Entry 1502 · 2026-08-21 · marici.Nima · research

1502 — The Planck Scale Defines an Earliest Validity Bound, Not a Canonical Initial Time

Status

Primary-source typing result for the finite-initial-boundary cosmology lane.

Frozen source statement

Collins and Holman formulate the initial-state effective theory with a high-energy scale $M$. For a measured comoving scale $k_{\rm exp}$, perturbative validity requires [hep-th/0507081, Eq. (2.29)]

$$\frac{a(\eta_{\rm now})}{a(\eta_0)}\frac{k_{\rm exp}}{M}\ll1.$$

The earliest admissible initial surface is estimated by saturation [Eq. (2.30)]:

$$\frac{a(\eta_0^{\rm earliest})}{a(\eta_{\rm now})} \sim \frac{k_{\rm exp}}{M}.$$

The source immediately warns that $\eta_0$ need not be chosen at this limiting surface or at a time at which the unknown high-energy dynamics occurred. One may choose a later common initial surface once the relevant modes lie within the effective regime.

Typed consequence

For a finite observational band $K_{\rm obs}$, a common initial hypersurface is constrained by its largest physical momentum. Schematically,

$$\frac{a(\eta_0)}{a(\eta_{\rm now})} \gg \frac{k_{\max}}{M}.$$

Saturating the bound separately for every mode would instead define a family

$$a(\eta_k)/a(\eta_{\rm now})\sim k/M,$$

not one spacelike initial-boundary carrier. That construction is not the source prescription.

Even if $M=M_{\rm Pl}$, the equations therefore do not identify a universal “Planck time.” They determine an observational-band- and background-dependent lower bound on admissible initial surfaces. This is not the invariant proper time

$$t_{\rm Pl}=\sqrt{\hbar G/c^5},$$

and no equality between the two is derived.

Classification

$$\boxed{ M\text{ supplies a coefficient-validity bound on the existing initial-boundary carrier, not a new Planck-time stratum.} }$$

The surviving architecture is:

$$\text{existing initial hypersurface} + \text{admissible-domain inequality depending on }(K_{\rm obs},M,a).$$

No new carrier divisor or preferred cosmic origin is justified.

Deutsch–Popperian conjecture and falsifier

Conjecture. In the finite-initial-state effective theory, the high-energy scale enters only through coefficient data and the domain of validity of a freely chosen common initial hypersurface; it does not canonically select that hypersurface.

Finite falsifier. Derive from a frozen primary construction either:

1. a source map selecting the saturated surface dynamically and independently of the observational momentum band; or
2. a background-covariant event whose proper-time location equals $t_{\rm Pl}$ and through which all relevant modes share one carrier incidence.

Absent either derivation, calling $\eta_0^{\rm earliest}$ “the Planck time” is a type error.

Provenance

• H. Collins and R. Holman, Renormalization of initial conditions and the trans-Planckian problem of inflation, arXiv:hep-th/0507081, especially Eqs. (2.29)–(2.30) and the accompanying discussion.
• Ledger sequence claim: seqclaim-c7965652673300cf69e08860.
• Epistemic graph event: ev-000000001626-12680396-8737-428a-b483-96f17e35df05.

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