Toward the Emergence of Continuum Spacetime in Causal Set Theory

In causal set theory (CST), the continuum spacetime manifold is postulated to be a low-energy approximation of a more fundamental discrete sub-structure of a locally finite partial ordered set, called as the causal set. In a collection of all n-element causal set Ωn with large n, almost all causal sets are non-manifold-like, i.e., the one that cannot be approximated by a Lorentzian manifold of any dimension. These non-manifold-like causal sets have to be suppressed by the appropriate CST dynamics. This chapter contains a discussion primarily based on the work of Loomis and Carlip and that of Mathur, Singh and Surya on the suppression of a particular type non-manifold-like causal sets, which dominates Ωn, in the causal set partition function (path-sum) by a simplified choice of causal set action. On these causal sets this choice is equivalent to the discrete Einstein–Hilbert action, and hence, such causal sets are suppressed in the full causal set quantum partition function.