Halo statistics in non-Gaussian cosmologies: the collapsed fraction, conditional mass function, and halo bias from the path-integral excursion set method

Abstract

Characterizing the level of primordial non-Gaussianity (PNG) in the initial conditions for structure formation is one of the most promising ways to test inflation and differentiate among different scenarios. The scale-dependent imprint of PNG on the large-scale clustering of galaxies and quasars has already been used to place significant constraints on the level of PNG in our observed Universe. Such measurements depend upon an accurate and robust theory of how PNG affects the bias of galactic halos relative to the underlying matter density field. We improve upon previous work by employing a more general analytical method - the path-integral extension of the excursion set formalism - which is able to account for the non-Markovianity caused by PNG in the random-walk model used to identify halos in the initial density field. This non-Markovianity encodes information about environmental effects on halo formation which have so far not been taken into account in analytical bias calculations. We compute both scale-dependent and -independent corrections to the halo bias, along the way presenting an expression for the conditional collapsed fraction for the first time, and a new expression for the conditional halo mass function. To leading order in our perturbative calculation, we recover the halo bias results of Desjacques et. al. (2011), including the new scale-dependent correction reported there. However, we show that the non-Markovian dynamics from PNG can lead to marked differences in halo bias when next-to-leading order terms are included. We quantify these differences here. [abridged]

Accepted for publication in MNRAS. Includes minor revisions recommended by referee, slightly revised notation for clarity, and corrected typos

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• Primordial Non-Gaussianity Estimation using 21 cm Tomography from the Epoch of Reionization
• Primordial Non-Gaussianity and Reionization
• Testing Multi-Field Inflation with Galaxy Bias
• Excursion Set Theory for Correlated Random Walks
• Imprint of primordial non-Gaussianity on dark matter halo profiles
• Effect of Priomordial non-Gaussianities on Galaxy Clusters Scaling Relations
• 21-cm power spectrum and ionization bias as a probe of long-mode modulated non Gaussian sky