Twelfth Application: Cosmology and the Quantum Vacuum

Part of the Lecture Notes in Physics book series (LNP, volume 855)

Abstract

Zeta regularization has proven to be a powerful and reliable tool for the regularization of the vacuum energy density in ideal situations. With the Hadamard complement, it has been shown to provide finite (and meaningful) answers too in more involved cases, as when imposing physical boundary conditions (BCs) in two (and higher) dimensional surfaces (being able to mimic in a very convenient way other ad hoc cut-offs, as non-zero depths, see Chap.  7). Also these techniques have been used in calculations of the contribution of the vacuum energy of the quantum fields pervading the universe to the cosmological constant (cc). Naive calculations of the absolute contributions of the known fields lead to a value which is off by roughly 120 orders of magnitude, as compared with observational tests, what is known as the new cosmological constant 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 et al., Padmanabhan, etc.) We address this issue, in this last chapter, 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), as 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 here show that this value acquires the correct order of magnitude (and may also have the right, repulsive sign, what is very non-trivial)—corresponding to the one coming from the observed acceleration in the expansion of our universe—in a number of quite reasonable models involving small and large compactified scales and/or brane BCs, and supergravitons.

Keywords

Scalar Field Vacuum Energy Density Cosmological Constant Problem Casimir Effect Specific Boundary Condition 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  1. 1.Institute of Space ScienceHigher Council for Scientific ResearchBellaterra (Barcelona)Spain

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