Creating a (Quantum?) Constraint, in Pre Planckian Space-Time Early Universe via the Einstein Cosmological Constant in a One to One and Onto Comparison between Two Action Integrals

We are looking at comparison of two action integrals and we identify the Lagrangian multiplier as setting up a constraint equation (on cosmological expansion). Two action integrals, one which is connected with quantum gravity is called equivalent to another action integral, and the 2nd action integral has a Lagrangian multiplier in it. Using the idea of a Lagrangian multiplier as a constraint equation, we draw our conclusions in a 1 to 1 and onto assumed equivalence between the two action integrals. The viability of the 1 to 1 and onto linkage between the two action integrals is open to question, but if this procedure is legitimate, the conclusions so assumed are fundamentally important.