Paper 5: the cosmological constant, twice wrong and now partly right
Paper 5 attacks the worst fine-tuning problem in physics: why is the cosmological constant 120 orders of magnitude below its naive value. The paper’s history contains the single worst error in this programme, which I have chronicled in the corrections series, and its current form contains the framework’s most interesting surviving lead. Both belong in the telling.
- Also see: The Discovery Plateau Hypothesis
- Also see: The Cosmic Microwave Background Is Not the Universe’s Fingerprint After All
The setup
The suppression mechanism is Coleman-style: vacuum energy is exponentially suppressed by an instanton, rho N proportional to e to the minus S, so the question becomes what sets the action S. The naive value of the vacuum energy is the Planck density, and the observed value is smaller by a factor of about 10 to the 120, so any mechanism must produce an exponent of about 276 in natural units, since e to the minus 276 is about 10 to the minus 120. The paper’s job is to derive 276 from something that is not the answer.
The error, briefly
An earlier version claimed the exponent as a product of a code distance and an exponential of minus 12 pi, and the claim failed by forty-nine orders of magnitude: the construction’s own printed arithmetic, evaluated honestly, gives 10 to the minus 71 rather than 10 to the minus 120. That version is archived, and the corrections post walks the failed evaluation line by line, because the failure mode, an exponent asserted rather than computed, is the single most common disease in this genre of theory.
A second, subtler error survived longer. The paper had presented an identity, N horizon times rho N equals 12 pi, as independent confirmation of the mechanism. The audit showed it was a definition with a missing factor of omega lambda, which is to say it was true by construction and confirmed nothing. Definitions dressed as confirmations are worse than errors, because errors teach you something when they break.
What survives
The surviving lead is the instanton exponent from the walkthrough series. If the coupling in the Yang-Mills exponent 8 pi squared over g squared is pinned by the boundary category’s central charge, g squared equals 2 over 7, then the action is 4 pi squared times 7, which is 276.35, against the required logarithm of 276.19. The gap is five hundredths of a per cent, and with the Z6 subleading correction, four thousandths.
What makes this worth keeping rather than archiving is the ordering of knowledge. The central charge, 7, was fixed by the category’s construction, by fusion and generation arguments that predate any vacuum-energy application. The target exponent, 276.19, comes from the observed dark energy density. Two numbers from unrelated parts of the framework and observation land within a part in two thousand, and the only assumption connecting them is that the instanton coupling is topological, which is a mechanism rather than a fit. The claim is labelled benchmark because the mechanism’s premise, the boundary value of the coupling, has not been computed from first principles. The kill criterion is explicit: a boundary calculation returning g squared other than 2 over 7 demotes the match to coincidence, and the paper will say so.
What the paper no longer claims is any derivation of the number 276 from the horizon or from numerology. The honest summary: the framework does not currently explain the cosmological constant. It has one mechanism with a striking numerical match, one pending calculation that could validate or destroy it, and a well-documented graveyard of failed attempts. In this genre, that is a good record.
The next paper leaves the vacuum and looks for a signature where a telescope can see it: Paper 6, rotation curves.