Linear Bias Factor Research Articles

Bias factor in anisotropic stochastic fields

The geometrical and topological measures enable us to characterize stochastic field systematically, and the relation between weighted and unweighted N-point functions is provided. One of such relations is given by the bias factor. In this paper, based on peak statistics, we study the bias factor for stochastic and anisotropic fields. Accordingly, we present the analytical description of local and linear bias factor. Doing simulations, we examine the validation of the derived analytical relation. Our results show that at high threshold level and large spatial separation, there exists a good agreement between the analytical calculation and numerical computations.

A new method to measure galaxy bias by combining the density and weak lensing fields

We present a new method to measure the redshift-dependent galaxy bias by combining information from the galaxy density field and the weak lensing field. This method is based on Amara et al. (2012), where they use the galaxy density field to construct a bias-weighted convergence field kg. The main difference between Amara et al. (2012) and our new implementation is that here we present another way to measure galaxy bias using tomography instead of bias parameterizations. The correlation between kg and the true lensing field k allows us to measure galaxy bias using different zero-lag correlations, such as <kgk>/<kk> or <kgkg>/<kgk>. Our method measures the linear bias factor on linear scales under the assumption of no stochasticity between galaxies and matter. We use the MICE simulation to measure the linear galaxy bias for a flux-limited sample (i < 22.5) in tomographic redshift bins using this method. This paper is the first that studies the accuracy and systematic uncertainties associated with the implementation of the method, and the regime where it is consistent with the linear galaxy bias defined by projected 2-point correlation functions (2PCF). We find that our method is consistent with linear bias at the percent level for scales larger than 30 arcmin, while nonlinearities appear at smaller scales. This measurement is a good complement to other measurements of bias, since it does not depend strongly on sigma8 as the 2PCF measurements. We apply this method to the Dark Energy Survey Science Verification data in a follow-up paper.

The non-linear power spectrum of the Lyman alpha forest

The Lyman alpha forest power spectrum has been measured on large scales by the BOSS survey in SDSS-III at z∼ 2.3, has been shown to agree well with linear theory predictions, and has provided the first measurement of Baryon Acoustic Oscillations at this redshift. However, the power at small scales, affected by non-linearities, has not been well examined so far. We present results from a variety of hydrodynamic simulations to predict the redshift space non-linear power spectrum of the Lyα transmission for several models, testing the dependence on resolution and box size. A new fitting formula is introduced to facilitate the comparison of our simulation results with observations and other simulations. The non-linear power spectrum has a generic shape determined by a transition scale from linear to non-linear anisotropy, and a Jeans scale below which the power drops rapidly. In addition, we predict the two linear bias factors of the Lyα forest and provide a better physical interpretation of their values and redshift evolution. The dependence of these bias factors and the non-linear power on the amplitude and slope of the primordial fluctuations power spectrum, the temperature-density relation of the intergalactic medium, and the mean Lyα transmission, as well as the redshift evolution, is investigated and discussed in detail. A preliminary comparison to the observations shows that the predicted redshift distortion parameter is in good agreement with the recent determination of Blomqvist et al., but the density bias factor is lower than observed. We make all our results publicly available in the form of tables of the non-linear power spectrum that is directly obtained from all our simulations, and parameters of our fitting formula.

Galaxy clustering using photometric redshifts

We investigate the evolution of the galaxy two point correlation function (CF) over a wide redshift range, 0.2 < z < 3. For the first time the systematic analysis covers the redshifts above 1 - 1.5. The catalogue of ~250000 galaxies with i+ < 25 and known photometric redshifts in the Subaru Deep field is used. The galaxies are divided into three luminosity classes and several distance/redshift bins. First, the 2D CF is determined for each luminosity class and distance bin. Calculations are based on the quantitative differences between the surface distributions of galaxy pairs with comparable and distinctly different photometric redshifts. The power law approximation for the CF is used. A limited accuracy of photometric redshifts as compared to the spectroscopic ones has been examined and taken into account. Then, the 3D functions for all the selected luminosities and distances are calculated. The power-law parameters of the CF, the slope and the correlation length, are determined. Both parameters do not show strong variations over the whole investigated redshift range. The slope of the luminous galaxies appears to be consistently steeper than that for the fainter ones. The linear bias factor, b(z), grows systematically with redshift; assuming the local normalization b(0) = 1.1-1.2, the bias reaches 3 - 3.5 at the high redshift limit.

The VIMOS Public Extragalactic Redshift Survey (VIPERS)

We investigate the higher-order correlation properties of the VIMOS Public Extragalactic Redshift Survey (VIPERS) to test the hierarchical scaling hypothesis at z~1 and the dependence on galaxy luminosity, stellar mass, and redshift. We also aim to assess deviations from the linearity of galaxy bias independently from a previously performed analysis of our survey (Di Porto et al. 2014). We have measured the count probability distribution function in cells of radii 3 < R < 10 Mpc/h, deriving $\sigma_{8g}$, the volume-averaged two-,three-,and four-point correlation functions and the normalized skewness $S_{3g}$ and kurtosis $S_{4g}$ for volume-limited subsamples covering the ranges $-19.5 \le M_B(z=1.1)-5log(h) \le -21.0$, $9.0 < log(M*/M_{\odot} h^{-2}) \le 11.0$, $0.5 \le z < 1.1$. We have thus performed the first measurement of high-order correlations at z~1 in a spectroscopic redshift survey. Our main results are the following. 1) The hierarchical scaling holds throughout the whole range of scale and z. 2) We do not find a significant dependence of $S_{3g}$ on luminosity (below z=0.9 $S_{3g}$ decreases with luminosity but only at 1{\sigma}-level). 3) We do not detect a significant dependence of $S_{3g}$ and $S_{4g}$ on scale, except beyond z~0.9, where the dependence can be explained as a consequence of sample variance. 4) We do not detect an evolution of $S_{3g}$ and $S_{4g}$ with z. 5) The linear bias factor $b=\sigma_{8g}/\sigma_{8m}$ increases with z, in agreement with previous results. 6) We quantify deviations from the linear bias by means of the Taylor expansion parameter $b_2$. Our results are compatible with a null non-linear bias term, but taking into account other available data we argue that there is evidence for a small non-linear bias term.

Extending the halo mass resolution of N-body simulations

We present a scheme to extend the halo mass resolution of N-body simulations of the hierarchical clustering of dark matter. The method uses the density field of the simulation to predict the number of sub-resolution dark matter haloes expected in different regions. The technique requires as input the abundance of haloes of a given mass and their average clustering, as expressed through the linear and higher order bias factors. These quantities can be computed analytically or, more accurately, derived from a higher resolution simulation as done here. Our method can recover the abundance and clustering in real- and redshift-space of haloes with mass below $\sim 7.5 \times 10^{13}h^{-1}M_{\odot}$ at $z=0$ to better than 10%. We demonstrate the technique by applying it to an ensemble of 50 low resolution, large-volume $N$-body simulations to compute the correlation function and covariance matrix of luminous red galaxies (LRGs). The limited resolution of the original simulations results in them resolving just two thirds of the LRG population. We extend the resolution of the simulations by a factor of 30 in halo mass in order to recover all LRGs. With existing simulations it is possible to generate a halo catalogue equivalent to that which would be obtained from a $N$-body simulation using more than 20 trillion particles; a direct simulation of this size is likely to remain unachievable for many years. Using our method it is now feasible to build the large numbers of high-resolution large volume mock galaxy catalogues required to compute the covariance matrices necessary to analyse upcoming galaxy surveys designed to probe dark energy.

Large-scale structure studies with AGN in the eROSITA/SRG All-Sky Survey

AbstractThe four-year X-ray all-sky survey (eRASS) of the eROSITA telescope aboard the Spektrum-Roentgen-Gamma satellite will detect ~ 3 million active galactic nuclei (AGN) with a median redshift of z≈1. We show that this unprecedented AGN sample, complemented with redshift information, will supply us with outstanding opportunities for large-scale structure research. For the first time with a sample of X-ray selected AGN, it will become possible to perform detailed redshift- and luminosity-resolved studies of the linear bias factor, and to convincingly detected baryonic acoustic oscillations (BAOs). To exploit the full potential of the eRASS AGN sample, photometric and spectroscopic surveys of large areas and a sufficient depth will be needed.

Nonlocal Lagrangian bias

Halos are biased tracers of the dark matter distribution. It is often assumed that the patches from which halos formed are locally biased with respect to the initial fluctuation field, meaning that the halo-patch fluctuation field can be written as a Taylor series in that of the dark matter. If quantities other than the local density influence halo formation, then this Lagrangian bias will generically be nonlocal; the Taylor series must be performed with respect to these other variables as well. We illustrate the effect with Monte-Carlo simulations of a model in which halo formation depends on the local shear (the quadrupole of perturbation theory), and provide an analytic model which provides a good description of our results. Our model, which extends the excursion set approach to walks in more than one dimension, works both when steps in the walk are uncorrelated, as well as when there are correlations between steps. For walks with correlated steps, our model includes two distinct types of nonlocality: one is due to the fact that the initial density profile around a patch which is destined to form a halo must fall sufficiently steeply around it -- this introduces k-dependence to even the linear bias factor, but otherwise only affects the monopole of the clustering signal. The other is due to the surrounding shear field; this affects the quadratic and higher order bias factors, and introduces an angular dependence to the clustering signal. In both cases, our analysis shows that these nonlocal Lagrangian bias terms can be significant, particularly for massive halos; they must be accounted for in analyses of higher order clustering such as the halo bispectrum in Lagrangian or Eulerian space. Although we illustrate these effects using halos, our analysis and conclusions also apply to the other constituents of the cosmic web -- filaments, sheets and voids.

Lagrangian bias in the local bias model

It is often assumed that the halo-patch fluctuation field can be written as a Taylor series in the initial Lagrangian dark matter density fluctuation field. We show that if this Lagrangian bias is local, and the initial conditions are Gaussian, then the two-point cross-correlation between halos and mass should be linearly proportional to the mass-mass auto-correlation function. This statement is exact and valid on all scales; there are no higher order contributions, e.g., from terms proportional to products or convolutions of two-point functions, which one might have thought would appear upon truncating the Taylor series of the halo bias function. In addition, the auto-correlation function of locally biased tracers can be written as a Taylor series in the auto-correlation function of the mass; there are no terms involving, e.g., derivatives or convolutions. Moreover, although the leading order coefficient, the linear bias factor of the auto-correlation function is just the square of that for the cross-correlation, it is the same as that obtained from expanding the mean number of halos as a function of the local density only in the large-scale limit. In principle, these relations allow simple tests of whether or not halo bias is indeed local in Lagrangian space. We discuss why things are more complicated inpractice. We also discuss our results in light of recent work on the renormalizability of halo bias, demonstrating that it is better to renormalize than not. We use the Lognormal model to illustrate many of our findings.

Peaks theory and the excursion set approach

We describe a model of dark matter halo abundances and clustering which combines the two most widely used approaches to this problem: that based on peaks and the other based on excursion sets. Our approach can be thought of as addressing the cloud-in-cloud problem for peaks and/or modifying the excursion set approach so that it averages over a special subset, rather than all possible walks. In this respect, it seeks to account for correlations between steps in the walk as well as correlations between walks. We first show how the excursion set and peaks models can be written in the same formalism, and then use this correspondence to write our combined excursion set peaks model. We then give simple expressions for the mass function and bias, showing that even the linear halo bias factor is predicted to be k-dependent as a consequence of the nonlocality associated with the peak constraint. At large masses, our model has little or no need to rescale the variable delta_c from the value associated with spherical collapse, and suggests a simple explanation for why the linear halo bias factor appears to lie above that based on the peak-background split at high masses when such a rescaling is assumed. Although we have concentrated on peaks, our analysis is more generally applicable to other traditionally single-scale analyses of large-scale structure.

Local gravity versus local velocity: solutions for β and non-linear bias

We perform a reconstruction of the cosmological large-scale flows in the nearby Universe using two complementary observational sets. The first, the SFI++ sample of Tully–Fisher (TF) measurements of galaxies, provides a direct probe of the flows. The second, the whole sky distribution of galaxies in the 2MASS (Two Micron All Sky Survey) redshift survey (2MRS), yields a prediction of the flows given the cosmological density parameter, Ω, and a biasing relation between mass and galaxies. We aim at an unbiased comparison between the peculiar velocity fields extracted from the two data sets and its implication on the cosmological parameters and the biasing relation. We expand the fields in a set of orthonormal basis functions, each representing a plausible realization of a cosmological velocity field smoothed in such a way as to give a nearly constant error on the derived SFI++ velocities. The statistical analysis is done on the coefficients of the modal expansion of the fields by means of the basis functions. Our analysis completely avoids the strong error covariance in the smoothed TF velocities by the use of orthonormal basis functions and employs elaborate mock data sets to extensively calibrate the errors in 2MRS predicted velocities. We relate the 2MRS galaxy distribution to the mass density field by a linear bias factor, b, and include a luminosity-dependent, ∝Lα, galaxy weighting. We assess the agreement between the fields as a function of α and β=f(Ω)/b, where f is the growth factor of linear perturbations. The agreement is excellent with a reasonable χ2 per degree of freedom. For α= 0, we derive 0.28 < β < 0.37 and 0.24 < β < 0.43, respectively, at the 68.3 per cent and 95.4 per cent confidence levels (CLs). For β= 0.33, we get α < 0.25 and α < 0.5, respectively, at the 68.3 per cent and 95.4 per cent CLs. We set a constraint on the fluctuation normalization, finding σ8= 0.66 ± 0.10, which is only 1.5σ deviant from Wilkinson Microwave Anisotropy Probe (WMAP) results. It is remarkable that σ8 determined from this local cosmological test is close to the value derived from the cosmic microwave background, an indication of the precision of the standard model.

The WiggleZ Dark Energy Survey: the selection function and z= 0.6 galaxy power spectrum

We report one of the most accurate measurements of the three-dimensional large-scale galaxy power spectrum achieved to date, using 56,159 redshifts of bright emission-line galaxies at effective redshift z=0.6 from the WiggleZ Dark Energy Survey at the Anglo-Australian Telescope. We describe in detail how we construct the survey selection function allowing for the varying target completeness and redshift completeness. We measure the total power with an accuracy of approximately 5% in wavenumber bands of dk=0.01 h/Mpc. A model power spectrum including non-linear corrections, combined with a linear galaxy bias factor and a simple model for redshift-space distortions, provides a good fit to our data for scales k < 0.4 h/Mpc. The large-scale shape of the power spectrum is consistent with the best-fitting matter and baryon densities determined by observations of the Cosmic Microwave Background radiation. By splitting the power spectrum measurement as a function of tangential and radial wavenumbers we delineate the characteristic imprint of peculiar velocities. We use these to determine the growth rate of structure as a function of redshift in the range 0.4 < z < 0.8, including a data point at z=0.78 with an accuracy of 20%. Our growth rate measurements are a close match to the self-consistent prediction of the LCDM model. The WiggleZ Survey data will allow a wide range of investigations into the cosmological model, cosmic expansion and growth history, topology of cosmic structure, and Gaussianity of the initial conditions. Our calculation of the survey selection function will be released at a future date via our website wigglez.swin.edu.au.

Large-scale bias and the inaccuracy of the peak-background split

The peak-background split argument is commonly used to relate the abundance of dark matter halos to their spatial clustering. Testing this argument requires an accurate determination of the halo mass function. We present a Maximum Likelihood method for fitting parametric functional forms to halo abundances which differs from previous work because it does not require binned counts. Our conclusions do not depend on whether we use our method or more conventional ones. In addition, halo abundances depend on how halos are defined. Our conclusions do not depend on the choice of link length associated with the friends-of-friends halo-finder, nor do they change if we identify halos using a spherical overdensity algorithm instead. The large scale halo bias measured from the matter-halo cross spectrum b_x and the halo autocorrelation function b_xi (on scales k~0.03h/Mpc and r ~50 Mpc/h) can differ by as much as 5% for halos that are significantly more massive than the characteristic mass M*. At these large masses, the peak background split estimate of the linear bias factor b1 is 3-5% smaller than b_xi, which is 5% smaller than b_x. We discuss the origin of these discrepancies: deterministic nonlinear local bias, with parameters determined by the peak-background split argument, is unable to account for the discrepancies we see. A simple linear but nonlocal bias model, motivated by peaks theory, may also be difficult to reconcile with our measurements. More work on such nonlocal bias models may be needed to understand the nature of halo bias at this level of precision.

DETERMINE THE GALAXY BIAS FACTORS ON LARGE SCALES USING THE BISPECTRUM METHOD

We study whether the bias factors of galaxies can be unbiasedly recovered from their power spectra and bispectra. We use a set of numerical N-body simulations and construct large mock galaxy catalogs based upon the semianalytical model of Croton et al. We measure the reduced bispectra for galaxies of different luminosity, and determine the linear and first nonlinear bias factors from their bispectra. We find that on large scales down to that of the wavenumber k = 0.1 h Mpc(-1), the bias factors b(1) and b(2) are nearly constant, and b(1) obtained with the bispectrum method agrees very well with the expected value. The nonlinear bias factor b(2) is negative, except for the most luminous galaxies with M(r) < -23 which have a positive b(2). The behavior of b(2) of galaxies is consistent with the b(2) mass dependence of their host halos. We show that it is essential to have an accurate estimation of the dark matter bispectrum in order to have an unbiased measurement of b(1) and b(2). We also test the analytical approach of incorporating halo occupation distribution to model the galaxy power spectrum and bispectrum. The halo model predictions do not fit the simulation results well on the precision requirement of current cosmological studies.

Large-scale structure in the H I Parkes All-Sky Survey: filling the voids with H I galaxies?

We estimate the two-point correlation function in redshift space of the recently compiled HI Parkes All-Sky Survey neutral hydrogen (HI) sources catalogue, which if modelled as a power law, xi(r) = (r(0)/r)(gamma), the best-fitting parameters for the HI selected galaxies are found to be r(0) = 3.3 +/- 0.3 h(-1) Mpc with gamma = 1.38 +/- 0.24. Fixing the slope to its universal value gamma = 1.8, we obtain r(0) = 3.2 +/- 0.2 h(-1) Mpc. Comparing the measured two-point correlation function with the predictions of the concordance cosmological model (Omega(Lambda) = 0.74), we find that at the present epoch the HI selected galaxies are antibiased with respect to the underlying matter fluctuation field with their bias value being b(0) similar or equal to 0.68. Furthermore, dividing the HI galaxies into two richness subsamples we find that the low-mass HI galaxies have a very low present bias factor (b(0) similar or equal to 0.48), while the high-mass HI galaxies trace the underlying matter distribution as the optical galaxies (b(0) similar or equal to 1). Using our derived present-day HI galaxy bias we estimate their redshift-space distortion parameter, and correct accordingly the correlation function for peculiar motions. The resulting real-space correlation length is r(0)(re) = 1.8 +/- 0.2 h(-1) Mpc r(0)(re) = 3.9 +/- 0.6 h(-1) Mpc for the low- and high-mass HI galaxies, respectively. The low-mass HI galaxies appear to have the lowest correlation length among all extragalactic populations studied to date. In order to corroborate these results we have correlated the IRAS-Point Source Catalogue for Redshift (PSCz) reconstructed density field, smoothed over scales of 5 h(-1) Mpc, with the positions of the HI galaxies, to find that indeed the HI galaxies are typically found in negative overdensity regions (delta rho/rho(PSCz) less than or similar to 0), even more so the low-mass HI galaxies. Finally, we also study the redshift evolution of the HI galaxy linear bias factor and find that the HI-galaxy population is antibiased up to z similar to 1.3. While at large redshifts similar to 3, we predict that the HI galaxies are strongly biased. Our bias evolution predictions are consistent with the observational bias results of Ly alpha galaxies.

Where are z= 4 Lyman Break Galaxies? Results from conditional luminosity function models of luminosity-dependent clustering★

Using the conditional luminosity function (CLF) - the luminosity distribution of galaxies in a dark matter halo - as a way to model galaxy statistics, we study how z = 4 Lyman Break Galaxies (LBGs) are distributed in dark matter haloes. For this purpose, we measure luminosity-dependent clustering of LBGs in the Subaru/XMM-Newton Deep Field by separating a sample of 16 920 galaxies to three magnitude bins in i' band between 24.5 and 27.5. Our model fits to data show a possible trend for more-luminous galaxies to appear as satellites in more-massive haloes; the minimum halo mass in which satellites appear is 3.9 +4.1 -3.5 x 10 12 , 6.2 +3.8 -4.9 × 10 12 and 9.6 +7.0 -4.6 x 10 12 M ⊙ (1σ errors) for galaxies with 26.5 < i' < 27.5, 25.5 < i' < 26.5 and 24.5 < i' < 25.5 mag, respectively. The satellite fraction of galaxies at z = 4 in these magnitude bins is 0.13-0.3, 0.09-0.22 and 0.03-0.14, respectively, where the 1σ ranges account for differences coming from two different estimates of the z = 4 LF from the literature. To jointly explain the LF and the large-scale linear bias factor of z = 4 LBGs as a function of rest UV luminosity requires central galaxies to be brighter in UV at z = 4 than present-day galaxies in same dark matter mass haloes. Moreover, UV luminosity of central galaxies in haloes with total mass greater than roughly 10 12 M ⊙ must decrease from z = 4 to today by an amount more than the luminosity change for galaxies in haloes below this mass. This mass-dependent luminosity evolution is preferred at more than 3σ confidence level compared to a pure-luminosity evolution scenario where all galaxies decrease in luminosity by the same amount from z = 4 to today. The scenario preferred by the data is consistent with the 'downsizing' picture of galaxy evolution.

Have We Detected Patchy Reionization in Quasar Spectra?

The Lyα forest at z 5.5 shows strong scatter in the mean transmission even when smoothed over extremely large spatial scales, 50 Mpc h-1. This has been interpreted as a signature of strongly fluctuating radiation fields or patchy reionization. To test this claim, we calculate the scatter arising solely from density fluctuations, assuming a uniform ionizing background, via analytic arguments and simulations. This scatter alone is comparable to that observed. It rises steeply with redshift and is of order unity by z ~ 6, even on ~50 Mpc h-1 scales. This arises because (1) at z ~ 6, transmission spectra, which are sensitive mainly to rare voids, are highly biased (with a linear bias factor b ≥ 4) tracers of underlying density fluctuations and (2) small-scale transverse modes are aliased to long-wavelength line-of-sight modes. Inferring patchy reionization from quasar spectra is therefore subtle and requires much more detailed modeling. Similarly, we expect density fluctuations alone to produce order unity transmission fluctuations in the z ~ 3 He II Lyα forest on the scales over which these measurements are typically made.

The Three‐Point Correlation Function of Galaxies Determined from the Two‐Degree Field Galaxy Redshift Survey

In a detailed analysis of the three-point correlation function (3PCF) for the 2dF Galaxy Redshift Survey (2dFGRS), we have accurately measured the 3PCF for galaxies of different luminosities. The 3PCF amplitudes [Qred or Qproj ] of the galaxies generally decrease with increasing triangle size and increase with the shape parameter v, in qualitative agreement with the predictions for the clustering of dark matter (DM) in popular hierarchical cold dark matter (CDM) models. The 2dFGRS results agree well with our results for the Las Campanas Redshift Survey (LCRS), although the measurement accuracy is greatly improved in the present study because the 2dFGRS is much larger in size than the LCRS. The dependence of the 3PCF on luminosity is not significant, but there seems to be a trend for the brightest galaxy sample to have a lower amplitude than the fainter ones. Comparing the measured 3PCF amplitudes [Qred or Qproj ] to the prediction of a WMAP (Wilkinson Microwave Anisotropy Probe) concordance model, we find that the measured values are consistently lower than the predicted ones for DM. This is most pronounced for the brightest galaxies (sample I), for which about one-half of the predicted Q-value provides a good description of Qproj for the 2dFGRS data. For the less luminous sample (sample II), the Q-values are also smaller than in the DM model on small scales, but on scales larger than s = 8 h-1 Mpc and rp = 3.25 h-1 Mpc they reach the model values. Therefore, the galaxies of sample II are unbiased tracers on linear scales, but the bright galaxies (sample I) have a linear bias factor of ~1.5. As for the LCRS data, we may state that the best-fit DM model gives higher values for the 3PCF than observed. This indicates that the simple DM models must be refined, by using either more sophisticated bias models or a more sophisticated combination of model parameters.

The angular power spectrum of NVSS radio galaxies

We measure the angular power spectrum of radio galaxies in the NRAO VLA Sky Survey (NVSS) using two independent methods: direct spherical harmonic analysis and maximum likelihood estimation. The results are consistent and can be understood using models for the spatial matter power spectrum and for the redshift distribution of radio galaxies at mJy flux-density levels. A good fit to the angular power spectrum can only be achieved if radio galaxies possess high bias with respect to mass fluctuations; by marginalizing over the other parameters of the model we derive a 68% confidence interval 1.53 < b_0 sigma_8 < 1.87, where b_0 is the linear bias factor for radio galaxies and sigma_8 describes the normalization of the matter power spectrum. Our models indicate that the majority of the signal in the NVSS angular power spectrum is generated at low redshifts. Individual redshifts for the NVSS sources are thus required to alleviate projection effects and probe directly the matter power spectrum on large scales.

Galaxy Bias in Quintessence Cosmological Models

We derive the evolution of the linear bias factor, $b(z)$, in cosmological models driven by an exotic fluid with an equation of state: $p_{x}=w\rho_{x}$, where $-1\le w<0$ (quintessence). Our aim is to put constrains on different cosmological and biasing models by combining the recent observational clustering results of optical ({\em 2dF}) galaxies (Hawkings et al.) with those predicted by the models. We find that our bias model when fitted to the {\em 2dF} clustering results predicts different bias evolution for different values of $w$. The models that provide the weak biasing ($b_{\circ} \sim 1.1$) of optical galaxies found in many recent observational studies are flat, $\Omega_{\rm m}=0.3$ with $w\le -0.9$. These models however, predict a weak redshift evolution of $b(z)$, not corroborated by N-body simulations.