Dark Energy as Evidence for Extra Dimensions

TL;DR

The paper proposes that quantum fluctuations in extra compactified dimensions could explain dark energy, with the size of these dimensions constrained to around 100 micrometers to match observations.

Contribution

It introduces the idea that dark energy may originate from quantum fluctuations in extra dimensions, linking their size to observable cosmological effects.

Findings

Extra dimensions of about 100 μm size produce the observed dark energy.

Too small extra dimensions lead to excessive dark energy.

Too large extra dimensions conflict with Newton's law tests.

Abstract

It is argued that fluctuations of quantum fields in four-dimensional space do not give rise to dark energy, but are rather a negligible contribution to dark matter. By (relativistic) dark matter we mean that the relation between pressure and energy density is $p=\frac13 u$, while dark energy is characterized by $p=-u$. A possible source of dark energy are the fluctuations in quantum fields, including quantum gravity, inhabiting extra compactified dimensions. These fluctuations have been computed for some simple geometries, such as $S^2$, $S^4$, and $S^6$. If the extra dimensions are too small, they would give rise to a dark energy larger than that observed, whereas if they are too large they would be in conflict with experimental tests of Newton's law. This notion suggests that the size of the extra dimensions is of order 100 $\mu$m. If the limit on the size of extra dimensions becomes lower than this bound, extra dimensions probably do not exist, and another source for cosmological dark energy will have to be found.