On Zeta Regularization and Some of its Uses in Cosmology

Abstract

Zeta regularization has been proven to be a fine, powerful and very reliable tool for the regularization of the vacuum energy density in ideal situations. With the additional help of the Hadamard calculus, we have shown it to yield also finite and physically meaningful answers in more involved cases, as when imposing physical boundary conditions in two-and higher-dimensional surfaces, being then able to mimic in a convenient way other ad hoc cut-offs, as non-zero depths. These recent developments are described in the first part of this presentation. Recently, those techniques have also been used in calculations of the contribution of the vacuum energy of the quantum fields which are presumably pervading the universe, to the cosmological constant. Naive calculations of the absolute contributions of all known fields 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 cosmological constant problem. This is very difficult to solve and we address here such issue only indirectly, by means of some specific examples.