Everything you always wanted to know about the cosmological constant problem (but were afraid to ask)

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 spacetime 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 supersymmetry. 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.

BeyondΛCDM: Problems, solutions, and the road ahead

“…In our modern picture of particle physics, there is no unique classical theory; there are instead many effective theories. EFT calculations of the SM show that the CC receives contributions from all massive particles in the SM, proportional to the fourth power of their masses [5]. Ignoring neutrinos, the smallest contribution comes from electrons, from which the CC should receive a contribution of m 4 e , which is 32 orders larger than the observed value.…”

“…condensates) at various scales -ranging from the quantum qravity scale, M Pl 1.2 · 10 19 GeV, to the quantum chromodynamics (QCD) confinement scale, M QCD 0.1 GeV. The well-studied quark-gluon and Higgs condensates alone (responsible for chiral and gauge symmetry-breaking in the SM respectively) have contributions to the ground state energy of the Universe that far exceed the observed absolute CC value today [5]. Regardless of how the observed CC is explained, these huge quantum vacuum contributions must be eliminated.…”

“…Curious discrepancies also appear to exist between the predicted clustering properties of CDM on small scales and observations. The cosmological constant is even more puzzling, giving rise to quite simply the biggest problem in all of fundamental physics: the question of why Λ appears to take such an unnatural value [5,6,7]. Inflation, the theory of the very early Universe, has also been criticized for being fine-tuned and under-predictive [8], and appears to leave many problems either unsolved or fundamentally unresolvable.…”

Massive scalar field evolution in de Sitter

“…The first approach is to choose a regularization that does not break covariance. Dimensional regularization is a prime example of a covariant regularization prescription where the generated divergences can be regulated with counter terms satisfying δρ + δp = 0, as discussed in [79,81]. This feature is present also when using the Pauli-Villars regularization [78].…”

“…Indeed, the non-vanishing of (3.19) can be traced to the fact that a cut-off violates general covariance, an issue which has been known already for a long time [78] and more recently discussed in [79][80][81]. There are three obvious ways of overcoming this problem.…”