HIGH-REDSHIFT QUASARS AND ALTERNATIVE SPECTRA FOR PRIMEVAL DENSITY-FLUCTUATIONS

Using the COBE normalization, the amplitude of the density fluctuation spectrum on small scales (galaxies and below) is discussed for several flat cosmological models advocated as alternatives to the standard CDM cosmogony. A comparison is made with the fluctuation amplitude inferred from the existence of high-redshift quasars. Low-OEMGA models are shown to provide enough small-scale power for lambda less than or similar to 0.75, almost fully including the range obtained from tests on larger scales. For models containing a mixture of hot and cold dark matter (hybrid models) and for models with a non-scale-free primeval density fluctuation spectrum (tilted models) there is a potential lack of sufficient small-scale power. Spectral indices smaller than n approximately 0.75 or a hot dark matter fraction bigger than 25 per cent are not consistent with the quasar luminosity function at z = 4. Furthermore, a significant tilt (n = 0.7) or hot dark matter fraction (30 per cent) is incompatible with suggestions that the UV background is produced by luminous quasars or massive young galaxies.