Cosmological Casimir effect and beyond

Zeta regularization techniques are used for calculating the contribution of the vacuum energy of quantum fields pervading the universe to the cosmological constant (cc). As well known, naive computation of the absolute contributions of all possible sources lead to a value which is off by roughly 120 orders of magnitude, as compared with the results obtained from observational fits, what is known as the new cc problem. This fundamental issue is difficult to solve. Here we just consider possible additional contributions to the 'ground value' of the cc that might come from a non-trivial topology of space and/or from specific boundary conditions (BCs) imposed on braneworld and other models (e.g. kind of Casimir effects at a cosmological scale). Starting from the hypothesis that it may be proven that the ground value of the cc is in fact zero (as many believe), we would then be left with this incremental value coming from the topology or BCs. The computed result is shown to exhibit the correct order of magnitude and the appropriate sign, corresponding to the value coming from the observed acceleration in the expansion of our universe, in a number of seemingly reasonable situations involving some small and large compact dimensions.