Microscopic origin of Einstein's field equations and the raison d'être for a positive cosmological constant

In the paradigm of effective field theory, one hierarchically obtains action Aeff[q,⋯] for some low(er) energy degrees freedom q, by integrating out high(er) ξ, in a path integral, based on an A[q,ξ,⋯]. We show how can integrate vector va A[Γ,v,⋯] and obtain Aeff[Γ,⋯] which, variation with respect to connection Γ, leads Einstein's equations metric compatible connection. The derivation predicts non-zero, positive, cosmological constant, which arises as integration constant. Euclidean A[Γ,v,⋯], has interpretation heat density null surfaces, when translated into Lorentzian spacetime. be interpreted analogue microscopic hosted any surface. Several implications this approach are discussed.