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Recently it has become fashionable to assume that galaxies and clusters formed from scale-invariant adiabatic perturbations. This idea is supported by Grand Unified Theories, which predict that primordial irregularities in the ratio of baryons to photons would not survive the epoch of baryosynthesis, and by inflationary models for the origin of perturbations. However, if axions (or some other pseudo-Goldstone bosons with similar properties) dominate the mass density of the Universe, scale-invariant isocurvature perturbations could have played an important role in galaxy formation. We investigate this possibility in detail, with special emphasis on the constraints set by observations of the microwave background radiation. Isocurvature perturbations lead to a new source of anisotropy on large angular scales (|1^|) which exceeds the familiar Sachs–Wolfe effect. If galaxies are unbiased tracers of the mass distribution, scale-invariant isocurvature perturbations in Ω=1 models with |h₀1\, (where\, h₀=H₀/ (100\, km\, s^-1\, Mpc^-1) | can be excluded by anisotropy limits on angular scales |6^|. Models with |h₀0. 75| are unacceptable even if the amplitude of the galaxy correlation function is four times that of the mass distribution (as predicted in some models of 'biased' galaxy formation). Anisotropy limits on arcminute scales are violated by models with |h₀0. 2|.
Efstathiou et al. (Wed,) studied this question.