Everything You Always Wanted To Know About The Cosmological Constant Problem (But Were Afraid To Ask) (1205.3365v1)

Abstract: This article aims at discussing the cosmological constant problem at a pedagogical but fully technical level. We review how the vacuum energy can be regularized in flat and curved space-time and how it can be understood in terms of Feynman bubble diagrams. In particular, we show that the properly renormalized value of the zero-point energy density today (for a free theory) is in fact far from being 122 orders of magnitude larger than the critical energy density, as often quoted in the literature. We mainly consider the case of scalar fields but also treat the cases of fermions and gauge bosons which allows us to discuss the question of vacuum energy in super-symmetry. Then, we discuss how the cosmological constant can be measured in cosmology and constrained with experiments such as measurements of planet orbits in our solar system or atomic spectra. We also review why the Lamb shift and the Casimir effect seem to indicate that the quantum zero-point fluctuations are not an artifact of the quantum field theory formalism. We investigate how experiments on the universality of free fall can constrain the gravitational properties of vacuum energy and we discuss the status of the weak equivalence principle in quantum mechanics, in particular the Collela, Overhausser and Werner experiment and the quantum Galileo experiment performed with a Salecker-Wigner-Peres clock. Finally, we briefly conclude with a discussion on the solutions to the cosmological constant problem that have been proposed so far.

• The paper provides a detailed analysis of the cosmological constant problem by contrasting vast theoretical vacuum energy predictions with the observed small value.
• It investigates how scalar, fermionic, and vector fields influence vacuum energy and discusses supersymmetry as a potential cancellation mechanism.
• The study applies advanced regularization techniques that respect Lorentz invariance, highlighting the persistent gap between theoretical models and cosmological observations.

Review of "Everything You Always Wanted To Know About The Cosmological Constant Problem (But Were Afraid To Ask)"

The paper authored by Jérôme Martin addresses one of the most persistent and perplexing issues in modern cosmology: the cosmological constant problem. The cosmological constant, denoted as Λ, appears in Einstein’s field equations and is associated with the energy density of empty space, or the vacuum energy. Although theoretically postulated to be enormous, empirical observations suggest a value that is 122 orders of magnitude smaller, leading to a significant incongruity known as the cosmological constant problem.

Overview and Findings

The paper is indeed comprehensive, providing a detailed technical and pedagogical survey of the problem. Initially, it revisits the fundamentals of vacuum energy and its role in cosmology. The vacuum energy, arising from quantum fluctuations, is expected to gravitate, building the premise that its contribution to the cosmological constant should be physically significant. However, the calculated value of this energy from field theoretic models, when plugged into Einstein's equations, predicts a universe that is vastly different from what we observe.

Martin methodically explores the role of different types of fields—scalars, fermions, and vector bosons—in contributing to vacuum energy. A salient point discussed is that while scalar fields lead to a positive contribution to the vacuum energy, fermions contribute negatively, leading physicists to consider supersymmetry as a potential framework for resolving the disparity. In a supersymmetric universe, every fermion is paired with a corresponding boson, potentially canceling out vacuum energies and solving the cosmological constant problem. However, as supersymmetry is broken in our present universe, it does not seem to offer a complete solution.

Implications

In addition to the above calculation challenges, the paper elucidates on the possible measures of Λ in cosmological contexts. Martin discusses how observations related to the accelerated expansion of the universe are often interpreted as requiring a non-zero cosmological constant. This interpretation is contingent on the assumption that general relativity and the homogeneity of the universe are applicable at cosmological scales, an assumption that alternative models of gravity challenge.

Regularization and Renormalization

An intriguing aspect of this article is the deep dive into the mathematics behind regularizing and renormalizing the vacuum energy. The author emphasizes that naive cutoff methods lead to incorrect equations of state for vacuum energy, which violate Lorentz invariance. Instead, methods like dimensional regularization are shown to respect this symmetry and yield results that theoretically alleviate some disparity, although they ultimately do not resolve the constant discrepancy between theoretical predictions and observations.

Conclusions

Overall, the paper leads to a candid acknowledgment that while the cosmological constant problem presents a severe challenge to our understanding of physics, it remains unresolved. Prospective solutions may arise from improvements in field theories, a better understanding of quantum gravity, or potentially new physics beyond the standard model.

This work offers a meticulous discussion on the intersection of quantum field theory, cosmology, and general relativity. Despite the complexities involved, it confirms the importance of the cosmological constant problem in modern physics and reinforces the necessity for multi-disciplinary approaches in pursuit of a compelling resolution. Future developments in observational cosmology and theoretical advancements in quantum theories may provide further illumination, potentially closing the gap exposed by current models.