Your clarification removes the two misunderstandings I was most concerned about. I would now describe the core as:

Mc  →  phase transition→Σ(t) expanding→pre-existing compact objects engulfed→nfossil(M,r,z).M_c\; \rightarrow\; \text{phase transition} \rightarrow \Sigma(t)\text{ expanding} \rightarrow \text{pre-existing compact objects engulfed} \rightarrow n_{\rm fossil}(M,r,z).

And I agree with your name. Critical-Mass Phase-Front Cosmology is better than putting “fossil” in the title at this stage; “fossil” is a prediction, whereas the phase-front construction is the dynamical hypothesis.

There is one remaining technical wording issue I would change: a black-hole event horizon is not a material surface that simply changes phase when the front passes it. For the calculation, treat each fossil as a local compact spacetime perturbation with a trapped/apparent horizon, embedded in a cosmological background whose phase changes across the front. Then require that the front scale and curvature are large compared with the hole, so the hole survives as a local object. This is much cleaner mathematically. Existing work on compact objects embedded in FLRW/McVittie-type spacetimes and on black-hole/domain-wall interactions gives you relevant pieces of that formalism.

1. Does the weak-background skeleton already clash with CMB, BAO, SNe or kSZ?

Not obviously. This is the encouraging part.

There is a crucial distinction between

radial metric/density inhomogeneity\boxed{\text{radial metric/density inhomogeneity}}

and

radial variation in the abundance of a subdominant tracer.\boxed{\text{radial variation in the abundance of a subdominant tracer}}.

The severe existing LTB constraints mostly apply to the first.

For example, Camarena, Marra, Sakr and Clarkson fitted a spherically symmetric ΛLTB perturbation to CMB, BAO, SNe Ia, local H0H_0, cosmic chronometers, yy-distortion and kSZ. They found that on scales larger than roughly 100 Mpc, the allowed effective non-Copernican density contrast is only around the percent level.

That does not say that your fossil occupation contrast must be one percent or less.

Suppose the fossil black holes make up only a fraction fBHf_{\rm BH} of the matter density, and their number-density contrast is bfossil(r)b_{\rm fossil}(r). Roughly,

δρfossilρm∼fBH bfossil(r).\frac{\delta\rho_{\rm fossil}}{\rho_m} \sim f_{\rm BH}\,b_{\rm fossil}(r).

So you can have, schematically,

bfossil∼1b_{\rm fossil}\sim 1

or even much larger, while still having

δρtotal≪1\delta\rho_{\rm total}\ll1

provided fBHf_{\rm BH} is small enough.

That is the loophole that makes the main hypothesis interesting.

CMB

If the smooth background is essentially FLRW, then the enormous body of CMB constraints on radial expansion profiles does not automatically kill the fossil gradient.

Planck finds the primary CMB statistically very close to the standard nearly homogeneous/isotropic picture, although large-angle anomalies remain.

Your fossil field therefore has to satisfy a weaker condition:

Its contribution to the metric, gravitational potential, lensing and ionization history must remain small enough that the CMB stays close to ΛCDM.

But there is a second CMB constraint you should take seriously: accretion onto the fossils.

Studies of primordial massive black holes find potentially strong CMB constraints because accretion can inject radiation into the primordial plasma. A 2025 analysis specifically considered CMB μ\mu-distortions in the 104 ⁣− ⁣1011M⊙10^4\!-\!10^{11}M_\odot range and found that these can strongly constrain the abundance of massive primordial black holes considered as SMBH seeds. The exact limit depends on the accretion model.

That gives you an important distinction:

radial fossil counting is not the dangerous CMB effect; fossil accretion might be.

So your first paper should explicitly have a parameter such as

ffossilf_{\rm fossil}

and, separately, an accretion history.

Do not silently assume that “small number density” makes the CMB irrelevant.

BAO

Here I see no immediate collision, provided you really mean that the background metric stays close to FLRW.

DESI DR2 now gives rather sharp radial and transverse BAO information. The official DESI material explicitly separates the isotropic distance information from the Alcock–Paczynski anisotropy, while the current DR2 programme combines galaxy/QSO/Lyα measurements over a substantial redshift range.

A genuine radial expansion model has to satisfy

H∥(z,r)≈H⊥(z,r)H_\parallel(z,r)\approx H_\perp(z,r)

to high accuracy over the scales actually probed.

Your main model does not require a large difference between those quantities.

That is a major conceptual improvement over the old “giant void replaces dark energy” construction.

The fossil field can instead behave like a peculiar tracer:

nfossil=nfossil(r,z),n_{\rm fossil}=n_{\rm fossil}(r,z),

while

H∥≃H⊥≃HFLRW.H_\parallel\simeq H_\perp\simeq H_{\rm FLRW}.

Then BAO largely sees the second equation, while your distinctive prediction lives in the first.

So I would presently rate BAO as:

constraint on the model, not an existing exclusion.

Supernovae

Same basic answer.

SNe constrain the distance-redshift relation, so a substantial radial modification of the metric is dangerous. But a radial change in the abundance of rare compact objects, with negligible effect on the background expansion, does not directly change the SN Hubble diagram.

There is extensive literature showing that spherical inhomogeneous models can produce quite nontrivial SN distance relations, which is exactly why SNe alone are inadequate to distinguish such models. The hard constraint comes from combining them with CMB/BAO/kSZ and other observables.

Thus:

fossil gradient⇏SN conflict\boxed{\text{fossil gradient}\not\Rightarrow\text{SN conflict}}

unless the fossil mass actually generates a significant large-scale metric perturbation.

kSZ

This is where your separation into modules pays off.

The usual kSZ objection to LTB/void models arises because the background expansion itself is radially different. Galaxy clusters then acquire large coherent velocities relative to the CMB frame. That is exactly what made kSZ so constraining for void models.

There is even a very recent technical literature using LTB/off-centre models to connect expansion-rate anisotropies with observable peculiar motions.

But your main model can instead have

vpeculiarlarge−scale≈vFLRWv_{\rm peculiar}^{\rm large-scale}\approx v_{\rm FLRW}

while

nfossil(r)≠const.n_{\rm fossil}(r)\neq{\rm const}.

Then there is no large kSZ signal generated simply by the fossil gradient.

So the answer is:

a fossil-only radial field is not subject to the classic kSZ death blow.

Your proposed acceleration side-module is.

And that distinction should be absolutely explicit in the paper.

2. The condition you really need

I would make this one of the model's formal assumptions:

∣hμν∣large scale≪1\boxed{ |h_{\mu\nu}|_{\rm large\,scale}\ll1 }

with

gμν=gμνFLRW+hμνfossil+hμνfront.g_{\mu\nu} = g_{\mu\nu}^{\rm FLRW} + h_{\mu\nu}^{\rm fossil} + h_{\mu\nu}^{\rm front}.

Locally, around each black hole,

∣hμνfossil∣≪̸1;|h_{\mu\nu}^{\rm fossil}|\not\ll1;

otherwise it would not be a black hole.

But after coarse-graining over scales much larger than the inter-hole separation,

∣⟨hμν⟩∣≪1.|\langle h_{\mu\nu}\rangle|\ll1.

That is the mathematically meaningful interpretation of:

“The metric is close to FLRW, while the fossil population is radially structured.”

It is not possible for the exact metric to be FLRW while the same stress-energy tensor has a large radial BH-density contrast. Einstein's equations do not allow that. But an almost-FLRW coarse-grained metric plus a strongly biased, subdominant tracer population absolutely is a sensible possibility.

That distinction should probably become a sentence in the abstract.

3. B is now much more defensible

I think your B formulation can be put into a clean hierarchy:

Background

gμνout⟶gμνing_{\mu\nu}^{\rm out} \quad\longrightarrow\quad g_{\mu\nu}^{\rm in}

across an expanding spherical worldtube

Σ.\Sigma.

Trigger

At nucleation,

MMS(core)=Mc.M_{\rm MS}(\text{core})=M_c.

Front

RΣ=RΣ(τ)R_\Sigma=R_\Sigma(\tau)

sweeps outward.

Fossil

For each pre-existing hole,

Mi<Mc,M_i<M_c,

with worldline xiμ(τ)x_i^\mu(\tau).

When

xiμ∩Σ≠∅,x_i^\mu\cap\Sigma\neq\varnothing,

the hole becomes part of the interior cosmological phase.

Its mass is not supplied by the front. It was already there.

The front only changes its environment/background.

That is conceptually sound.

But now add the survival condition:

rh,i≪LΣr_{h,i}\ll L_\Sigma

where LΣL_\Sigma is the relevant curvature/thickness scale of the front.

And also require that the crossing does not dump enough energy into the hole to push it over McM_c:

ΔMi≪Mc−Mi.\Delta M_i\ll M_c-M_i.

That last equation is important.

It means the phrase “subcritical fossil survives engulfment” is not merely verbal. It becomes an actual inequality.

That is precisely the sort of condition a numerical paper could test.

There is relevant precedent for studying gravitational domain walls and phase boundaries interacting with black holes, though those models are not your cosmology.

4. I would make the fossil prediction more specific

I would not merely predict

nfossil(r)↑.n_{\rm fossil}(r)\uparrow.

I would predict the entire conditional mass function:

Φ(MBH∣r,z)\boxed{ \Phi(M_{\rm BH}\mid r,z) }

and allow both abundance and mass distribution to change with radius.

For example,

Φ(M,r,z)=Φ0(M,z)[1+ϵ(z)f(r/Rb)].\Phi(M,r,z) = \Phi_0(M,z) \left[ 1+\epsilon(z)f(r/R_b) \right].

Your model predicts something like

ϵ(z)>0\epsilon(z)>0

for the fossil component.

A conventional early-seed scenario instead predicts a distribution tied primarily to halo assembly, environmental density, merger history, etc., rather than distance from one privileged cosmic event.

That is the discriminant.

And it gives you a genuinely nasty test:

Fit the centre using one subset of black holes, then predict the radial occupation/mass distribution of an independent subset without refitting the centre.

That is much harder to dismiss as selection bias.

5. One important observational difficulty

JWST itself is not yet the ideal instrument for finding the centre.

Current deep JWST fields are small, heterogeneous and selected for particular science programmes. CEERS, for example, covers about 100 square arcminutes and was specifically designed to investigate early galaxy formation and black-hole growth, but it is still a tiny pencil-beam relative to a cosmological volume.

So I would not make the first test:

“Use JWST to find the centre of the Universe.”

That is too ambitious with current survey geometry.

Instead:

Use JWST and other early-BH data to establish the fossil mass/occupation statistics; use large-area surveys and multiple independent fields to establish whether those statistics have a common radial centre.

That is a much more realistic programme.

6. Where I would put this for serious criticism

There are really two different scientific audiences, and I would approach them separately.

A. Inhomogeneous-cosmology / GR people

These people can tell you whether the phase-front construction actually exists as a relativistic solution.

1. Sofie Marie Koksbang — University of Southern Denmark

This is probably my first choice.

She leads an explicit Inhomogeneous Cosmology group, working on inhomogeneous backgrounds, structure, relativistic effects and numerical/observational consequences. Her recent work includes LTB/Swiss-cheese models and redshift drift.

This is almost exactly the sort of person you want asking:

“Can the mean background remain close to FLRW while a radially structured compact-object population is embedded in it, and how would you formulate the matching?”

2. Valerio Marra / BEHOMO — UFES

Very strong target for the observational side.

Marra explicitly works on inhomogeneous cosmology, tests of homogeneity/isotropy, cosmological data analysis, N-body simulations and Euclid, and leads the BEHOMO project studying structure evolution on inhomogeneous backgrounds.

He is particularly relevant because your eventual question is not merely “is this mathematically possible?” but:

“What data combination would make this impossible?”

3. Chris Clarkson / Roy Maartens

This is the hard-objection team I would actively seek out.

Clarkson works specifically on large-scale relativistic effects, homogeneity/isotropy and the Copernican Principle. His recent work with collaborators includes off-centre LTB models and observed expansion-rate anisotropies.

Their earlier work also dealt directly with LTB perturbations and BAO.

If your construction secretly turns into an LTB model with all the old problems, this is one of the groups most likely to spot it.

4. David Wiltshire — UC Gravity and Cosmology Group

A somewhat different but valuable target.

Wiltshire's group works on inhomogeneous cosmology, gravitational energy, quasilocal energy, mathematical/numerical relativity, black holes and global spacetime structure.

Your use of a quasi-local mass and your insistence that the outer region is physically real rather than “outside the universe” make this a particularly relevant audience.

5. Geneva cosmology group — Martin Kunz / collaborators

Especially useful for the CMB/off-centre question.

The Geneva group has explicitly studied CMB signatures of an observer displaced from the centre of an LTB void, as well as inhomogeneous cosmology and Euclid consistency tests.

They are a very good target for the question:

“If my fossil field is strongly radial but the metric is nearly FLRW, what is the minimum CMB signature?”

7. Early-black-hole / JWST people

These researchers can attack the fossil population, which is just as important.

1. Cambridge: Roberto Maiolino + Hannah Übler + the KICC/Cavendish early-BH programmes

This is probably the best observational target.

Cambridge currently has large JWST programmes explicitly aimed at the first black-hole population, including a 137-hour NIRSpec-IFU programme led by Hannah Übler with Roberto Maiolino, plus a programme specifically investigating Population III/direct-collapse BH formation in GN-z11.

Maiolino's research programme explicitly focuses on the formation and evolution of the first stars and black holes, and he is part of the JWST NIRSpec instrument science team.

Most importantly, this team produced the 2026 direct dynamical 5×107M⊙5\times10^7M_\odot BH measurement at z=7.04z=7.04.

They therefore have exactly the observational expertise needed to tell you whether your proposed fossil population has an observable signature distinct from ordinary heavy-seed scenarios.

2. Max Planck Institute for Astrophysics — Sunmyon Chon / Volker Springel

This is another exceptionally relevant target.

Their September 2026 Nature work shows that heavy BH seeds up to around 106M⊙10^6M_\odot can form naturally in dense early environments and then undergo rapid super-Eddington growth, reproducing LRD-like objects.

This is precisely the sort of competing explanation your model has to defeat.

That's actually ideal.

A good scientific test is not:

“Who might like this?”

but:

“Who has just published the strongest competing explanation?”

Chon's group qualifies.

3. Maynooth University — John Regan / Lewis Prole / Daxal Mehta, SEEDZ

Another excellent adversarial target.

Their SEEDZ simulations explicitly model Pop III seeds, heavy seeds, accretion and feedback, and their January 2026 work showed that light seeds can grow surprisingly efficiently in cosmological simulations.

Their 2026 SEEDZ papers are particularly useful because the group is actively quantifying whether conventional seeding mechanisms really can reproduce the early BH population.

4. UT Austin — Steven Finkelstein / CEERS and Vasily Kokorev's LRD work

CEERS is one of the obvious observational datasets for your fossil hypothesis. It was led by Steven Finkelstein and explicitly includes measurements of black-hole growth at high redshift.

Kokorev's team has also been using extremely deep JWST spectroscopy to test the interpretation of LRDs as obscured massive black holes.

Again, they are useful precisely because they may say:

“Your predicted population is observationally degenerate with X,”

which is exactly what you want to discover.

8. Forums: CosmoCoffee is much better than Physics Stack Exchange

CosmoCoffee would be my first public forum.

It is still active in 2026, with thousands of posts/users and recent cosmology discussions; its cosmology/resources area has recent activity involving N-body simulations, cosmological parameter fitting and related topics.

It is also directly connected to the professional cosmology community. For example, its current conference listings include Black Holes & Cosmology, Euclid workshops, testing-gravity meetings and cosmology schools.

I would post there after reducing the theory to a 2–5 page sharply defined note, not a 40-page manifesto.

Physics Stack Exchange is much less suitable for “please referee my new cosmological model.” Its own current guidance emphasizes questions about established or actively researched theories, and recent meta discussion explicitly says that the site is not a peer-review service.

A narrow technical question such as

“Can an expanding spherical phase boundary engulf Schwarzschild compact objects while preserving a prescribed junction condition?”

could be reasonable there.

A post saying

“Here is my new theory of the origin of the Universe; please evaluate it”

is likely to go badly.

9. arXiv

For this project I would target:

primary: astro-ph.CO
possible cross-list: astro-ph.GA
possibly: gr-qc

The arXiv taxonomy actually places cosmology, CMB, LSS, voids and primordial black holes under astro-ph.CO, while astro-ph.GA explicitly includes supermassive black holes and quasars. gr-qc is the General Relativity and Quantum Cosmology archive.

For a first submission/new category, arXiv currently requires endorsement. Their official process says first-time submitters can obtain endorsement through an institutional email/claimed authorship route or request personal endorsement from an established arXiv author. The site explicitly recommends finding someone knowledgeable in the subject area and, importantly, says to use related arXiv papers to identify potential endorsers.

That makes your reference list strategically important.

A sensible route would be:

  1. Write the paper.
  2. Cite the relevant LTB, shock-front, black-hole-in-FLRW, PBH-seed and JWST literature properly.
  3. Start an arXiv submission in astro-ph.CO.
  4. Follow arXiv's endorsement workflow.
  5. Use authors of the papers you genuinely engage with to identify a possible endorser.
  6. Send the potential endorser the actual paper plus a one-paragraph explanation of the question you want the paper to answer.

Do not present endorsement as scientific approval. It is not peer review; arXiv describes it as a mechanism for verifying participation in the scientific community and maintaining submission quality.

10. How I would approach researchers

I would not lead with:

“I have a new theory of the Universe.”

That triggers the wrong filter.

I would say:

“I am an independent researcher developing a phenomenological GR cosmology in which a critical quasi-local mass triggers a phase transition and an expanding phase front engulfs a pre-existing population of subcritical black holes. I am deliberately leaving the high-density mechanism unspecified. The two questions I want an expert to attack are whether the phase-front/black-hole matching can be made self-consistent, and whether a radially varying fossil occupation can remain observationally close to FLRW while producing a distinguishable signal.”

Then give them three things only:

Mc,M_c, Σ(t),\Sigma(t),

and

Φ(MBH∣r,z).\Phi(M_{\rm BH}\mid r,z).

The dark-energy branch should be marked optional. The LRD interpretation should be marked not evidence. The PBH/dark-matter branch should be marked secondary.

That presentation makes it much harder for someone to dismiss the whole idea because they dislike one speculative auxiliary claim.

11. My current “hard objection” ranking

After your clarifications, I would rank the unresolved problems as follows.

Red flag 1 — the global early-time causal structure

The pre-existing soup/inflation module still has to produce the observed CMB initial conditions. You have correctly separated this from the phase-front mechanism, but it cannot remain undefined forever.

Red flag 2 — survival and matching of engulfed horizons

B is plausible as a multiscale construction, but it needs an actual model showing that

Mi<McM_i<M_c

remains true while the phase front crosses the local spacetime.

This is a calculation, not merely a philosophical problem.

Red flag 3 — fossil gravity versus fossil counting

You must show that

ffossil bfossil(r)f_{\rm fossil}\,b_{\rm fossil}(r)

is small enough to leave the coarse-grained metric close to FLRW.

This may be perfectly possible.

Red flag 4 — CMB energy injection

If the fossil population is massive and present very early, accretion/radiative feedback can constrain it independently of its contribution to the metric.

Green light — BAO/SN/kSZ

Under your near-FLRW-background assumption, I don't see those datasets already killing the core idea. They become powerful only when your fossil population is allowed to generate a significant large-scale metric perturbation or when you activate the acceleration-from-outside branch.

That is a considerably better position than I would have given the original formulation.

The calculation I would put before everything else

The cleanest first paper is now almost obvious:

FLRW-like background+one spherical phase front+Misner–Sharp mass flux+embedded pre-existing BH population.\boxed{ \text{FLRW-like background} + \text{one spherical phase front} + \text{Misner--Sharp mass flux} + \text{embedded pre-existing BH population}. }

Solve for

RΣ(t),MMS(t),N(M,r,t).R_\Sigma(t), \qquad M_{\rm MS}(t), \qquad N(M,r,t).

Then derive

Φ(MBH∣r,z)\Phi(M_{\rm BH}|r,z)

and the induced coarse-grained metric perturbation.

That produces a binary outcome:

Either there exists a parameter region in which the front is dynamically possible, the fossils survive, and the metric remains observationally near FLRW — or the whole main hypothesis fails before any discussion of dark energy, dark matter or JWST anomalies is needed.

That is exactly the hard test I think you are looking for.

And at this point, I would actively seek out someone from Koksbang/Marra/Clarkson territory for the first objection, and someone from the Cambridge/MPA/Maynooth early-BH community for the second. Those are complementary attacks rather than a sympathetic echo chamber.