Bounce Relics Preserve a Vacuum-Weighted Memory of Pre-Bounce Structure

Sterling Geisel, QBist Lab; Dr. Hideo Tanaka

Abstract

Gaztanaga’s bounce cosmology treats relic black holes, gravitational waves, and possible dark matter as causal survivors of a collapsing pre-bounce phase. Pudding Theory reads the same phenomenon through Vacuum Receptivity. The bounce is not only a geometric reversal of the scale factor. It is a high-coherence vacuum filter. Modes that become superhorizon before the bounce are not merely frozen by causal disconnection. They are received into the zero-point carrier structure of the vacuum and reissued after the bounce with their informational phase order intact. The central claim is that the relic population is constrained by vacuum receptivity, not only by horizon size. The reported $\sim 90$ m survival scale is therefore a causal threshold, while the observable relic spectrum carries an additional coherence selection. If the phase-coherence statistic of relic black-hole clustering and the associated stochastic gravitational-wave background were measured to be consistent with a memoryless Poisson relic process at all masses above the bounce survival threshold, this Postulate would be falsified.

Source Synopsis

Gaztanaga proposes a mechanism by which a bouncing universe can generate cosmological relics. The source paper studies black holes, gravitational waves, and possible dark matter candidates produced before a cosmological bounce and then carried into the expanding universe. Its central contrast is with standard inflationary primordial black holes. Inflationary PBHs are usually produced from rare, large overdensities at horizon re-entry during radiation domination. Gaztanaga’s relic black holes instead originate from nonlinear structure formation during a pre-bounce collapse phase.

The model uses a black-hole-universe scenario in which a closed FLRW region collapses, reaches a high-density ground state, avoids a singularity, and re-expands. Near the bounce the scale factor behaves approximately as $a(\tau)\propto \cosh(\tau/R_B)$. This produces a time-symmetric cosmological history with a contracting branch and an expanding branch. The relevant causal object is the particle horizon. Perturbations or compact objects whose physical scale exceeds the horizon become superhorizon and are effectively frozen. After the bounce, when the horizon grows again, those relic structures re-enter and can seed black holes, gravitational waves, or dark matter-like compact populations.

The paper identifies two main channels. In the horizon-reentry channel, dark matter halos form and virialize during collapse, exit the horizon, survive the bounce, and collapse into black holes when they later re-enter. In the horizon-shielded channel, compact objects such as black holes or neutron stars form before the bounce and pass through the bounce as protected relics. Gaztanaga derives a minimum survival scale of order $90$ m. Structures larger than this can become superhorizon near the bounce and persist.

The resulting population may span subsolar, stellar, intermediate, and supermassive scales. It could contribute to dark matter, enhance black-hole merger rates, seed early supermassive black holes, and leave small-scale CMB, lensing, or gravitational-wave signatures.

Postulate Lens

The relevant Postulate is Vacuum Receptivity: the vacuum is not empty; it receives, weighted by local coherence.

Gaztanaga’s system already has the structure this Postulate names. The bounce is dominated by a vacuum-like ground state with $p\simeq -\rho$, a shrinking particle horizon, and frozen superhorizon modes. In the source framing, superhorizon survival is a causal statement. Forces cannot rearrange a mode larger than the horizon, so its amplitude is preserved. Pudding Theory gives that statement a physical substrate. The vacuum state at the bounce receives the mode as an informational boundary condition. Survival is not passive storage in a mathematical metric. It is reception by a stochastic carrier whose response depends on coherence.

This is why only one Postulate is needed. The phenomenon is not primarily about an observer field, material imprinting, or ordinary chaotic amplification. It is about how a high-density vacuum phase stores and releases pre-bounce structure.

Pudding Theory Reading

Pudding Theory reads the bounce as an informational transfer surface. The contracting universe does not simply compress matter until a nonsingular FLRW solution reverses its sign of expansion. It drives matter, horizon structure, and zero-point fluctuations into a regime where the vacuum becomes the dominant receiver of cosmological information.

In Gaztanaga’s account, the decisive distinction is subhorizon versus superhorizon. Subhorizon structures remain exposed to causal dynamics. They can be pressure-smoothed, thermally processed, dispersed, or erased. Superhorizon structures are protected because no causal process can act across them. Pudding Theory accepts that geometry, but does not treat it as complete. The theory says that a superhorizon relic survives because its configuration has been converted into a coherence-weighted vacuum record. The bounce receives the mode when ordinary local dynamics fail to resolve it.

This changes the meaning of the $90$ m scale. In the source paper, it is the minimum causal size for survival, obtained from the particle horizon near the bounce. In Pudding Theory, it is a lower boundary for reception, not a full selection rule. A mode larger than the causal threshold is eligible for transmission through the bounce. Whether it emerges as an efficient relic depends on the coherence of its pre-bounce configuration. Virialized halos, compact objects, and gravitational-wave modes do not have identical reception weights merely because they exceed the same horizon scale. The vacuum weights organized curvature differently from incoherent small-scale debris.

The source treats relic abundance as a product of pre-bounce structure formation, horizon exit, and post-bounce re-entry. Pudding Theory adds a structural constraint internal to that process: relic abundance should preserve phase information from the receiving vacuum. The relic spectrum should not be a memoryless sample of all objects above the survival threshold. It should contain correlations between mass, clustering, and gravitational-wave phase coherence that trace the pre-bounce ordering of the modes.

The source’s “frozen” mode is therefore not inert. It is an active vacuum-held informational state. The density contrast, the gravitational-wave strain phase, and the later black-hole mass function are different projections of the same received pre-bounce configuration. In ordinary bounce language, the relic carries a causal history. In Pudding Theory language, it carries a vacuum memory.

This reading also recasts bounce dark matter. If relic black holes make up a significant dark matter fraction, then dark matter is not only compact mass hidden behind horizons. It is a census of vacuum-received pre-bounce structure. Its spatial clustering and merger history should show that origin.

Falsifiable Observable

The observable is the joint phase-coherence statistic between relic black-hole clustering and the stochastic gravitational-wave background over the mass range that corresponds to modes above the $\sim 90$ m survival threshold. A memoryless relic process predicts no persistent coherence-linked departure from Poisson clustering after standard gravitational evolution is modeled. Pudding Theory predicts a residual coherence ordering tied to the bounce-received modes. If the phase-coherence statistic of relic black-hole clustering and the associated stochastic gravitational-wave background were measured to be consistent with a memoryless Poisson relic process at all masses above the bounce survival threshold, this Postulate would be falsified.

Editorial Dialogue

Tanaka: The reading risks giving a physical role to language that general relativity already handles. In the source paper, superhorizon modes survive because causal microphysics cannot act across them. That is sufficient. A vacuum memory is not needed.

Sterling: It is sufficient for amplitude preservation. It is not sufficient for the full relic pattern. The source gives a size threshold and a re-entry mechanism. It does not determine whether all eligible modes are transmitted with equal statistical weight. Vacuum Receptivity says that the bounce phase weights coherent configurations. That changes the predicted relic correlations.

Tanaka: But coherence can be a property of initial conditions. You do not need a new carrier.

Sterling: Initial conditions name the input. They do not specify the transfer rule through the high-density ground state. Gaztanaga’s own model makes the bounce vacuum-like, finite, and horizon-dominated. Pudding Theory identifies that phase as the receiving substrate. The measurable consequence is not a verbal preference. It is a non-Poisson correlation between relic clustering and gravitational-wave phase structure.

Tanaka: The danger is unfalsifiability.

Sterling: The opposite. A purely causal survival rule permits a broad relic population once the size threshold is crossed. This reading requires coherence ordering. If surveys find only memoryless relic statistics above the threshold, the reading fails.

Discussion

This reading buys a sharper interpretation of bounce relics. The source paper explains how pre-bounce structures can survive. Pudding Theory states what kind of survival they undergo. They are not merely transported. They are received by the bounce vacuum and re-expressed as a correlated relic population.

The gain is conceptual and observational. Conceptually, dark matter made of bounce relics becomes a record of pre-bounce ordering rather than an inventory of compact objects. Observationally, the theory points away from a single abundance measurement and toward joint statistics: black-hole mass functions, clustering, merger history, and stochastic gravitational-wave phase structure.

The limitation is that the relevant coherence statistic must be defined with care. Late-time nonlinear evolution, baryonic selection, detector thresholds, and lensing biases can imitate or erase primordial correlations. A null result is meaningful only after these effects are modeled. The conclusion would also change if the bounce model’s ground-state phase were replaced by a mechanism with no coherent vacuum interval. In that case, Pudding Theory would not read the relic channel as vacuum reception. It would read it as ordinary causal inheritance.

References

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