The 2dF Galaxy Redshift Survey has now measured in excess of 160 000 galaxy redshifts. This paper presents the power spectrum of the galaxy distribution, calculated using a direct Fourier transform based technique. We argue that, within the k‐space region , the shape of this spectrum should be close to that of the linear density perturbations convolved with the window function of the survey. This window function and its convolving effect on the power spectrum estimate are analysed in detail. By convolving model spectra, we are able to fit the power‐spectrum data and provide a measure of the matter content of the Universe. Our results show that models containing baryon oscillations are mildly preferred over featureless power spectra. Analysis of the data yields 68 per cent confidence limits on the total matter density times the Hubble parameter , and the baryon fraction , assuming scale‐invariant primordial fluctuations.

We constrain flat cosmological models with a joint likelihood analysis of a new compilation of data from the cosmic microwave background (CMB) and from the 2dF Galaxy Redshift Survey (2dFGRS). Fitting the CMB alone yields a known degeneracy between the Hubble constant h and the matter density Ωm, which arises mainly from preserving the location of the peaks in the angular power spectrum. This ‘horizon‐angle degeneracy’ is considered in some detail and is shown to follow the simple relation Ωmh3.4= constant. Adding the 2dFGRS power spectrum constrains Ωmh and breaks the degeneracy. If tensor anisotropies are assumed to be negligible, we obtain values for the Hubble constant of h= 0.665 ± 0.047, the matter density Ωm= 0.313 ± 0.055, and the physical cold dark matter and baryon densities Ωch2= 0.115 ± 0.009, Ωbh2= 0.022 ± 0.002 (standard rms errors). Including a possible tensor component causes very little change to these figures; we set an upper limit to the tensor‐to‐scalar ratio of r < 0.7 at a 95 per cent confidence level. We then show how these data can be used to constrain the equation of state of the vacuum, and find w < −0.52 at 95 per cent confidence. The preferred cosmological model is thus very well specified, and we discuss the precision with which future CMB data can be predicted, given the model assumptions. The 2dFGRS power‐spectrum data and covariance matrix, and the CMB data compilation used here, are available from http://www.roe.ac.uk/~wjp/.

A B S T R A C TWe compare the amplitudes of fluctuations probed by the 2dF Galaxy Redshift Survey (2dFGRS) and by the latest measurements of the cosmic microwave background (CMB) anisotropies. By combining the 2dFGRS and CMB data, we find the linear-theory rms mass fluctuations in 8 h 21 Mpc spheres to be s 8m ¼ 0:73^0:05 (after marginalization over the matter density parameter V 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 scaleindependent bias parameter of present-epoch L s ¼ 1:9L * APM-selected galaxies to be bðL s ; z ¼ 0Þ ¼ 1:10^0:08 on comoving scales of 0:02 , k , 0:15 h Mpc 21 . If luminosity segregation operates on these scales, L * galaxies would be almost unbiased, bðL * ; z ¼ 0Þ < 0:96. These results are derived by assuming a flat LCDM Universe, and by marginalizing over other free parameters and fixing the spectral index n ¼ 1 and the optical depth due to reionization t ¼ 0. We also study the best-fitting pair (V m , b), and the robustness of the results to varying n and t. 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 Sloan Digital Sky Survey (SDSS), cluster abundance and cosmic shear.

A B S T R A C TWe present the bivariate brightness distribution (BBD) for the 2dF Galaxy Redshift Survey (2dFGRS) based on a preliminary subsample of 45 000 galaxies. The BBD is an extension of the galaxy luminosity function, incorporating surface brightness information. It allows the measurement of the local luminosity density, j B , and of the galaxy luminosity and surface brightness distributions, while accounting for surface brightness selection biases.The recovered 2dFGRS BBD shows a strong luminosity±surface brightness relation M B G 2X4^1 X5 0X5 m e Y providing a new constraint for galaxy formation models. In terms of the number density, we find that the peak of the galaxy population lies at M B $ 216X0 magX Within the well-defined selection limits (224 , M B , 216X0 magY 18X0 , m e , 24X5 mag arcsec 22 ) the contribution towards the luminosity density is dominated by conventional giant galaxies (i.e., 90 per cent of the luminosity density is contained within 222X5 , M , 217X5Y 18X0 , m e , 23X0X The luminosity-density peak lies away from the selection boundaries, implying that the 2dFGRS is complete in terms of sampling the local luminosity density, and that luminous low surface brightness galaxies are rare. The final value we derive for the local luminosity density, inclusive of surface brightness corrections, is j B 2X49^0X20 Â 10 8 h 100 L ( Mpc 23 X Representative Schechter function parameters are M* 219X75^0X05Y f* 2X02^0X02 Â 10 22 and a 21X09^0X03X Finally, we note that extending the conventional methodology to incorporate surface brightness selection effects has resulted in an increase in the luminosity density of ,37 per cent. Hence surface brightness selection effects would appear to explain much of the discrepancy between previous estimates of the local luminosity density. q 2001 RAS