Large-Scale Structure of the Universe and Cosmological ...

such as the abundance of massive clusters [538,385,691,522].
Results on the redshift-space bispectrum in the CfA/PPS sample [31] (see
Fig. 57) and the skewness of CfA/SSRS surveys [246] were used in [224] to
put constraints on the non-local (scale-dependent) bias in the cooperative
galaxy formation (CGF) model [96] proposed to generate enough large-scale
power in the context of otherwise-standard CDM. This model corresponds to
a (density-dependent) threshold bias model where galaxies form in regions
satisfying δ > νσ − κδ(Rs), where κ is the strength of cooperative effects
and Rs describes the “scale of influence” of non-locality. Figure 57 shows the
predictions of CGF models for (κ, Rs) = (0.84, 10 h −1 Mpc) (dot-long-dashed),
(2.29, 20 h −1 Mpc) (solid) , and (4.48, 30 h −1 Mpc) (dot-short-dashed), all of
which have similar large-scale power to a Γ = 0.2 CDM model. Because of
the scale dependence induced by the CGF models, additional linear bias is
required to suppress these features, which in turns implies non-zero non-linear
bias to maintain agreement with Q3 ∼ 0.5 and also would be in disagreement
with the normalization implied by the CMB [596]. In addition, this would
make the agreement with the simple prediction of PT from Gaussian initial
conditions purely accidental. Similar results follow from the analysis of the
skewness S3, see [224].
As discussed in Sect. 8.3.3, the detection of the configuration dependence of the
bispectrum in IRAS surveys (see e.g. Fig. 58) gives a tool to constrain galaxy
bias, primordial non-Gaussianity, and break degeneracies present in two-point
statistics. Using a maximum likelihood method that takes into account the
non-Gaussianity of the cosmic distribution function and the covariance matrix
of the bispectrum [566], the constraints on local bias parameters from IRAS
surveys assuming Gaussian initial conditions 146 read [567,211]
1
b1
1
b1
1
b1
=1.32 +0.36
−0.58 ,
=1.15 +0.39
−0.39,
=1.20 +0.18
−0.19,
b2
b2 1
b2
b2 1
b2
b2 1
= −0.57 +0.45
−0.30 , (2Jy.) (630)
= −0.50 +0.31
−0.51, (1.2Jy.) (631)
= −0.42 +0.19
−0.19, (PSCz) (632)
with the best fit model shown as a dashed line in Fig. 58 for the PSCz
case. These results for the linear bias of IRAS galaxies, when coupled with
measurements of the power spectrum redshift distortions, which determine
β = Ω 0.6
m /b1 ≃ 0.4 ± 0.12 for the PSCz survey [299,643], allows the break of
the degeneracy between linear bias and Ωm, giving Ωm = 0.16 ± 0.1.
If bias is local in Lagrangian, rather than Eulerian, space the bispectrum
146 In addition, these constraints assume a fixed linear power spectrum shape given
by Γ = 0.21, in agreement with power spectrum measurements. See [566,567] for sensitivity
of bias parameters on the assumed power spectrum shape. The dependence
of the bispectrum on the assumed Ωm is negligible, as first pointed out in [313].
257