Quantum vacuum fluctuations and the cosmological constant

Zeta function regularization techniques are optimally suited for the calculation of the contribution of fluctuations of the vacuum energy of the quantum fields pervading the universe to the cosmological constant (cc). The order of magnitude calculations of the absolute contributions of all fields is known to lead to a value which is off by over 120 orders, as compared with the results obtained from observational fits, known as the new cc problem. This is difficult to solve and many authors still stick to the old problem to try to prove that basically its value is zero with some perturbations thereof leading to the (small) observed result (Burgess C P et al 2006 Preprints hep-th/0606020, 0510123, Padmanabhan T 2006 Preprint gr-qc/0606061, etc). We also address this issue in a somewhat similar way, by considering the additional contributions to the cc that may come from the possibly non-trivial topology of space and from specific boundary conditions imposed on braneworld and other seemingly reasonable models that are being considered in the literature (mainly with other purposes too) - kind of a Casimir effect at cosmological scale. If the ground value of the cc would be indeed zero, we would then be left with this perturbative quantity coming from the topology or BCs. We review the status of this approach, in particular the fact that the computed number is of the right order of magnitude (and has the right sign, what is also non-trivial) when compared with the observational value, in some of the aforementioned examples. © 2007 IOP Publishing Ltd.