Observed Cosmological Reexpansion in Minimal QFT with Bose and Fermi Fields

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.