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low a mass ~ 101E/i_2M©. Baryonic fluctuations would survive on scales above the baryon
damping length, equivalent to a mass scale ~ 1012n^1/,2/i~5/2M©, but with amplitude re-
duced by a factor ~ fit/flj, ~ 0.1. We conclude that in a neutrino-dominated Universe, the
galaxy forming fluctuations must have large amplitude (> 0.01) on scales 1010 — 1013M©,
whereas in a cold dark matter dominated Universe, where accretion occurs much earlier,
the relevant scale is < 109M© if 6rma ~ 0.1.
The inhomogeneous fluctuation spectrum cannot extend much beyond 1012 — 1013M©,
or we would begin to violate constraints that derive from the clustering of galaxies. Hier-
archical clustering occurs continuously, with the typical scale becoming non-linear today
over ~ 8/i-1 Mpc or ~ 3 x lO14^-1^© (ref. 11). Hence, fluctuations containing ~ 1012Af©
would have gone non-linear at z ~ 300 and could arise from primordial fluctuations with
Srm* ~ 0.01. To avoid excessive clustering inhomogeneity in a cold dark matter-dominated
Universe, the large amplitude mass fluctuations should not extend beyond ~ 10105^SM©.
This is a weaker, but more rigorous, constraint than the smaller mass scale inferred from
the argument given previously which utilized the internal density, since the number of
surviving objects is certain in a continuous clustering, non-dissipative cold dark matter
scenario. Non-linear gravitational clustering ensues that the galaxy correlation function
will have the correct slope for an appropriate choice of 6rma and seed mass, although there
is a legitimate worry as to whether in the transition region where the correlation function
is of order unity, there may be excessive correlations induced by the large-scale fluctuation
component. This potential difficulty is avoided in a hot dark matter model where the large
coherence length effectively suppresses contributions from the large-scale fluctuations to
the small-scale correlations.
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Silk, J. & Turner, M. S. Double Inflation, report, April 1, 1986; United States. (https://digital.library.unt.edu/ark:/67531/metadc1094833/m1/20/: accessed July 16, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.