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By Cosmological constant here I mean the constant as would be predicted by the vacuum. The one and the same that if compared to the actual expansion of the universe it is off by a factor of $10^{120}$. I am curious since Dirac's remarkable equation does predict a considerable number of elementary particles I am wondering if it says anything about space time or it's expansion. They may be disparate concepts in this context.

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No: the cosmological constant is not predicted by any known physical model. In the context of particle physics, $\Lambda$ is one of the multiple free parameters of the Standard Model. As this model does not include gravitation, it is customary to set $\Lambda=0$, because the origin of energies is arbitrary anyway (in the absence of gravity). The condition $\Lambda=0$ is in fact a renormalisation condition, and it effectively eliminates all vacuum diagrams.

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