Cosmological constant and vacuum energy: old and new ideas (1306.1527v3)

Abstract: The cosmological constant (CC) term in Einstein's equations, Lambda, was first associated to the idea of vacuum energy density. Notwithstanding, it is well-known that there is a huge, in fact appalling, discrepancy between the theoretical prediction and the observed value picked from the modern cosmological data. This is the famous, and extremely difficult, "CC problem". Paradoxically, the recent observation at the CERN Large Hadron Collider of a Higgs-like particle, should actually be considered ambivalent: on the one hand it appears as a likely great triumph of particle physics, but on the other hand it wide opens Pandora's box of the cosmological uproar, for it may provide (alas!) the experimental certification of the existence of the electroweak (EW) vacuum energy, and thus of the intriguing reality of the CC problem. Even if only counting on this contribution to the inventory of vacuum energies in the universe, the discrepancy with the cosmologically observed value is already of 55 orders of magnitude. This is the (hitherto) "real" magnitude of the CC problem, rather than the (too often) brandished 123 ones from the upper (but fully unexplored!) ultrahigh energy scales. Such is the baffling situation after 96 years of introducing the Lambda-term by Einstein. In the following I will briefly (and hopefully pedagogically) fly over some of the old and new ideas on the CC problem. Since, however, the Higgs boson just knocked our door and recalled us that the vacuum energy may be a fully tangible concept in real phenomenology, I will exclusively address the CC problem from the original notion of vacuum energy, and its possible "running" with the expansion of the universe, rather than venturing into the numberless attempts to replace the CC by the multifarious concept of dark energy.

• The paper proposes a dynamic view of the cosmological constant, showing it evolves with the universe’s expansion to address the vacuum energy discrepancy.
• The paper integrates historical insights with modern quantum field theory, contrasting Einstein’s static approach with current dark energy observations.
• The paper employs renormalization group techniques to quantify vacuum fluctuations, suggesting measurable effects on cosmic microwave background and galaxy distributions.

Analyzing "Cosmological Constant and Vacuum Energy: Old and New Ideas"

This paper by Joan Solà explores the cosmological constant (CC) problem, which is one of the central issues in contemporary theoretical physics. It investigates both historical and recent theories concerning the vacuum energy and its influence on the accelerated expansion of the universe. This discussion provides a comprehensive framework for understanding contributions from different fields such as quantum field theory (QFT) and cosmology and poses significant challenges to reconcile theoretical concepts with observational data.

Joan Solà begins with a historical overview highlighting the introduction of the cosmological constant by Einstein and its role in the context of general relativity. The cosmological constant is initially considered as a fudge factor to allow for a static universe, though later it was abandoned when the universe was discovered to be expanding. In modern cosmology, this constant is linked to dark energy, which is thought to be responsible for the accelerated expansion of the universe as observed in supernovae and cosmic microwave background data.

The core issue addressed by Solà is the discrepancy between the theoretically predicted value of the vacuum energy density and the value deduced from cosmological observations, which expands over 55 and even up to 123 orders of magnitude depending on the context. This is identified as the cosmological constant problem. Solà revisits different contributions to vacuum energy, including zero-point energies of quantum fields and symmetry-breaking phenomena at the electroweak scale, to illustrate the gravity of this discrepancy.

Solà hypothesizes a dynamical view of vacuum energy, contrasting with the traditional perception of a static cosmological constant. He explores a cohesive framework where the cosmological constant is not a fixed quantity but one that varies with the cosmic expansion, suggesting expressions such as $(H)$ reflecting the dependence on the Hubble parameter. The potential for this expression to evolve over cosmic timescales introduces a pivotal approach to resolve ongoing issues with the cosmological constant problem by allowing it to run with the expansion of the universe.

He elaborates on scenarios where the cosmological constant evolves over large scales influenced by quantum effects, suggesting that these might produce observable effects in the cosmic microwave background radiation or galaxy distribution patterns. Solà also tackles the implications of quantum field contributions on curved spacetimes, determining that this framework could lead to a reevaluation of how vacuum fluctuations within quantum field theory impact curvature and the universe's expansion rate.

Solà makes a compelling case for the running vacuum model, underpinned by renormalization group techniques in quantum field theory. This model implies that vacuum fluctuations contribute to dark energy and have observable consequences on cosmic scales. Thus, solving the cosmological constant problem might not just be about mathematical tweak but also demands a rethinking of fundamental physics principles. The model suggests new experimental and observational fronts that could validate or refute such theories.

Solà's research is enduringly relevant, providing new incentives to reconcile the contrasting scales between particle physics and cosmology via mechanisms that allow quantum field theoretical constructs to manifest observably on macro scales. Addressing these theoretical challenges offers the potential to significantly advance our understanding of fundamental constants, dark energy, and the fate of the universe. This paper indicates that continuing efforts in both theoretical physics and observational cosmology are essential to unlocking deeper universal truths.