How the huge energy of quantum vacuum gravitates to drive the slow accelerating expansion of the Universe

We investigate the gravitational property of the quantum vacuum by treating its large energy density predicted by quantum field theory seriously and assuming that it does gravitate to obey the equivalence principle of general relativity. We find that the quantum vacuum would gravitate differently from what people previously thought. The consequence of this difference is an accelerating universe with a small Hubble expansion rate $H\propto \mathrm{\Lambda }{e}^{-\beta \sqrt{G}\mathrm{\Lambda }}\to 0$ instead of the previous prediction $H=\sqrt{8\pi G{\rho }^{\mathrm{vac}}/3}\propto \sqrt{G}{\mathrm{\Lambda }}^2\to \infty$ which was unbounded, as the high energy cutoff $\mathrm{\Lambda }$ is taken to infinity. In this sense, at least the “old” cosmological constant problem would be resolved. Moreover, it gives the observed slow rate of the accelerating expansion as $\mathrm{\Lambda }$ is taken to be some large value of the order of Planck energy or higher. This result suggests that there is no necessity to introduce the cosmological constant, which is required to be fine tuned to an accuracy of ${10}^{-120}$, or other forms of dark energy, which are required to have peculiar negative pressure, to explain the observed accelerating expansion of the Universe.

Figure 1

Plot of the expectation value of the square of the energy density difference as a function of spacial separation $\mathrm{\Lambda }\mathrm{\Delta }x$.

Figure 2

Plot of the normalized covariance $\chi$ as a function of temporal separation $\mathrm{\Lambda }\mathrm{\Delta }t$.

Figure 3

Plot of the power spectrum density of the varying part of ${\mathrm{\Omega }}^2(t,\mathbf{0})$ (except for the constant ${\mathrm{\Omega }}_0^2$ part).

Figure 4

Numeric result for $\log |a_o(t)|$ for a single real massless scalar field. It shows that as $\mathrm{\Lambda }$ increases, the slope of $\log |a_o(t)|$ decreases.

Figure 5

Numeric result for $\log |a_o(t)|$ when two scalar fields are present and it shows that as $\mathrm{\Lambda }$ increases, the slope of $\log |a_o(t)|$ decreases.

Figure 6

The plot of $\log (H/\mathrm{\Lambda })$ over $\mathrm{\Lambda }$. The fitting result shows that $\alpha =e^{4.6}\approx 100$ and $\beta =0.12$ in this two-field case.

Figure 7

Plot of correlation coefficient ${\rho }_{x,x^{\prime }}$ as a function of time separation $\mathrm{\Lambda }\mathrm{\Delta }t$ in the case $\mathrm{\Delta }x=0$.

Figure 8

Plot of correlation coefficient ${\rho }_{x,x^{\prime }}$ as a function of spatial separation $\mathrm{\Lambda }\mathrm{\Delta }x$ in the case $\mathrm{\Delta }t=0$.