Effects of the Quantum Vacuum at a Cosmic Scale and Dark Energy

Einstein equation approximated to second order in Newton constant G is quantized and applied to a large region of the universe. The two-point correlations of the vacuum energy density and pressure are included and the resulting metric agrees with the one derived from the $\Lambda CDM$ cosmological model plus an additional contribution of the quantum vacuum. The conclusion is that at least a part of the acceleration in the expansion of the universe is due to the vacuum fluctuations.