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Characterizing the level of primordial non-Gaussianity (PNG) in the initialconditions for structure formation is one of the most promising ways to testinflation and differentiate among different scenarios. The scale-dependentimprint of PNG on the large-scale clustering of galaxies and quasars hasalready been used to place significant constraints on the level of PNG in ourobserved Universe. Such measurements depend upon an accurate and robust theoryof how PNG affects the bias of galactic halos relative to the underlying matterdensity field. We improve upon previous work by employing a more generalanalytical method - the path-integral extension of the excursion set formalism- which is able to account for the non-Markovianity caused by PNG in therandom-walk model used to identify halos in the initial density field. Thisnon-Markovianity encodes information about environmental effects on haloformation which have so far not been taken into account in analytical biascalculations. We compute both scale-dependent and -independent corrections tothe halo bias, along the way presenting an expression for the conditionalcollapsed fraction for the first time, and a new expression for the conditionalhalo mass function. To leading order in our perturbative calculation, werecover the halo bias results of Desjacques et. al. (2011), including the newscale-dependent correction reported there. However, we show that thenon-Markovian dynamics from PNG can lead to marked differences in halo biaswhen next-to-leading order terms are included. We quantify these differenceshere. [abridged]

monthly notices of the royal astronomical society

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