Calculating Vacuum Energy as a Possible Explanation of the Dark Energy

Abstract: We carried out a study of the properties of the $\lambda \phi^4$ field solutions. By constructing Gaussian wave packets to calculate the $S$ matrix, we show that the probability of the vacuum unbroken state transfers to the broken state is about $10^{-52}$. After adding this probability restriction condition as modulation factor in the summation of vacuum energy, we thus get a result that the vacuum energy density is about $10^{-47}GeV^4$, which is exact same as the observed dark energy density value, and maybe served as a possible explanation of the dark energy. Also our result shows that the vacuum energy density is proportional to the square of the universe's age, which fits the Dirac large numbers hypothesis.