  We compare the amplitudes of fluctuations probed by the 2dF Galaxy Redshift
Survey and by the latest measurements of the Cosmic Microwave Background
anisotropies. By combining the 2dFGRS and CMB data we find the linear-theory
rms mass fluctuations in 8 Mpc/h spheres to be sigma_8 = 0.73 +-0.05 (after
marginalization over the matter density parameter Omega_m and three other free
parameters). This normalization is lower than the COBE normalization and
previous estimates from cluster abundance, but it is in agreement with some
revised cluster abundance determinations. We also estimate the
scale-independent bias parameter of present-epoch L_s = 1.9L_* APM-selected
galaxies to be b(L_s,z=0) = 1.10 +- 0.08 on comoving scales of 0.02 < k < 0.15
h/Mpc. If luminosity segregation operates on these scales, L_* galaxies would
be almost un-biased, b(L_*,z=0) = 0.96. These results are derived by assuming a
flat Lambda-CDM Universe, and by marginalizing over other free parameters and
fixing the spectral index n=1 and the optical depth due to reionization tau=0.
We also study the best fit pair (Omega_m,b), and the robustness of the results
to varying n and tau. Various modelling corrections can each change the
resulting b by 5-15 per cent. The results are compared with other independent
measurements from the 2dFGRS itself, and from the SDSS, cluster abundance and
cosmic shear.
