The Cosmological Constant Problem: Why it's hard to get Dark Energy from Micro-physics (1309.4133v1)

Abstract: These notes present a brief introduction to naturalness' problems in cosmology, and to the Cosmological Constant Problem in particular. The main focus is theold' cosmological constant problem, though the more recent variants are also briefly discussed. Several notions of naturalness are defined, including the closely related ideas of technical naturalness and `t Hooft naturalness, and it is shown why these naturally arise when cosmology is embedded within a framework --- effective field theories --- that efficiently captures what is consistent with what is known about the physics of smaller distances. Some care is taken to clarify conceptual issues, such as the relevance or not of quadratic divergences, about which some confusion has arisen over the years. A set of minimal criteria are formulated against which proposed solutions to the problem can be judged, and a brief overview made of the general limitations of most of the approaches. A somewhat more in-depth discussion is provided of what I view as the most promising approach. These notes are aimed at graduate students with a basic working knowledge of quantum field theory and cosmology, but with no detailed knowledge of particle physics.

• The paper shows that quantum field theory predicts a vacuum energy 122 orders of magnitude larger than observed, highlighting a significant theoretical gap.
• The paper employs effective field theory and naturalness principles to evaluate the mismatch between microscopic predictions and cosmological observations.
• The paper discusses potential solutions, including modified symmetries and extra dimensions, to reconcile quantum physics with dark energy data.

The Cosmological Constant Problem: An Analysis

The paper under discussion addresses the cosmological constant problem, primarily focusing on its implications for dark energy and its origins in micro-physics. This problem pertains to the interaction between quantum field theory (QFT) and general relativity, where the predicted vacuum energy density diverges significantly from observational data. Specifically, while QFT anticipates a vacuum energy many orders of magnitude larger than observed, cosmological measurements indicate a much smaller actual value, suggesting something significant is missing or misunderstood in the current theoretical framework.

Key Concepts and Mathematical Framework

The cosmological constant problem involves understanding how the energy of the vacuum—manifesting through quantum fluctuations—gravitates. This discrepancy is termed as the "old" cosmological constant problem, distinguished from the "new" variants that address the observable dark energy density. The "old" problem arises from the quantum predictions of vacuum energy that are inconsistent with a cosmological constant derived from astronomical observations. Fundamental concepts such as naturalness, effective field theories (EFTs), and associated technical challenges are at the forefront of this discussion.

The paper explores defining various naturalness concepts, including technical and 't Hooft naturalness. It utilizes these to evaluate the cosmological constant's behavior within an EFT framework. In doing so, the document seeks to determine the consistency of vacuum energy predictions with known physics from smaller scales considering quantum field behavior from various theoretical constructs.

Numerical Insights and Constraints

The paper contends that the vacuum energy, based on QFT, is expected to be about 122 orders of magnitude larger than what is inferred from cosmological observations. This immense gap poses a challenge that current models have yet to address adequately. The paper further explores the robustness of the large predicted value, arguing that the vacuum energy discrepancy persists despite numerous experimental verifications of QFT predictions, such as those from quantum electrodynamics.

Proposed Solutions and Theoretical Implications

The document outlines several proposals to resolve this cosmological constant issue. However, many are limited by their inability to reconcile the theoretical values with empirical data. Some approaches suggest modifications to fundamental theories, such as the introduction of additional symmetries (e.g., supersymmetry) or altering gravitational theories themselves. Notably, the paper identifies a set of minimal criteria that any viable solution should satisfy, emphasizing that theoretical resolutions must align with empirical observations without contriving additional inconsistencies.

Future Prospects and Speculations

Looking forward, the research highlights potential directions involving modifications in EFT or considering new symmetries that could inherently lower the predicted vacuum energy. Additionally, ideas involving large extra dimensions and their impact on gravitational interactions are discussed as intriguing avenues that could offer new perspectives beyond traditional 4-dimensional viewpoints.

Conclusion

The paper delivers an in-depth examination of one of the seminal issues in modern physics, the cosmological constant problem, linking the expansions of the universe to quantum properties at microscopic scales. Through this rigorous exploration of theoretical constructs and numerical dilemmas, the research underscores the necessity for a novel reconciliatory framework between QFT and cosmological data to further our understanding of the universe's expansion and dark energy characteristics. As theoretical and observational tools develop, the potential for revolutionary insights into the nature of vacuum energy and its cosmological implications remains substantial.