The Bias and Mass Function of Dark Matter Halos in Non-Markovian Extension of the Excursion Set Theory

The excursion set theory based on spherical or ellipsoidal gravitational collapse provides an elegant analytic framework for calculating the mass function and the large-scale bias of dark matter haloes. This theory assumes that the perturbed density field evolves stochastically with the smoothing scale and exhibits Markovian random walks in the presence of a density barrier. Here we derive an analytic expression for the halo bias in a new theoretical model that incorporates non-Markovian extension of the excursion set theory with a stochastic barrier. This model allows us to handle non-Markovian random walks and to calculate perturbativly these corrections to the standard Markovian predictions for the halo mass function and halo bias. Our model contains only two parameters: kappa, which parameterizes the degree of non-Markovianity and whose exact value depends on the shape of the filter function used to smooth the density field, and a, which parameterizes the degree of stochasticity of the barrier. Appropriate choices of kappa and a in our new model can lead to a closer match to both the halo mass function and halo bias in the latest N-body simulations than the standard excursion set theory.Comment: 10 pages, 1 figure, MNRAS, in press. Minor change

Excursion set theory for generic moving barriers and non-Gaussian initial conditions

Excursion set theory, where density perturbations evolve stochastically with the smoothing scale, provides a method for computing the mass function of cosmological structures like dark matter haloes, sheets and filaments. The computation of these mass functions is mapped into the so-called first-passage time problem in the presence of a moving barrier. In this paper we use the path-integral formulation of the excursion set theory developed recently to analytically solve the first-passage time problem in the presence of a generic moving barrier, in particular the barrier corresponding to ellipsoidal collapse. We perform the computation for both Gaussian and non-Gaussian initial conditions and for a window function which is a top-hat in wavenumber space. The expression of the halo mass function for the ellipsoidal collapse barrier and with non-Gaussianity is therefore obtained in a fully consistent way and it does not require the introduction of any form factor artificially derived from the Press-Schechter formalism based on the spherical collapse and usually adopted in the literatur

Conditional probabilities in the excursion set theory: generic barriers and non-Gaussian initial conditions

The excursion set theory, where density perturbations evolve stochastically with the smoothing scale, provides a method for computing the dark matter halo mass function. The computation of the mass function is mapped into the so-called first-passage time problem in the presence of a moving barrier. The excursion set theory is also a powerful formalism to study other properties of dark matter haloes such as halo bias, accretion rate, formation time, merging rate and the formation history of haloes. This is achieved by computing conditional probabilities with non-trivial initial conditions, and the conditional two-barrier first-crossing rate. In this paper we use the path integral formulation of the excursion set theory to calculate analytically these conditional probabilities in the presence of a generic moving barrier, including the one describing the ellipsoidal collapse, and for both Gaussian and non-Gaussian initial conditions. While most of our analysis associated with Gaussian initial conditions assumes Markovianity (top-hat in momentum space smoothing, rather than generic filters), the non-Markovianity of the random walks induced by non-Gaussianity is consistently accounted for. We compute, for a generic barrier, the first two scale-independent halo bias parameters, the conditional mass function and the halo formation time probability, including the effects of non-Gaussianities. We also provide the expression for the two-constant-barrier first-crossing rate when non-Markovian effects are induced by a top-hat filter function in real spac

Conditional probabilities in the excursion set theory: generic barriers and non-Gaussian initial conditions

The excursion set theory, where density perturbations evolve stochastically with the smoothing scale, provides a method for computing the dark matter halo mass function. The computation of the mass function is mapped into the so-called first-passage time problem in the presence of a moving barrier. The excursion set theory is also a powerful formalism to study other properties of dark matter haloes such as halo bias, accretion rate, formation time, merging rate and the formation history of haloes. This is achieved by computing conditional probabilities with non-trivial initial conditions, and the conditional two-barrier first-crossing rate. In this paper we use the path integral formulation of the excursion set theory to calculate analytically these conditional probabilities in the presence of a generic moving barrier, including the one describing the ellipsoidal collapse, and for both Gaussian and non-Gaussian initial conditions. While most of our analysis associated with Gaussian initial conditions assumes Markovianity (top-hat in momentum space smoothing, rather than generic filters), the non-Markovianity of the random walks induced by non-Gaussianity is consistently accounted for. We compute, for a generic barrier, the first two scale-independent halo bias parameters, the conditional mass function and the halo formation time probability, including the effects of non-Gaussianities. We also provide the expression for the two-constant-barrier first-crossing rate when non-Markovian effects are induced by a top-hat filter function in real space

Halo abundances and counts-in-cells: The excursion set approach with correlated steps

The Excursion Set approach has been used to make predictions for a number of interesting quantities in studies of nonlinear hierarchical clustering. These include the halo mass function, halo merger rates, halo formation times and masses, halo clustering, analogous quantities for voids, and the distribution of dark matter counts in randomly placed cells. The approach assumes that all these quantities can be mapped to problems involving the first crossing distribution of a suitably chosen barrier by random walks. Most analytic expressions for these distributions ignore the fact that, although different k-modes in the initial Gaussian field are uncorrelated, this is not true in real space: the values of the density field at a given spatial position, when smoothed on different real-space scales, are correlated in a nontrivial way. As a result, the problem is to estimate first crossing distribution by random walks having correlated rather than uncorrelated steps. In 1990, Peacock & Heavens presented a simple approximation for the first crossing distribution of a single barrier of constant height by walks with correlated steps. We show that their approximation can be thought of as a correction to the distribution associated with what we call smooth completely correlated walks. We then use this insight to extend their approach to treat moving barriers, as well as walks that are constrained to pass through a certain point before crossing the barrier. For the latter, we show that a simple rescaling, inspired by bivariate Gaussian statistics, of the unconditional first crossing distribution, accurately describes the conditional distribution, independently of the choice of analytical prescription for the former. In all cases, comparison with Monte-Carlo solutions of the problem shows reasonably good agreement. (Abridged)Comment: 14 pages, 9 figures; v2 -- revised version with explicit demonstration that the original conclusions hold for LCDM, expanded discussion on stochasticity of barrier. Accepted in MNRA

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

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]Comment: Accepted for publication in MNRAS. Includes minor revisions recommended by referee, slightly revised notation for clarity, and corrected typo

Transvaginal ultrasonography with vs without bowel preparation in the diagnosis of rectosigmoid endometriosis: prospective study

Objectives: The primary aim of this study was to compare the diagnostic accuracy of transvaginal sonography (TVS) with vs without bowel preparation (BP) in detecting the presence of rectosigmoid endometriosis. Secondary objectives were to compare the diagnostic accuracy of the two techniques in estimating infiltration of the submucosa, length of the largest rectosigmoid nodules, distance of the nodules from the anal verge and presence of multifocal disease. Methods: This was a prospective study of patients with symptoms of pelvic pain for more than 6 months and/or suspicion of endometriosis referred to our institution between October 2016 and April 2018. Participants underwent a first TVS without BP followed by TVS with BP within a time interval of 1 week to 3 months. The examinations were performed independently and blindly by two sonographers. Only patients who underwent laparoscopy within the 6 months following the second ultrasound examination were included. Ultrasound results using the two techniques were compared with surgical and histological findings. Results: Of the 262 patients included in the study, 118 had rectosigmoid endometriosis confirmed at surgery. There was no significant difference in accuracy between TVS with and that without BP in diagnosing the presence of rectosigmoid endometriosis (93.5% vs 92.3%; P = 0.453). No significant difference was observed in accuracy between TVS with and that without BP in diagnosing submucosal infiltration (88.8% vs 84.6%; P = 0.238) and multifocal disease (97.2% vs 95.2%; P = 0.727) in patients diagnosed sonographically with rectosigmoid endometriosis. The accuracy of TVS with BP was similar to that of TVS without BP in estimating the maximum diameter of the largest nodule (P = 0.644) and the distance between the more caudal rectosigmoid nodule and the anal verge (P = 0.162). Conclusion: BP does not improve the diagnostic performance of TVS in detecting rectosigmoid endometriosis and in assessing characteristics of endometriotic nodules

Perturbative and non-perturbative aspects of the two-dimensional string/Yang-Mills correspondence

It is known that YM_2 with gauge group SU(N) is equivalent to a string theory with coupling g_s=1/N, order by order in the 1/N expansion. We show how this results can be obtained from the bosonization of the fermionic formulation of YM_2, improving on results in the literature, and we examine a number of non-perturbative aspects of this string/YM correspondence. We find contributions to the YM_2 partition function of order exp{-kA/(\pi\alpha' g_s)} with k an integer and A the area of the target space, which would correspond, in the string interpretation, to D1-branes. Effects which could be interpreted as D0-branes are instead stricly absent, suggesting a non-perturbative structure typical of type 0B string theories. We discuss effects from the YM side that are interpreted in terms of the stringy exclusion principle of Maldacena and Strominger. We also find numerically an interesting phase structure, with a region where YM_2 is described by a perturbative string theory separated from a region where it is described by a topological string theory.Comment: 24 pages, 5 figure