Abstract
When dealing with observables, one needs to generalize the bias relation between the observed galaxy fluctuation field to the underlying matter distribution in a gauge-invariant way. We provide such relation at second-order in perturbation theory adopting the local Eulerian bias model and starting from the observationally motivated uniform-redshift gauge. Our computation includes the presence of primordial non-Gaussianity. We show that large scale-dependent relativistic effects in the Eulerian bias arise independently from the presence of some primordial non-Gaussianity. Furthermore, the Eulerian bias inherits from the primordial non-Gaussianity not only a scale-dependence, but also a modulation with the angle of observation when sources with different biases are correlated.
Highlights
Cosmological inflation [1] has become the dominant paradigm to understand the initial conditions for the Cosmic Microwave Background (CMB) anisotropies and Large Scale Structure (LSS) formation
There is a distinction between quantities that are automatically gauge-independent, i.e., those that have no gauge dependence, and quantities that are in general gauge-dependent but can have a gauge-invariant definition once their gauge-dependence is fixed
In this paper we have described the computation of the Eulerian bias at second-order in perturbation theory
Summary
Cosmological inflation [1] has become the dominant paradigm to understand the initial conditions for the Cosmic Microwave Background (CMB) anisotropies and Large Scale Structure (LSS) formation. Present and future [3] data may be sensitive to the non-linearities of the cosmological perturbations at the level of second- or higher-order perturbation theory. The detection of these non-linearities through the non-Gaussianity (NG) [4] has become one of the primary experimental targets. In this paper we address these points and show that a refined gauge-invariant treatment of the Eulerian bias at second-order in perturbation theory leads to the prediction that the bias is scale-dependent on large scales even in the absence of primordial NG and that the latter generates an angular modulation if sources with different biases are cross-correlated.
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