Abstract
The cosmological constant (CC) term in Einstein's equations, Λ, 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 Λ-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.
Highlights
The most prominent performance of modern cosmology has been to provide observational evidence for the accelerated expansion of the universe [1, 2, 3, 4] and for the existence of large scale dynamical phenomena possibly caused by forms of matter beyond the usual baryonic component
We should seriously worry about the fact that such mass scale is some 30 orders of magnitude smaller than the mass scale which these models aim to explain – namely the millielectronvolt (∼ 10−3 eV) mass scale associated to the cosmological constant (CC) term! Why such strategy is not perceived as trying to solve a big problem by creating an even major one? The answer is perhaps another profound mystery of Nature; quite likely it must be that the CC problem is such a disproportionately big problem that we are – too soon – ready to redefine dramatically the scope and limits of our physical perceptions
But where does the curvature of spacetime enter the previous discussion on the zero-point energy (ZPE) in Sect. 5 or the Higgs potential in Sect. 6? Nowhere! it should be quite natural to discuss the vacuum energy in a curved background, if we aim at elucidating its possible connection to the value of the cosmological term, shouldn’t it? we are going to summarize the effects of curvature for the calculation of the ZPE
Summary
The most prominent performance of modern cosmology has been to provide observational evidence for the accelerated expansion of the universe [1, 2, 3, 4] and for the existence of (other) large scale dynamical phenomena possibly caused by forms of matter beyond the usual baryonic component. In the following I will not elaborate on the whereabouts of the hypothetical DM particles, I will rather focus on a few aspects of the DE problem, or the cosmological constant (CC) problem [6, 7, 8], which is perhaps the most intriguing of all cosmological puzzles It is often stated in the literature that the CC term, and its association with the notion of vacuum energy, cannot be a valid theoretical explanation for the accelerated expansion of the universe, and that we necessarily have to “go beyond Λ”. I will discuss some intriguing phenomenological implications of the dynamical vacuum framework as a potential source for a mild variability of the fundamental “constants” of Nature This could help in effectively testing these ideas using present day tech facilities in the ground lab and in the sky. For a more detailed and technical presentation, see e.g. [15]; and for a summarized introduction to time evolving vacuum models along these lines, see [16, 17]
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