When Cold Dark Matter ( CDM ) power spectrum normalized by COBE results , its amplitude at smaller scales can be parametrized by \Gamma \sim \Omega _ { 0 } h .
The expected variations of Hubble flows in two samples , the sample of 36 clusters in the Mark III catalogue , and the sample of 20 Type Ia supernovae ( SNe ) , are calculated for the power spectrum in critical-density CDM models ( including tilted CDM models and vacuum-dominated CDM models ) .
The comparison between the expectations and the real variations in the data offers a bias-free way to constrain the power spectrum .
The cluster sample yields \Gamma \leq 0.30 - 0.88 ( n _ { ps } -1 ) +1.9 ( n _ { ps } -1 ) ^ { 2 } at 95 \% C.L. , with best fits \Gamma = 0.15 - 0.39 ( n _ { ps } -1 ) +0.37 ( n _ { ps } -1 ) ^ { 2 } , where n _ { ps } is the spectral index of the power spectrum .
The Type Ia SN sample yields \Gamma \leq 0.25 - 0.80 ( n _ { ps } -1 ) +1.6 ( n _ { ps } -1 ) ^ { 2 } at 95 \% C.L. , strongly favoring lower \Gamma ’ s .
The results are inconsistent with a critical-density matter-dominated universe with n _ { ps } \ga 0.8 and H _ { 0 } \ga 50 km/sec/Mpc .