We re-examine the effect of zero-point quantum fluctuations in
cosmology, proposing that their contribution to the cosmic expansion should be computed subtracting the flat-space contribution from the zero-point energy density computed in a FRW background. We discuss theoretical motivation for this subtraction. This treatment of vacuum fluctuations eliminates the quartically divergent term in the vacuum energy responsible for the cosmological constant problem. The vacumm energy density associated to zero-point fluctuations becomes a fixed fraction of the critical density at any time, providing a specific model of early dark energy. We discuss the implications of this result for the coincidence problem and we estimate the parameters of a cosmological model that takes into account this effect performing a full likelihood analysis using current CMB, SNe Ia and BAO data.