dicke scalar field, non-minimally coupled to gravity, and sets the value of the Planck mass. Other (dimensionless) parameters are assumed not to contain hierarchical differences. The model is devoid of any fine-tuning and gives a small value of the effective cosmological constant even if the real "bare" cosmological constant is quite large.