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

Based on the Veneziano ghost theory of QCD, we estimate the cosmological constant $\mathrm{\Lambda }$, which is related to the vacuum energy density, ${\rho }_{\mathrm{\Lambda }}$, by $\mathrm{\Lambda }=8\pi G{\rho }_{\mathrm{\Lambda }}$. In the recent Veneziano ghost theory ${\rho }_{\mathrm{\Lambda }}$ 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 $<0\mathrm{\mid }:\bar{q}q:\mathrm{\mid }0>\simeq -(235MeV{)}^3$, the generally accepted value. The quark current mass is $m_q\simeq$ 4.0 Mev. This gives the same result for ${\rho }_{\mathrm{\Lambda }}$ as found by previous authors, which is somewhat larger than the observed value. However, when we make use of the nonlocal quark condensate, $<0\mathrm{\mid }:\bar{q}(x)q(0):\mathrm{\mid }0>=g(x)<0\mathrm{\mid }:\bar{q}q:\mathrm{\mid }0>$, with g(x) estimated from our previous work, we find $\mathrm{\Lambda }$ is in a good agreement with the observations.