Casimir Effect and the Cosmological Constant

Any quantum theory of gravity at the quantum gravity scale has the expectation of the existence of a minimal observable length. It is also expected that this fundamental length has a principal role in nature at the quantum gravity scale. From the uncertainty principle that influences the quantum measurement process, the existence of a minimal measurable length can be heuristically deduced. The existence of this minimal measurable length leads to an apparent discretization of spacetime, as distinguishing below this minimal length becomes impossible. In topologically non-trivial cosmological models, the Casimir effect is significant since it alters the spectrum of vacuum fluctuations and leads to a non-zero Casimir energy density. This suggests that the topology of the Universe could influence its vacuum energy, potentially affecting its expansion dynamics. In this sense, the Casimir effect could contribute to the observed acceleration of the Universe’s expansion. Here, we use the Casimir effect to determine the value of the electromagnetic zero-point energy in the Universe, applying it to the regions outside and inside the Universe horizon or Hubble horizon and assuming the existence of this minimal length. The Casimir effect is directly related to the boundary conditions imposed by the geometry and symmetries of the Hubble horizon. The agreement of the obtained value with the observed cosmological constant is not exact and therefore the contribution of non-electromagnetic radiation (gravitational effects) must be take into account.