Prediction of Cosmological Constant $\Lambda$ In Veneziano Ghost Theory of QCD$^{*}$

Abstract

Based on the Veneziano ghost theory of QCD, we estimate the cosmological constant $\Lambda$, which is related to the vacuum energy density, $\rho_{\Lambda}$, by $\Lambda = 8\pi G \rho_{\Lambda}$. In the recent Veneziano ghost theory $\rho_{\Lambda}$ is given by the absolute value of the product of the local quark condensate and quark current mass:$\rho_{\Lambda} = \frac{2N_{f}H}{m_{\eta'}}c |m_{q}<0|:\bar{q}q:|0>|$. By solving Dyson-Schwinger Equations for a dressed quark propagator, we found the local quark condensate $<0|:\bar{q}q:|0> \simeq -(235 MeV)^{3}$, the generally accepted value. The quark current mass is $m_{q} \simeq$ 4.0 Mev. This gives the same result for $\rho_{\Lambda}$ as found by previous authors, which is somewhat larger than the observed value. However, when we make use of the nonlocal quark condensate, $<0|:\bar{q}(x)q(0):|0>= g(x)<0|:\bar{q}q:|0>$, with g(x) estimated from our previous work, we find $\Lambda$ is in a good agreement with the observations.