The DWT Power Spectrum of the two-degree Field Galaxy Redshift Survey

The power spectrum of the two-degree Field Galaxy Redshift Survey (2dFGRS) sample is estimated with the discrete wavelet transform (DWT) method. The DWT power spectra within $0.04 <k< 2.3 h$Mpc$^{-1}$ are measured for three volume-limited samples defined in connective absolute magnitude bins $-19 \sim -18$, $-20 \sim -19$ and $-21 \sim -20$. We show that the DWT power spectrum can effectively distinguish $\Lambda$CDM models of $\sigma_8=0.84$ and $\sigma_8=0.74$. We adopt maximum likelihood method to perform three-parameter fitting with bias parameter $b$, pairwise velocity dispersion $\sigma_{pv}$ and redshift distortion parameter $\beta=\Omega_m^{0.6}/b$ to the measured DWT power spectrum. Fitting results denotes that in a $\sigma_8=0.84$ universe the best fitted $\Omega_m$ given by the three samples are consistent in the range $0.28 \sim 0.36$, and the best fitted $\sigma_{pv}$ are $398^{+35}_{-27}$, $475^{+37}_{-29}$ and $550 \pm 20$km/s for the three samples, respectively. However in the model of $\sigma_8=0.74$, our three samples give very different values of $\Omega_m$. We repeat the fitting by using empirical formula of redshift distortion. The result of the model of low $\sigma_8$ is still poor, especially, one of the best value $\sigma_{pv}$ is as large as $10^3$km/s. The power spectrum of 2dFGRS seems in disfavor of models with low amplitude of density fluctuations.