The cosmological constant problem or how the quantum vacuum drives the slow accelerating expansion of the Universe

I argue that a solution to the cosmological constant problem is to assume that the expectation value of the quantum vacuum stress-energy tensor is proportional to the metric tensor with a negative energy density and positive pressure. This assumption is confirmed by an explicit calculation of the vacuum expectation for the free electromagnetic and Dirac fields of quantum electrodynamics. As a consequence the metric of the universe might correspond to a FLRW with accelerating expansion only after averaging over large scales, but at small scales it gives rise to an extremely rapid fluctuation between expansion and contraction in every small region, with different phases in different points. The vacuum stress-energy tensor has fluctuations that lead to short periods of expansion. A calculation with plausible approximations leads to an estimate of the accelerating expansion that fits in the observed value.