Can dark energy emerge from quantum effects in a compact extra dimension?

The origin of the accelerated expansion of the universe is a major problem in both modern cosmology and theoretical physics. In quantum field theory, simple estimations of the vacuum contribution to the density energy of the Universe are known to lead to catastrophically high values compared to observations. A gravitational Casimir effect from an additional compact dimension of space is known to lead to an effective cosmological constant. Nevertheless, such a contribution by itself is usually not regarded as a plausible source for accelerating the expansion, given the constraints on such scenarios. Here, we propose that the Casimir vacuum contribution of the gravitational field actually provides a low positive value to the density energy of the universe. The key new ingredient is to assume that only modes with shorter wavelengths than the Hubble radius contribute to the vacuum energy. Such a contribution gives a positive energy density, has a naturally Lorentz invariant equation of state in the usual 4D spacetime, and can thus be interpreted as a cosmological constant. Its value agrees with observations for a radius of a fifth extra dimension given by 35 μm. The implied modification of the gravitational inverse square law is close but below existing limits from experiments testing gravity at short range.