## Using “Enhanced Quantization” to Bound the Cosmological Constant, (For a Bound-on Graviton Mass), by Comparing Two Action Integrals(one Being from General Relativity) at the Start of Inflation

**Authors:** Andrew Beckwith

We are looking at comparison of two action integrals and we identify the Lagrangian multiplier as setting up a constraint equation (on cosmological expansion). This is a direct result of the fourth equation of our manuscript which unconventionally compares the action integral of General relativity with the second derived action integral, which then permits equation 5, which is a bound on the Cosmological constant. What we have done is to replace the Hamber Quantum gravity reference-based action integral with a result from John Klauder’s “Enhanced Quantization” . In doing so, with Padamabhan’s treatment of the inflaton, we then initiate an explicit bound upon the cosmological constant. The other approximation is to use the inflaton results and conflate them with John Klauder’s Action principle for a way to, if we have the idea of a potential well, generalized by Klauder, with a wall of space time in the Pre Planckian-regime to ask what bounds the Cosmological constant prior to inflation. And, get an upper bound on the mass of a graviton. We conclude with a redo of a multiverse version of the Penrose cyclic conformal cosmology to show how this mass of a heavy graviton is consistent from cycle to cycle. All this is possible due to equation 4. And we compare all this with results of reference [1] in the conclusion.

**Comments:** 10 Pages. For possible inclusion into FFP 15, pending acceptance by Jesus Cancier, of Alicante, Spain, and the FFP 15 committee

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### Submission history

[v1] 2018-02-21 22:20:41

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