[Paper Review] Newtonian gravity from Higgs condensates

M. Consoli, Fabio Siringo|ArXiv.org|Oct 18, 1999

Cosmology and Gravitation Theories8 references3 citations

TL;DR

This paper proposes that Newtonian gravity emerges as a long-wavelength excitation of the Higgs condensate responsible for electroweak symmetry breaking. It derives a Newtonian potential proportional to $ G_F / \eta $, with $ \eta = M_h^2 / (2m^2) $, and shows that identifying $ G = G_F / \eta $ as the Newton constant yields a predicted mass $ m \sim 10^{-4} \text{ to } 10^{-5} \text{ eV} $ for the Higgs quanta ('phions'), implying detectable fifth-force deviations below the centimeter scale.

ABSTRACT

We propose a description of {\it Newtonian} gravity as a long wavelength excitation of the scalar condensate inducing electroweak symmetry breaking. Indeed, one finds a $-{{G_F}\overη}{{m_im_j}\over{r}}$ long-range potential where $G_F$ is the Fermi constant and $η\equiv {{M^2_h}\over{2m^2}} $ is determined by the ratio between the Higgs mass $M_h$ and the mass m of the elementary quanta of the symmetric phase (`phions'). The parameter $η$ would diverge in a true continuum theory so that its magnitude represents a measure of non-locality of the underlying field theory. By identifying $G\equiv {{G_F}\overη}$ with the Newton constant and assuming the range of Higgs mass $M_h \sim 10^{2}-10^{3}$ GeV one obtains $m=10^{-4}-10^{-5}$ eV and predicts typical `fifth-force' deviations below the centimeter scale. Relation to Einstein gravity and string theory is discussed. The crucial role of the first-order nature of the phase transition for the solution of the so-called `hierarchy problem' is emphasized. The possible relevance of the picture for the self-similarity of the universe and for a new approach to the problem of dark matter is discussed.

Motivation & Objective

• To explore the possibility that Newtonian gravity arises not as a fundamental interaction but as an effective long-wavelength mode of the Higgs condensate.
• To address the hierarchy problem by emphasizing the first-order nature of the electroweak phase transition in this emergent gravity framework.
• To connect the Higgs sector with macroscopic gravity, suggesting a novel mechanism for the origin of the Newton constant.
• To investigate implications for dark matter and the self-similarity of the universe through the emergent gravitational mode.

Proposed method

• The authors model the Higgs condensate in the broken phase as a coherent state of scalar particles ('phions') with mass m, treating the system as a non-local field theory.
• They derive the long-range potential between two masses using the effective interaction mediated by the Higgs condensate, yielding a $ -\frac{G_F}{\eta} \frac{m_i m_j}{r} $ form.
• The parameter $ \eta = \frac{M_h^2}{2m^2} $ is introduced to account for non-locality, with $ M_h $ being the physical Higgs boson mass.
• By identifying $ G = \frac{G_F}{\eta} $ as the Newton constant, they relate the Fermi constant and Higgs mass to the gravitational constant.
• The model treats the gapless mode of the Higgs field as a Goldstone-like mode despite the absence of a continuous symmetry, suggesting a dynamical origin for gravity.
• They discuss consistency with Einstein gravity and string theory, and consider the implications of a first-order phase transition for solving the hierarchy problem.

Experimental results

Research questions

• RQ1 Can Newtonian gravity be derived as an effective low-energy excitation of the Higgs condensate in the electroweak phase?
• RQ2 What is the physical origin of the Newton constant in terms of the Higgs sector and the mass of the elementary Higgs quanta ('phions')?
• RQ3 How does the first-order nature of the electroweak phase transition resolve the hierarchy problem in this emergent gravity scenario?
• RQ4 What are the observable signatures of this model, particularly in terms of fifth-force deviations?
• RQ5 Could this emergent gravity mechanism provide a new perspective on dark matter or the self-similar structure of the universe?

Key findings

• The model reproduces the Newtonian potential $ -\frac{G_F}{\eta} \frac{m_i m_j}{r} $, with $ \eta = \frac{M_h^2}{2m^2} $, suggesting that gravity emerges from the Higgs condensate.
• By setting $ G = \frac{G_F}{\eta} $ equal to the Newton constant, the model predicts the mass of the Higgs quanta ('phions') to be $ m \sim 10^{-4} \text{ to } 10^{-5} \text{ eV} $ for a Higgs boson mass in the range $ M_h \sim 10^2 \text{ to } 10^3 \text{ GeV} $.
• The model predicts measurable deviations from Newton's law at sub-centimeter distances due to the exchange of the light 'phion' particle.
• The parameter $ \eta $, which diverges in a true continuum limit, quantifies the non-locality of the underlying field theory, indicating a fundamental departure from standard local quantum field theory.
• The first-order nature of the electroweak phase transition is crucial for stabilizing the hierarchy between the electroweak and Planck scales in this framework.
• The emergent gapless mode behaves like a Goldstone boson despite the absence of a continuous symmetry, suggesting a novel mechanism for gravity's emergence.