An initial estimate of the convolved,
redshift-space power spectrum of the 2dFGRS was determined by
Percival et al. [72] for a sample of
160,000 redshifts. On scales
, the data are fairly robust and the
shape of the power spectrum is not significantly affected by
redshift-space distortion or non-linear effects, while its overall
amplitude is increased due to the linear redshift-space distortion
effect (see Section 5).
|
The recent results of atmospheric and solar
neutrino oscillations [24, 1] imply non-zero
mass-squared differences of the three neutrino flavours. While
these oscillation experiments do not directly determine the
absolute neutrino masses, a simple assumption of the neutrino mass
hierarchy suggests a lower limit on the neutrino mass density
parameter, . Large scale structure data can put an upper limit
on the ratio
due to the neutrino ’free streaming’
effect [33]. By comparing the 2dF
galaxy power-spectrum of fluctuations with a four-component model
(baryons, cold dark matter, a cosmological constant, and massive
neutrinos) it was estimated that
(95% CL), or with concordance prior of
,
, or an upper limit of
on the total
neutrino mass, assuming a prior of
[20, 19] (see Figure 24
). In order to
minimize systematic effects due to biasing and non-linear growth,
the analysis was restricted to the range
. Additional cosmological data sets bring down this
upper limit by a factor of two [79
].
While the CMB probes the fluctuations in matter, the galaxy redshift surveys measure the perturbations in the light distribution of particular tracer (e.g., galaxies of certain type). Therefore, for a fixed set of cosmological parameters, a combination of the two can better constrain cosmological parameters, and it can also provide important information on the way galaxies are ‘biased’ relative to the mass fluctuations,
The CMB fluctuations are commonly represented by
the spherical harmonics . The connection between the
harmonic
and
is roughly
Recent CMB measurements have been used in
combination with the 2dF power spectrum. Efstathiou et
al. [17] showed
that 2dFGRS+CMB provide evidence for a positive cosmological
constant (assuming
),
independently of the studies of supernovae Ia. As explained
in [72], the
shapes of the CMB and the 2dFGRS power spectra are insensitive to
Dark Energy. The main important effect of the dark energy is to
alter the angular diameter distance to the last scattering, and
thus the position of the first acoustic peak. Indeed, the latest
result from a combination of WMAP with 2dFGRS and other probes
gives
,
,
,
,
,
and
(95% CL, assuming
) [79
].
An independent measurement of cosmological
parameters on the basis of 2dFGRS comes from redshift-space
distortions on scales : a
correlation function
in parallel and transverse
pair separations
and
. As described in
Section 5, the distortion pattern
is a combination of the coherent infall, parameterized by
and random motions modelled by an exponential
velocity distribution function (see Equation (133
)). This methodology
has been applied by many authors. For instance, Peacock et
al. [66] derived
, and Hawkins et al. [30] obtained
and a velocity dispersion
. Using the full 2dF+CMB likelihood
function on the
) plane, Lahav et al. [42] derived a
slightly larger (but consistent within the quoted error-bars)
value,
.
It is well established that important information on the non-linear growth of structure is encoded at the high order moments, e.g., the skewness or its Fourier version, the bi-spectrum. Verde et al. [95] computed the bi-spectrum of 2dFGRS and used it to measure the bias parameter of the galaxies. They assumed a specific quadratic biasing model:
By analysing 80 million triangle configurations in the wavenumber range