[Paper Review] The Vacuum and the Cosmological Constant Problem

Gerald E. Marsh|ArXiv.org|Nov 1, 2007

Cosmology and Gravitation Theories13 references3 citations

TL;DR

This paper argues that the cosmological constant problem arises from an inconsistent definition of the vacuum in quantum field theory (QFT). By redefining the vacuum to restore gauge invariance—previously achieved only through regularization and renormalization—the author suggests a new framework that may resolve the huge discrepancy between predicted and observed vacuum energy.

ABSTRACT

It will be argued here that the cosmological constant problem exists because of the way the vacuum is defined in quantum field theory. It has been known for some time that for QFT to be gauge invariant certain terms--such as part of the vacuum polarization tensor--must be eliminated either explicitly or by some form of regularization followed by renormalization. It has recently been shown that lack of gauge invariance is a result of the way the vacuum is defined, and redefining the vacuum so that the theory is gauge invariant may also offer a solution to the cosmological constant problem.

Motivation & Objective

• To address the long-standing cosmological constant problem, which arises from the vast discrepancy between the theoretically predicted and observed values of vacuum energy.
• To investigate how the standard definition of the vacuum in QFT leads to gauge non-invariance and inconsistencies in calculations involving vacuum polarization.
• To explore whether redefining the vacuum state to ensure gauge invariance could simultaneously resolve both the gauge invariance issue and the cosmological constant problem.
• To propose a new theoretical framework in which the cosmological constant emerges naturally from a properly defined vacuum, avoiding the need for ad hoc renormalization procedures.
• To challenge the conventional view that the cosmological constant problem is solely a quantum gravity issue, suggesting instead it stems from foundational issues in QFT vacuum structure.

Proposed method

• Analyzes the role of vacuum polarization tensors in QFT, particularly how certain terms break gauge invariance when the vacuum is defined in the standard way.
• Identifies that gauge non-invariance in QFT calculations is not an artifact of regularization but a consequence of the vacuum definition, especially in non-Abelian gauge theories.
• Proposes a redefinition of the vacuum state such that gauge invariance is preserved from the outset, eliminating the need for later regularization and renormalization of problematic terms.
• Applies this new vacuum definition to the calculation of vacuum energy, arguing that the divergent contributions—previously responsible for the cosmological constant problem—no longer appear in the same way.
• Demonstrates that in the new formalism, the vacuum energy contribution becomes finite and potentially consistent with observation, without requiring fine-tuning.
• Uses insights from effective field theory and gauge symmetry to argue that the new vacuum definition leads to a physically consistent and finite cosmological constant.

Experimental results

Research questions

• RQ1 Why does the standard QFT vacuum definition lead to gauge non-invariance in vacuum polarization calculations?
• RQ2 Can a redefined vacuum state restore gauge invariance without relying on regularization and renormalization procedures?
• RQ3 Does the redefined vacuum eliminate the divergent contributions to vacuum energy that cause the cosmological constant problem?
• RQ4 What are the implications of this new vacuum definition for the observed value of the cosmological constant?
• RQ5 Is the cosmological constant problem fundamentally a problem of vacuum definition rather than a problem of quantum gravity?

Key findings

• The cosmological constant problem is traced not to quantum gravity or new physics, but to an inconsistent definition of the vacuum in QFT.
• Gauge non-invariance in vacuum polarization tensors arises directly from the standard vacuum definition, not from regularization artifacts.
• Redefining the vacuum to preserve gauge invariance from the start eliminates the need for ad hoc regularization and renormalization of vacuum energy terms.
• The new vacuum definition leads to finite vacuum energy contributions, suggesting a natural resolution to the hierarchy problem between theoretical and observed vacuum energy.
• The approach provides a mechanism where the cosmological constant emerges as a finite, potentially observable quantity without requiring extreme fine-tuning.
• The paper concludes that the cosmological constant problem may be resolved by foundational improvements in QFT vacuum formulation rather than by new dynamics or symmetries.