Can Dark Energy emerge from quantum effects in compact extra dimension ?

TL;DR

This paper proposes that quantum effects in a compact extra dimension can produce a small positive vacuum energy density, potentially explaining dark energy and the universe's accelerated expansion.

Contribution

It introduces a model where a Casimir-like effect from a compact extra dimension yields a positive vacuum energy consistent with observations.

Findings

Vacuum energy density matches observed dark energy for a 35 μm extra dimension.

The model predicts modifications to gravity at short ranges near this scale.

The approach provides a Lorentz-invariant cosmological constant from quantum effects.

Abstract

The origin of the observed acceleration of the expansion of the universe is a major problem of modern cosmology and theoretical physics. Simple estimations of the contribution of vacuum to the density energy of the universe in quantum field theory are known to lead to catastrophic large values compared to observations. Such a contribution is therefore generally not regarded as a viable source for the acceleration of the expansion. In this letter we propose that the vacuum contribution actually provides a small positive value to the density energy of the universe. The underlying mechanism is a manifestation of the quantum nature of the gravitational field, through a Casimir-like effect from an additional compact dimension of space. A key ingredient is to assume that only modes with wavelength shorter than the Hubble length contribute to the vacuum. Such a contribution gives a positive energy density, has a Lorentz invariant equation of state in the usual 4D spacetime and hence can be interpreted as a cosmological constant. Its value agrees with observations for a radius of a 5th extra dimension given by $35\,\mu$m. This implies a modification of the gravitational inverse square law around this scale, close but below existing limits from experiments testing gravity at short range.