Cosmological constant and vacuum energy: old and new ideas

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.

Running vacuum cosmological models: linear scalar perturbations

“…Therefore, we can rewrite eq. (1) as: 11,49,50], which can be integrated to . Accordingly, for the post-inflationary universe the terms of O(H 4 ) do not contribute effectively, and then, the last expression reduces to Λ(…”

“…In the general relativity context, a bare CC needs a fine-tuning of about 100 orders of magnitude, so that combined with the expected value of the vacuum energy density in quantum field theory, reproduce the effective dark energy density estimated from astronomical observations. This theoretical conundrum is known as the CC problem [7][8][9][10][11]. Another hassle is that in spite of behaving quite differently with respect to the cosmic expansion the CDM and DE are found to contribute to the energy content of the universe today with amounts of the same order, this riddle is known as the cosmic coincidence problem.…”

Galaxy clusters and structure formation in quintessence versus phantom dark energy universe

“…Clearly, a divergence from these assumptions deserves separate investigation, since the results could quantitatively (or even qualitatively) change. Such could be the more general case of a time-varying w and/or time-varying cosmological constant [42][43][44][45][46], remaining in the linear equation of state, or even going to more general equation of states such is the generalized polytropic one [81][82][83][84]. These extensions are under investigation and are going to be presented in a future publication.…”

“…In this work we assume that w = const, as we want to consider the simplest possible setup, in order to understand the basic effects of dark energy. The extension to the full time-varying w and/or time-varying cosmological constant [42][43][44][45][46], as well as the incorporation of possible dark-energy dark-matter interactions [47][48][49][50] and the corresponding complicated analysis, will follow in a subsequent work.…”

“…In TIS model the dark-matter halo is assumed to be spherical, isothermal and in equilibrium (that is an isothermal sphere), formed from the collapse and virialization of "top-hat" density-perturbations. The TIS scenario is a unique, non-singular solution of the Emden equation, modified with a cosmological constant [76], corresponding to the minimum-energy solution under constant external pressure, while the gas and the dark-matter halo are assumed to have the same distribution as in equation (45). The difference of TIS with our analysis is that we consider all non-singular solutions of the modified Emden equation (32) and not only the specific TIS one.…”