Primordial structure formation in a Milne cosmology: QGP–bubble baryogenesis, diffusion survival and linear growth without dark matter

In this paper, we develop a picture in the observed cosmic web of galaxy clusters at the nodes of a filament/wall network surrounding voids could be seeded topologically by a first-order quark–gluon plasma (QGP) phase transition in an open (k = –1) Milne cosmology, with the cosmological scale factor [Formula: see text], without any dark matter. Such a linear expansion can be physically realized in non-minimally coupled scalar–tensor (induced) gravity theories having a Higgs-sector false vacuum with a vanishing effective gravitational constant. This yields an effectively empty, coasting universe, while true-vacuum bubbles nucleated in a first-order transition carry the canonical Newton constant in their interiors. Baryon overdensities form at colliding bubble walls. The comoving baryon diffusion length from the QGP epoch to recombination, computed on the Milne background, evaluates to [Formula: see text] (radiation drag; density-independent) and [Formula: see text] (effective combined) — more than three orders of magnitude below cluster scales, so that wall overdensities can never be diffused away. Guided by the 4 He “baryometer" of Milne-background nucleosyn-thesis, all density-dependent results are reported for both [Formula: see text] and [Formula: see text]. The linear growth equation, admits an exact solution in terms of modified Bessel functions, confirmed by direct numerical integration. The growth factor from recombination to the present is [Formula: see text] (for [Formula: see text]) or [Formula: see text] (for [Formula: see text]), versus 1101 in Einstein–de Sitter, because the Milne expansion rate at high z is a factor [Formula: see text] smaller while the gravi-tational source is identical. The comoving Jeans length at recombination is [Formula: see text], far below cluster scales. An initial wall overdensity of only [Formula: see text] ([Formula: see text] for [Formula: see text]) suffices for cluster collapse by [Formula: see text], while [Formula: see text] at the walls yields free-fall collapse within [Formula: see text] Myr of recombination. The diagnostic [Formula: see text] is not an impediment: the Milne metric is a kinematic background on which Einstein's equations are imposed only at the perturbative level, and the Friedmann constraint is never invoked for the bulk.