The effect of primordial non-Gaussianity on halo bias (0801.4826v2)

Abstract: It has long been known how to analytically relate the clustering properties of the collapsed structures (halos) to those of the underlying dark matter distribution for Gaussian initial conditions. Here we apply the same approach to physically motivated non-Gaussian models. The techniques we use were developed in the 1980s to deal with the clustering of peaks of non-Gaussian density fields. The description of the clustering of halos for non-Gaussian initial conditions has recently received renewed interest, motivated by the forthcoming large galaxy and cluster surveys. For inflationary-motivated non-Gaussianites, we find an analytic expression for the halo bias as a function of scale, mass and redshift, employing only the approximations of high-peaks and large separations.

• The paper demonstrates how inflationary-motivated non-Gaussian models alter halo bias through analytical derivations.
• It employs high-peaks and large separation approximations to quantify scale-dependent bias, accounting for non-zero three-point correlations.
• The findings offer actionable insights for refining cosmological parameter estimation and understanding early universe conditions.

Analyzing the Influence of Primordial Non-Gaussianity on Halo Bias

The paper "The effect of primordial non-Gaussianity on halo bias" by Sabino Matarrese and Licia Verde addresses the implications of non-Gaussian initial conditions on the clustering behavior of dark matter halos. The authors provide an in-depth analytical strategy to compute halo bias, rooted in the theoretical framework and computational methods devised in the 1980s, extending them to accommodate inflationary-motivated non-Gaussian models. This work is anchored in the context of prospective large-scale galaxy and cluster surveys, which aim to refine our understanding of cosmic structures.

Background and Approach

The paper of halo bias is crucial for understanding cosmic structure formation, providing a direct link between the distribution of dark matter and the observable universe. Traditional models have mostly considered Gaussian initial conditions, which simplify the correlation between dark matter and halos. Matarrese and Verde, however, delve into non-Gaussian models, thereby potentially offering enhanced insights that could be significant for forthcoming galaxy and cluster surveys.

Their methodological framework employs the high-peaks and large separations approximations to derive an analytic expression for the halo bias that varies with scale, mass, and redshift. This approach relies heavily on comprehensive mathematical constructs to extend the Gaussian paradigm to non-Gaussian scenarios.

Analytical Derivations and Numerical Results

The paper mathematically derives the halo bias under non-Gaussian initial conditions, considering the local model for simplicity, but also suggests a generalizable framework for complex non-local models. They analytically express the bias in terms of the halo power spectrum, incorporating a correction factor due to the presence of non-Gaussianity. This correction is attributable to the non-zero three-point correlation functions that are neglected in Gaussian models.

The numerical results, represented graphically in the paper, depict how the non-Gaussian correction creates a perceptible scale-dependent influence on halo bias. For practical illustration, the paper computes the form factor $\mathcal{F}_R(k)$ across varying masses of dark matter halos, demonstrating a distinct scale dependency. Across different redshifts and mass scales, this scale-dependent bias presents as a substantive marker for the signature of non-Gaussianity.

Implications and Future Prospects

Theoretically, the evidence of scale-dependent bias in non-Gaussian models can significantly affect parameter estimation in cosmology, particularly those tied to the early universe's initial conditions and the nature of inflation. Practically, these results have tangible implications for the design and data interpretation of galaxy and cluster surveys. For instance, discerning non-Gaussianity in large volumes could provide critical insights into the early universe's physical processes. Additionally, the findings suggest potential constraints on the non-Gaussianity parameter, $f_{\rm NL}$, which could be refined further with cross-correlation techniques across diverse data sources.

The authors' framework, though constrained to local non-Gaussian models, provides a springboard for analyzing more complex models. Future developments could involve adapting these techniques to accommodate scale-dependent non-Gaussianity and further testing against detailed numerical simulations to ensure the robustness of the analytical predictions.

In conclusion, this work constitutes a pivotal advance in cosmological perturbation theory, reinforcing the necessity for multifaceted models in deciphering the universe's vast structure. The authors set the stage for deeper explorations into non-Gaussian effects in cosmic contexts, which are fundamental to the accurate modeling of the universe's early conditions and subsequent development. As forthcoming observational data become available, these theoretical constructs will undoubtedly play a crucial role in unveiling the intricacies of cosmic evolution.