Non-Gaussian Mass functions and halo bias

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The description of the abundance and clustering of halos for non-Gaussian initial conditions has recently received renewed interest. In fact future surveys could potentially yield constraints of order unity on the non gaussianity parameter fNL. Here fNL parameterizes departures from Gaussian initial conditions of the type called "local non-Gaussianity". Values of fNL of order unity or larger are predicted in many inflationary models. There are two teoretically motivated and analytically-derived expressions for the non gaussian mass function.

MVJ Matarrese, Verde, Jimenez, 2000, ApJ, 541, 10

LoVerde et al 2008 LoVerde, Miller, Shandera, Verde, 2008, JCAP, 04, 014

These mass functions have been tested and calibrated on n-body simulations in Grossi et al 2009.

Both expressions for the mass function have been derived within the Press Schecter approach: they should be used to compute the ratio, R, between the non-Gaussian and the Gaussian mass function. Then, to obtain a non-gaussian mass function this ratio should be multiplied by a form of the Gaussian mass function that has been extensively tested and calibrated on simulations such as the Sheth and Tormen (1999), Jenkins et al (2001) or Warren et al (2006). The figure shows the ratio R for fNL values of 100 and -100. Points are from the simulations of Grossi et al. (2009). Here we provide all the necessary inputs to compute these mass functions for a LCDM cosmology. Note that we use the large-scale structure convention for fNL. More information in the readme file.

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Primordial non gaussianity has also an effect on the large scale clustering of halos, the effect is called "non-Gaussian halo bias". See Dalal et al. (2008) and Matarrese & Verde (2008) for details. Primordial non-Gaussianity of the local type introduces a strongly scale-dependent and redshift dependent halo bias on large scales. In the figure for example we show the effect of fNL=+50 and -50 on the power spectrum at z=0 for halo of masses above 1.d13 solar masses. This has also been calibrated on N-body simulations in Grossi et al. (2009). Here we also provide the necessary inputs to compute this effect for a LCDM cosmology. Note that we use the large-scale structure convention for fNL. Please see the readme file for details.

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If you use these files in your publications, please reference the above papers.
Contact liciaverde[at]icc.ua.edu, carbone[at]ieec.uab.es, margot[at]mpa-garching.mpg.de if you have any questions.