COBE -normalized flat ( matter plus cosmological constant ) and open Cold Dark Matter ( CDM ) models are tested by comparing their expected Hubble flow variations and the observed variations in a Type Ia supernova sample and a Tully Fisher cluster sample .
The test provides a probe of the CDM power spectrum on scales of 0.02 h Mpc ^ { -1 } \la k \la 0.2 h Mpc ^ { -1 } , free of the bias factor b .
The results favor a low matter content universe , or a flat matter-dominated universe with a very low Hubble constant and/or a very small spectral index n _ { ps } , with the best fits having \Omega _ { 0 } \sim 0.3 to 0.4 .
The test is found to be more discriminative to the open CDM models than to the flat CDM models .
For example , the test results are found to be compatible with those from the X-ray cluster abundance measurements at smaller length scales , and consistent with the galaxy and cluster correlation analysis of Peacock and Dodds ( 1994 ) at similar length scales , if our universe is flat ; but the results are marginally incompatible with the X-ray cluster abundance measurements if our universe is open .
The open CDM results are consistent with that of Peacock and Dodds only if the matter density of the universe is less than about 60 % of the critical density .
The shortcoming of the test is discussed , so are ways to minimize it .