A Remnant Inside the Bubble

What a piece of the previous cycle would look like if we could see one, and why it is not a shell at z = 1.588

Warning

Speculative!

The cyclic picture in A Universe That Boils has our bubble nucleating in a medium that still carries material from earlier cycles (\mathcal{B}^{-1}, \mathcal{B}^{-2}, …). An earlier version of this paper claimed to see that material: a “moraine crust” that our bubble wall was supposed to have crossed at z \approx 2.2–0.5, imprinted on the DESI data as an undular bore. That claim is retracted. This page records why. It then asks what a previous-cycle remnant would look like in a version of the picture that hangs together, and how one would look for it.

What was claimed

The moraine was pictured as a shell of organized remnant vorticity around our bubble’s nucleation point. The bubble’s expansion was described by a Mach number M(z) = H(z)\,d_\text{proper}(z)/c, which crosses unity at z = 1.588 for Planck parameters. That crossing was presented as a zero-parameter prediction of where the flow went from supercritical to subcritical. A 15-knot spline fit to DESI BAO and the Jia H_0(z) reconstruction was read as the three-piece anatomy of a transcritical dispersive shock: a soliton at z \approx 2.3, a wake at 2.0, a node at 1.6, and a chirped downstream train toward z = 0.

Why it fails

The geometry.

  1. M = 1 is the turnover of the angular-diameter distance. H\,d_p = c is algebraically d(d_p)/dz = 0, the maximum of d_A, at z \approx 1.59. Every comoving observer finds it in their own sky. It describes our past light cone, not the medium.
  2. The Hubble flow has no local Mach number. The Hubble flow is the substrate’s own bulk flow (Spacetime Dynamics). Material at any redshift is at rest relative to its local substrate. Its recession speed relative to us depends on the observer, and a Mach number has to be local.
  3. A physical shell has one centre. It would sit on our Hubble sphere only if we were at the nucleation point. Otherwise it would appear at different redshifts in different directions. A very large bubble does not make an observer equidistant from its shell. It only makes the anisotropy small when the observer’s offset is small compared with the shell’s radius.
  4. The inflation chapter has no wall left to hit anything. Inflation ends when the bubble wall exits our past light cone (Spacetime Dynamics § The number of e-foldings). After that, everything in our observable volume has been inside the bubble the whole time. No wall is available to strike a remnant at z \approx 2.2.

The data (detail).

  • Too many knots. Fifteen spline knots on 18 data points leaves about three degrees of freedom.
  • The key features sit in a data gap. The soliton, wake and node knots fall between the last QSO point (z = 1.484) and Lyα (z = 2.33), where DESI has no BAO points.
  • The two data sets overlap. The Jia reconstruction is built from DESI with Pantheon+ calibration, so the joint fit counts DESI twice.
  • BAO alone prefers \LambdaCDM. DESI BAO by itself drives the crust amplitude to zero.

The homogeneous part of the dark-energy story does not need any of this. It is in Dark Energy as a Disequilibrium Residual. The homogeneous clock offered there in place of the moraine has since been fitted and excluded (§ The n_\text{tr} clock).

A consistent remnant

Take the inflation chapter at its word. The bubble nucleated at roughly the coherence-length scale and inflated by \sim 60 e-folds, and its wall left our past light cone when inflation ended. Any remnant material from \mathcal{B}^{-1} that sat in the volume the bubble swept over during inflation was engulfed and stretched along with our patch. Afterwards it is ordinary comoving material: at rest in its local substrate, diluting with the Hubble flow, at some position that has no reason to be centred on us.

Where should we expect to find one? Inflation dilutes whatever it swallows. Material engulfed with \Delta N e-folds still to go has its number density reduced by e^{-3\Delta N}. Only material swallowed in the last few e-folds survives at any appreciable density. By then the wall is close to where it ends up, which the e-fold count puts near the present Hubble scale (N_* \approx \ln(c/H_0\xi)). So the geometry favours remnants that are distant, a sizeable fraction of a Hubble radius away and seen at intermediate-to-high redshift, over nearby ones. A remnant large enough to contain us, such as a local void, needs either an early engulfment that survived heavy dilution or a very large parent structure. Individual nearby objects (the erratics reading of interstellar visitors) are the most strained case. This is a rough argument, not a calculation; the survival fraction is part of WIP-39.

What would such a remnant do?

  • A region where the dark-matter density differs. In the substrate, dark matter is the medium’s mean density. An engulfed remnant is a region where that density was, and may still be, offset from the cosmic mean: denser if the remnant carried extra organized vorticity, sparser if it was a depleted wake. Its mixing with the new cycle’s contents would be slow, set by the same boundary physics that governs every other interface in the framework.
  • Anisotropy, not a redshift shell. A remnant of comoving radius R at comoving distance D from us subtends a disk of angular radius \approx \arcsin(R/D) when we are outside it. If we sit inside it off-centre, it shows up as a dipole in distances and in inferred H_0. An isotropic feature at one redshift in every direction is the one signature it cannot give, unless we happen to sit at its centre.
  • A local H_0 offset if we are inside an underdensity. A large local underdensity expands faster than the mean, so supernovae within it read a higher H_0. This is the inhomogeneous (LTB) route to the Hubble tension, and it needs an inhomogeneous fit, not the Friedmann equation.
  • A shifted MOND scale (framework-specific, and the sharpest). In Galactic Dynamics § Why now?, a_0 tracks the diluting mean density. A region whose mean dark-matter density differs by a fraction \delta would have a_0 shifted by about \delta/2. Galaxies inside a remnant and galaxies outside it would sit on slightly different radial-acceleration relations. The observed tightness of the RAR in nearby samples bounds \delta locally. A comparison across widely separated sky regions at larger distances does not yet exist.

The erratics chapter is the small-scale end of the same idea. It looks for individual objects whose composition marks them as survivors of \mathcal{B}^{-1}, rather than for a large-scale density offset.

How to look

The established literature closest to this is not dark-energy fitting but searches for anisotropy:

  1. Hemisphere splits. Split DESI BAO and the supernova samples (Pantheon+, DES-SN5YR) by sky hemisphere along a grid of axes, and look for a coherent offset in distances or inferred H_0 beyond the kinematic dipole. A remnant predicts one axis; noise predicts none. This is WIP-39.
  2. The dipole anomalies. The quasar number-count dipole exceeds the kinematic expectation from our CMB-frame motion, the bulk flow refuses to decay, and the cluster H_0 sky leans (The Two Dipoles). If an engulfed remnant is real, its axis should line up with at least one of these.
  3. Bubble-collision searches. A collision with another bubble shows up as a disk in the CMB, and searches have been run (Aguirre & Johnson 2011; Feeney et al. 2011).1 An engulfed remnant is not a collision, but the disk statistics and the existing limits are the right template. Which of those limits carry over is part of the task.
  4. The KBC void. Keenan, Barger & Cowie report a local underdensity of a few hundred Mpc.2 Haslbauer, Banik & Kroupa argue that such a void, grown under Milgromian dynamics, can account for the Hubble tension where \LambdaCDM cannot.3 A framework that already predicts a_0 = c\sqrt{G\rho_\text{DM}} is a natural home for that argument. An engulfed remnant is one candidate origin for the void.
  5. Regional a_0. Compare the fitted MOND scale in rotation-curve samples from well-separated sky regions and distances. A remnant predicts a coherent regional offset; the homogeneous picture predicts none.

What would retire this page too: hemisphere splits showing no coherent axis at the percent level, dipole anomalies that resolve into systematics, and a regionally uniform a_0. Any one of these makes an engulfed remnant unobservable in practice, and the cyclic picture would then rest on its theoretical motivation alone.

Footnotes

  1. Aguirre, A. & Johnson, M.C., “A status report on the observability of cosmic bubble collisions,” Rep. Prog. Phys. 74, 074901 (2011), arXiv:0908.4105. Feeney, S.M., Johnson, M.C., Mortlock, D.J. & Peiris, H.V., “First observational tests of eternal inflation,” Phys. Rev. Lett. 107, 071301 (2011), arXiv:1012.1995.↩︎

  2. Keenan, R.C., Barger, A.J. & Cowie, L.L., “Evidence for a ~300 Megaparsec Scale Under-density in the Local Galaxy Distribution,” ApJ 775, 62 (2013), arXiv:1304.2884.↩︎

  3. Haslbauer, M., Banik, I. & Kroupa, P., “The KBC void and Hubble tension contradict ΛCDM on a Gpc scale — Milgromian dynamics as a possible solution,” MNRAS 499, 2845 (2020), arXiv:2009.11292.↩︎