Cosmological constant and vacuum energy: old and new ideas

TL;DR

This paper reviews the longstanding cosmological constant problem, emphasizing the discrepancy between theoretical vacuum energy predictions and observations, especially in light of recent Higgs boson discoveries, and explores old and new ideas focused on vacuum energy and its potential running.

Contribution

It provides a pedagogical overview of the cosmological constant problem, highlighting the significance of vacuum energy and recent developments related to the Higgs boson.

Findings

The discrepancy between vacuum energy predictions and observed cosmological constant is about 55 orders of magnitude.

Recent Higgs boson discovery relates to the tangible concept of vacuum energy in phenomenology.

The paper emphasizes the importance of the original vacuum energy notion over dark energy models.

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.