Reformulation of the Cosmological Constant Problem

The standard formulation of the cosmological constant problem is based on one critical assumption—the spacetime is homogeneous and isotropic, which is true only on cosmological scales. However, this problem is caused by extremely small scale (Planck scale) quantum fluctuations and, at that scale, the spacetime is highly inhomogeneous and anisotropic. The homogeneous Friedmann-Lemaître-Robertson-Walker metric used in the standard formulation is inadequate to describe such small scale dynamics of the spacetime. In this Letter, we reformulate the cosmological constant problem by using a general inhomogeneous metric. The fine-tuning problem does not arise in the reformulation since the large gravitational effect of the quantum vacuum is hidden by small scale spacetime fluctuations. The stress energy tensor fluctuations of the quantum fields vacuum could serve as “dark energy” to drive the accelerating expansion of the Universe through a weak parametric resonance effect.

Figure 1

Schematic plots of the oscillations of the local scale factor $a$, the local determinant $h=a^6$. As $a$ goes across 0, $h$ decreases continuously to 0 and then increases back to positive values. The amplitude of $a$ grows exponentially with a tiny exponent $H=\alpha \mathrm{\Lambda }{e}^{-\beta (\sqrt{-{\lambda }_B}/\mathrm{\Lambda })}$ (Eq. (29)) which gives an accelerating universe.