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We show that when the bare cosmological constant in the Einstein field equations takes large negative values, the average distance between any two nearby geodesics moving in the spacetime sourced by quantum fields vacuum would gradually increase at a slow accelerating rate due to the weak parametric resonance effect caused by the fluctuations of the quantum vacuum energy density. In this scenario, the extreme fine tuning of the cosmological constant is not needed. This resolves the cosmological constant problem and provides an explanation to the accelerating expansion of the universe.