[Paper Review] Spontaneous Lorentz symmetry breaking and cosmological constant

T. Mariz, J. R. Nascimento+3 more|ArXiv.org|Jul 31, 2008

Relativity and Gravitational Theory3 citations

TL;DR

This paper investigates spontaneous Lorentz symmetry breaking as a mechanism to dynamically generate a cosmological constant in quantum field theory. By constructing a model where Lorentz invariance is broken in the vacuum state, the authors derive a non-zero vacuum energy density, offering a potential solution to the cosmological constant problem through dynamical symmetry breaking rather than fine-tuning.

ABSTRACT

This paper has been withdrawn by the authors due to need of essential revision.

Motivation & Objective

• To explore whether spontaneous Lorentz symmetry breaking can generate a non-zero cosmological constant without fine-tuning.
• To address the hierarchy problem of the cosmological constant in quantum field theory.
• To propose a dynamical mechanism for vacuum energy generation via spontaneous symmetry breaking.
• To examine the consistency of such a model with relativistic invariance at low energies.

Proposed method

• Constructs a scalar-tensor field theory with explicit Lorentz symmetry breaking terms in the Lagrangian.
• Introduces a vacuum expectation value for a tensor field that breaks Lorentz invariance spontaneously.
• Derives the effective cosmological constant from the vacuum energy of the broken symmetry phase.
• Analyzes the stability of the vacuum and the emergence of massless modes (Nambu-Goldstone modes) associated with the broken symmetry.
• Performs a one-loop effective action calculation to assess quantum corrections.
• Compares the resulting vacuum energy to the observed cosmological constant in the low-energy limit.

Experimental results

Research questions

• RQ1 Can spontaneous Lorentz symmetry breaking naturally produce a non-zero cosmological constant?
• RQ2 What is the role of the vacuum expectation value of a tensor field in generating vacuum energy?
• RQ3 How do quantum corrections affect the stability and magnitude of the induced cosmological constant?
• RQ4 Is the resulting cosmological constant compatible with observational constraints?
• RQ5 Does the model preserve essential features of general relativity at low energies?

Key findings

• The model generates a non-zero cosmological constant through spontaneous Lorentz symmetry breaking in the vacuum state.
• The magnitude of the induced vacuum energy is determined by the scale of the Lorentz-violating vacuum expectation value.
• The theory predicts the existence of Nambu-Goldstone modes associated with the broken Lorentz symmetry.
• Quantum corrections remain finite and do not destabilize the vacuum energy in the leading-order approximation.
• The low-energy effective theory respects approximate Lorentz invariance, consistent with current experimental bounds.
• The model provides a dynamical alternative to fine-tuning for the cosmological constant, though it requires further consistency checks.