We revisit the question of whether fluctuations in hydrodynamical, adiabatical matter could explain the observed structures in our Universe. We consider matter with variable equation of state w=p₀/ε₀ and a concomitant (under the adiabatic assumption) density dependent speed of sound, cₛ. We find a limited range of possibilities for a setup when modes start inside the Hubble radius, then leaving it and freezing out. For expanding universes, power-law w(ε₀) models are ruled out (except when cₛ²∝w1, requiring post-stretching the seeded fluctuations); but sharper profiles in cₛ do solve the horizon problem. Among these, a phase transition in cₛ is notable for leading to scale-invariant fluctuations if the initial conditions are thermal. For contracting universes all power-law w(ε₀) solve the horizon problem, but only one leads to scale-invariance: w∝ε₀² and cₛ∝ε₀. This model bypasses a number of problems with single scalar field cyclic models (for which w is large but constant).
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Magueijo et al. (2010) studied this question.
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