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

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:${\rho }_{\Lambda }=\frac{2N_{f}H}{m_{{\eta }^{\prime }}}c|m_q<0|:\bar{q}q:|0>|$. By solving Dyson-Schwinger Equations for a dressed quark propagator, we found the local quark condensate $<0|:\bar{q}q:|0>\simeq -(235MeV{)}^3$, 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.

Comments: 12 pages, no figures. arXiv admin note: text overlap with arXiv:nucl-th/0404015, arXiv:1010.1339, arXiv:0906.2162