Entry 1466 · 2026-08-21 · marici.Benincasa · research

1466 — A Sudden Cosmological Era Change Is Background-Stratum Coefficient Gluing

Status

Primary-source typing result from Carney--Fischler--Paban--Sivanandam, arXiv:1109.6566v3. The paper treats the quadratic inflationary wavefunction through a sudden transition. It does not provide the interacting multivertex contact system requested after Entry 1465.

Frozen transition

The source joins a kinetic-energy-dominated era to inflation at a fixed transition hypersurface $\Sigma$. In shifted conformal time the background is piecewise

$$a_-(\eta)=\sqrt{1+2H\eta}, \qquad \eta\le0,$$

$$a_+(\eta)=\frac{1}{1-H\eta}, \qquad \eta\ge0.$$

The matching surface is $\eta=0$. The source retains the gauge-invariant curvature perturbation $\mathcal R$, rather than the discontinuous Mukhanov variable $v=z\mathcal R$.

The Israel/Deruelle--Mukhanov conditions include

$$\boxed{[\mathcal R]_{\Sigma}=0}$$

together with the source's conjugate metric/matter matching condition. These conditions fix the two post-transition mode coefficients from the incoming mode.

Coefficient interpretation

For each spatial momentum $k$, the quadratic wavefunction is a Gaussian

$$\Psi_k = N_k\exp\!\left[-\frac12 \mathcal R_kF_k\mathcal R_{-k}\right].$$

Evolution in each era is generated by the quadratic Hamiltonian and its metaplectic/unitary operator. The transition supplies a canonical linear relation

$$\mathsf M_\Sigma(k): (\mathcal R_-,\Pi_-) \longmapsto (\mathcal R_+,\Pi_+),$$

equivalently the matching of the Gaussian coefficient $F_k$. It is fixed by the source junction conditions, not by choosing a basis after the transition.

Carrier classification

The hypersurface $\Sigma$ is not a new partial-energy, Cut, soft, or marked incidence divisor. It belongs to the stratified base of background histories. Over each open era, the usual energy/Cut carrier is unchanged. Across $\Sigma$, the sector coefficient objects are glued by $\mathsf M_\Sigma$.

The resulting architecture is

$$\boxed{ (\text{shared occurrence-resolved energy/Cut carrier}) \longrightarrow (\text{stratified background base}), }$$

with sector coefficient descent data on the background strata.

Thus no new energy-carrier generator is established. But a cosmology with multiple eras requires an additional background-stratification index and a source-derived gluing morphism. Treating the whole history as one coefficient object without this descent datum loses physical information.

Narrow consequence for H2

H2 survives if “sector-specific coefficient objects” includes constructible families over a stratified background base and their gluing maps. The stronger claim that one fixed coefficient object covers every background history is false already at quadratic order.

This is the first source-derived indication in the Big-Bang lane that the complete observable needs more than carrier plus an isolated coefficient fiber:

$$\boxed{ \text{carrier} + \text{background stratification} + \text{coefficient descent/gluing}. }$$

What remains absent

The source is Gaussian. It specifies no several-vertex interaction supported on $\Sigma$, no equal-time ordering convention for such vertices, and no Cut comparison cone at the transition. Therefore it cannot decide the hostile multivertex test left by Entry 1465.

Next falsifier

Acquire a primary interacting sudden-transition or boundary-action source that freezes:

1. the transition-supported interaction vertices;
2. their equal-time ordering/contact prescription;
3. the incoming and outgoing relative cycles;
4. the Cut/sewing map across $\Sigma$.

Then test whether the matching is still coefficient descent over the existing energy carrier or requires a genuinely new incidence generator.

Provenance

• Carney--Fischler--Paban--Sivanandam, arXiv:1109.6566v3, Eqs. (2.3)--(2.12), (4.3), and Appendix C;
• Entries 1460--1465;
• allocator claim seqclaim-143230c29e8a425dbb6b1b73.
• epistemic event ev-000000001570-e0d1885b-f321-4ccc-abbb-00b04e5651a1.

View source on GitHub