The fluctuation amplitude

What structures might emerge in a universe that was initially smoother (Q smaller) or rougher (Q larger) than ours? Were Q of order 10_6, there would be no clusters of galaxies; moreover, the only galaxies would be small and anaemic. They would form much later than galaxies did in our actual universe. Because they would be loosely bound, processed material would be expelled from shallow potential wells; there may therefore be no second-generation stars and no planetary systems. If Q were even smaller than 10"6, there would be no star formation at all; very small structures of dark matter would turn around late and their constituent gas would be too dilute to undergo the radiative cooling that is a prerequisite for star formation.3

Hypothetical astronomers in a universe with Q = 10_4 might find their cosmic environment more varied and interesting than ours. Galaxies and clusters would span a wider range of masses. The biggest clusters would be 1000 times more massive than any in our actual universe. There could be individual galaxies - perhaps even disc galaxies - with masses up to that of the Coma cluster and internal velocity dispersions up to 2000kms_1. These would have condensed when the age of our universe was only 3 x 108 y and when Compton cooling on the microwave background was still effective.

However, a universe where Q were larger still - more than (say) 10_3 -would be a violent and inhospitable place. Huge gravitationally bound systems would collapse, trapping their radiation and being unable to fragment, soon after the epoch of recombination. (Collapse at, say, 107 y would lead to sufficient partial ionization via strong shocks to recouple the baryons and the primordial radiation.) Such structures, containing the bulk of the material,

3 In a A-dominated universe, isolated clumps could survive for an infinite time without merging into a larger scale in the hierarchy. So eventually, for any Q > 10_8, a 'star' could form — but by that time it might be the only bound object within the horizon.

would turn into vast black holes. It is unlikely that galaxies of any kind would exist; nor is it obvious that much baryonic material would ever go into stars. Even if it did so, they would be in very compact highly bound systems.4

According to most theories of the ultra-early universe, Q is imprinted by quantum effects: microscopic fluctuations, after exponential expansion, give rise to the large-scale irregularities observed in the microwave background sky, which are the seeds for galaxies and clusters. In a wide class of theories, Q depends on the detailed physics during an inflationary era. But, as yet, no independent evidence constrains such theories, so we cannot pin down Q.

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