  In this work we aim at explaining the re-acceleration of the expansion of the
universe, or equivalently, the hierarchy problem, with the help of a simple
field-theoretical model. In particular, we want to account for the notorious
discrepancy between the observed value of the cosmological expansion term and
theoretical values of the vacuum energy of free quantum fields. Rendered
infinite by short-wavelength fluctuations, evaluation up to a cutoff in
momentum space at the Planck scale leads to contributions of the order of
$10^{76} \,\mathrm{GeV}^4$. The observed value of the cosmic expansion being of
the order of $10^{-47} \mathrm{GeV}^4$, this is a difference of $123$ orders of
magnitude. We propose a possible resolution of the hierarchy problem by a
cancelation of divergences by equivalent contributions of bosonic and fermionic
fields of the system, albeit after some fine-tuning of the parameters of the
field theory. We show that in principle nothing beyond conventional ingredients
of quantum field theory is necessary to provide us with a possible explanation
of the observed dark energy, and thus with a solution to the hierarchy problem.
