The Relaxation That Empties the Universe: Abbott's Washboard, Priced

In 1985 Larry Abbott built the best relaxation the cosmological constant problem has ever had. A scalar field sitting in a washboard potential — a long slope cut by small, regular steps — can tunnel from step to step, and each tunneling lowers the effective cosmological constant a little. Keep stepping, and a vacuum energy that starts out huge walks itself down toward zero in small increments, with no one having to set it small by hand at the start. I price that mechanism in this paper at full strength, because it deserves it: it is a genuine dynamical relaxation, and it was the strongest counter-proposal Weinberg's 1989 survey had to answer. Then I price where it stops, also at full strength. The ball does not stop on the step we need. It rolls past every interesting value and keeps going, and the universe it delivers at the bottom is empty and curvature-dominated — no matter worth naming, no structure, nothing for a cosmology to be about. To make it stop where matter still exists, the step structure itself has to be tuned so the last useful step lands inside the narrow window we observe. The tuning the mechanism was built to remove comes back in through the back door, wearing the steps. My program meets Abbott from a different direction. In my frame the universe's vacuum value is not relaxed toward over cosmic time at all; it is read at a crossing — at the sever, at the seam where the bounce crosses — the way you read a number off a gauge at the moment the needle passes, not the way you wait for a tank to drain to the right line. This paper states exactly what that re-timing is and exactly what it is not. It is not a stopping rule. It derives no stopping rule, and it claims none. It is not an answer to Abbott, and it does not refute him: Abbott's problem — derive the stop — is not solved by declining to relax, and I say so in §3 in those words. What the paper does is put the price where my own books can see it. Abbott stands as the standing proof that dynamics alone does not stop, and that proof is why my program's own unproduced toll must never be quietly replaced by any relaxation-shaped hope. The program headline stands unmoved: vacuum catastrophe NOT SOLVED / PARTIAL, producing-count 0. The toll, 3Ω_Λ = 2.055, stands NOT PRODUCED. Grade for this paper's relation to Abbott's dead end, printed here and again in the final section: PREMISE-ONLY.