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We present a simple heuristic model to demonstrate how feedback related to the galaxy formation process can result in a scale-dependent bias of mass versus light, even on very large scales. The model invokes the idea that galaxies form initially in locations determined by the local density field, but the subsequent formation of galaxies is also influenced by the presence of nearby galaxies that have already formed. The form of bias that results possesses some features that are usually described in terms of stochastic effects, but our model is entirely deterministic once the density field is specified. Features in the large-scale galaxy power spectrum (such as wiggles that might in an extreme case mimic the effect of baryons on the primordial transfer function) could, at least in principle, arise from spatial modulations of the galaxy formation process that arise naturally in our model. We also show how this fully deterministic model gives rise to apparently stochasticity in the galaxy distribution.
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We forecast the future constraints on scale-dependent parametrizations of galaxy bias and their impact on the estimate of cosmological parameters from the power spectrum of galaxies measured in a spectroscopic redshift survey. For the latter we assume a wide survey at relatively large redshifts, similar to the planned Euclid survey, as baseline for future experiments. To assess the impact of the bias we perform a Fisher matrix analysis and we adopt two different parametrizations of scale-dependent bias. The fiducial models for galaxy bias are calibrated using a mock catalogs of H$alpha$ emitting galaxies mimicking the expected properties of the objects that will be targeted by the Euclid survey. In our analysis we have obtained two main results. First of all, allowing for a scale-dependent bias does not significantly increase the errors on the other cosmological parameters apart from the rms amplitude of density fluctuations, $sigma_{8}$, and the growth index $gamma$, whose uncertainties increase by a factor up to two, depending on the bias model adopted. Second, we find that the accuracy in the linear bias parameter $b_{0}$ can be estimated to within 1-2% at various redshifts regardless of the fiducial model. The non-linear bias parameters have significantly large errors that depend on the model adopted. Despite of this, in the more realistic scenarios departures from the simple linear bias prescription can be detected with a $sim2,sigma$ significance at each redshift explored. Finally, we use the Fisher Matrix formalism to assess the impact of assuming an incorrect bias model and found that the systematic errors induced on the cosmological parameters are similar or even larger than the statistical ones.
We present a mitigation strategy to reduce the impact of non-linear galaxy bias on the joint `$3 times 2 $pt cosmological analysis of weak lensing and galaxy surveys. The $Psi$-statistics that we adopt are based on Complete Orthogonal Sets of E/B Integrals (COSEBIs). As such they are designed to minimise the contributions to the observable from the smallest physical scales where models are highly uncertain. We demonstrate that $Psi$-statistics carry the same constraining power as the standard two-point galaxy clustering and galaxy-galaxy lensing statistics, but are significantly less sensitive to scale-dependent galaxy bias. Using two galaxy bias models, motivated by halo-model fits to data and simulations, we quantify the error in a standard $3 times 2$pt analysis where constant galaxy bias is assumed. Even when adopting conservative angular scale cuts, that degrade the overall cosmological parameter constraints, we find of order $1 sigma$ biases for Stage III surveys on the cosmological parameter $S_8 = sigma_8(Omega_{rm m}/0.3)^{alpha}$. This arises from a leakage of the smallest physical scales to all angular scales in the standard two-point correlation functions. In contrast, when analysing $Psi$-statistics under the same approximation of constant galaxy bias, we show that the bias on the recovered value for $S_8$ can be decreased by a factor of $sim 2$, with less conservative scale cuts. Given the challenges in determining accurate galaxy bias models in the highly non-linear regime, we argue that $3 times 2$pt analyses should move towards new statistics that are less sensitive to the smallest physical scales.
Baryonic acoustic oscillations (BAOs) modulate the density ratio of baryons to dark matter across large regions of the Universe. We show that the associated variation in the mass-to-light ratio of galaxies should generate an oscillatory, scale-dependent bias of galaxies relative to the underlying distribution of dark matter. A measurement of this effect would calibrate the dependence of the characteristic mass-to-light ratio of galaxies on the baryon mass fraction in their large scale environment. This bias, though, is unlikely to significantly affect measurements of BAO peak positions.
Primordial non-Gaussianity introduces a scale-dependent variation in the clustering of density peaks corresponding to rare objects. This variation, parametrized by the bias, is investigated on scales where a linear perturbation theory is sufficiently accurate. The bias is obtained directly in real space by comparing the one- and two-point probability distributions of density fluctuations. We show that these distributions can be reconstructed using a bivariate Edgeworth series, presented here up to an arbitrarily high order. The Edgeworth formalism is shown to be well-suited for local cubic-order non-Gaussianity parametrized by g_NL. We show that a strong scale-dependence in the bias can be produced by g_NL of order 10,000, consistent with CMB constraints. On correlation length of ~100 Mpc, current constraints on g_NL still allow the bias for the most massive clusters to be enhanced by 20-30% of the Gaussian value. We further examine the bias as a function of mass scale, and also explore the relationship between the clustering and the abundance of massive clusters in the presence of g_NL. We explain why the Edgeworth formalism, though technically challenging, is a very powerful technique for constraining high-order non-Gaussianity with large-scale structures.
We measure the large-scale bias of dark matter halos in simulations with non-Gaussian initial conditions of the local type, and compare this bias to the response of the mass function to a change in the primordial amplitude of fluctuations. The two are found to be consistent, as expected from physical arguments, for three halo-finder algorithms which use different Spherical Overdensity (SO) and Friends-of-Friends (FoF) methods. On the other hand, we find that the commonly used prediction for universal mass functions, that the scale-dependent bias is proportional to the first-order Gaussian Lagrangian bias, does not yield a good agreement with the measurements. For all halo finders, high-mass halos show a non-Gaussian bias suppressed by 10-15% relative to the universal mass function prediction. For SO halos, this deviation changes sign at low masses, where the non-Gaussian bias becomes larger than the universal prediction.
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