220 research outputs found
The Halo Mass Function from Excursion Set Theory with a Non-Gaussian Trispectrum
A sizeable level of non-Gaussianity in the primordial cosmological
perturbations may be induced by a large trispectrum, i.e. by a large connected
four-point correlation function. We compute the effect of a primordial
non-Gaussian trispectrum on the halo mass function, within excursion set
theory. We use the formalism that we have developed in a previous series of
papers and which allows us to take into account the fact that, in the presence
of non-Gaussianity, the stochastic evolution of the smoothed density field, as
a function of the smoothing scale, is non-markovian. In the large mass limit,
the leading-order term that we find agrees with the leading-order term of the
results found in the literature using a more heuristic Press-Schecther
(PS)-type approach. Our approach however also allows us to evaluate
consistently the subleading terms, which depend not only on the four-point
cumulant but also on derivatives of the four-point correlator, and which cannot
be obtained within non-Gaussian extensions of PS theory. We perform explicitly
the computation up to next-to-leading order.Comment: LaTeX file, 15 page
Strongly Scale-dependent Non-Gaussianity
We discuss models of primordial density perturbations where the
non-Gaussianity is strongly scale-dependent. In particular, the non-Gaussianity
may have a sharp cut-off and be very suppressed on large cosmological scales,
but sizeable on small scales. This may have an impact on probes of
non-Gaussianity in the large-scale structure and in the cosmic microwave
background radiation anisotropies.Comment: 4 page
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
The halo mass function from excursion set theory with a non-Gaussian trispectrum
A sizeable level of non-Gaussianity in the primordial cosmological perturbations may be induced by a large trispectrum, i.e. by a large connected four-point correlation function. We compute the effect of a primordial non-Gaussian trispectrum on the halo mass function, within excursion set theory. We use the formalism that we have developed in a previous series of papers and which allows us to take into account the fact that, in the presence of non-Gaussianity, the stochastic evolution of the smoothed density field, as a function of the smoothing scale, is non-Markovian. In the large mass limit, the leading-order term that we find agrees with the leading-order term of the results found in the literature using a more heuristic Press-Schechter (PS)-type approach. Our approach however also allows us to evaluate consistently the subleading terms, which depend not only on the four-point cumulant but also on derivatives of the four-point correlator, and which cannot be obtained within non-Gaussian extensions of PS theory. We perform explicitly the computation up to next-to-leading orde
Path Integral Approach to non-Markovian First-Passage Time Problems
The computation of the probability of the first-passage time through a given
threshold of a stochastic process is a classic problem that appears in many
branches of physics. When the stochastic dynamics is markovian, the probability
admits elegant analytic solutions derived from the Fokker-Planck equation with
an absorbing boundary condition while, when the underlying dynamics is
non-markovian, the equation for the probability becomes non-local due to the
appearance of memory terms, and the problem becomes much harder to solve. We
show that the computation of the probability distribution and of the
first-passage time for non-Markovian processes can be mapped into the
evaluation of a path-integral with boundaries, and we develop a technique for
evaluating perturbatively this path integral, order by order in the
non-Markovian terms.Comment: 5 pages, 1 figur
The Halo Mass Function from Excursion Set Theory. II. The Diffusing Barrier
In excursion set theory the computation of the halo mass function is mapped
into a first-passage time process in the presence of a barrier, which in the
spherical collapse model is a constant and in the ellipsoidal collapse model is
a fixed function of the variance of the smoothed density field. However, N-body
simulations show that dark matter halos grow through a mixture of smooth
accretion, violent encounters and fragmentations, and modeling halo collapse as
spherical, or even as ellipsoidal, is a significant oversimplification. We
propose that some of the physical complications inherent to a realistic
description of halo formation can be included in the excursion set theory
framework, at least at an effective level, by taking into account that the
critical value for collapse is not a fixed constant , as in the
spherical collapse model, nor a fixed function of the variance of the
smoothed density field, as in the ellipsoidal collapse model, but rather is
itself a stochastic variable, whose scatter reflects a number of complicated
aspects of the underlying dynamics. Solving the first-passage time problem in
the presence of a diffusing barrier we find that the exponential factor in the
Press-Schechter mass function changes from to
, where and is the
diffusion coefficient of the barrier. The numerical value of , and
therefore the corresponding value of , depends among other things on the
algorithm used for identifying halos. We discuss the physical origin of the
stochasticity of the barrier and we compare with the mass function found in
N-body simulations, for the same halo definition.[Abridged]Comment: 7 pages, 5 figures. v3: significant conceptual improvements. More
detailed comparison with N-body simulations. References adde
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
The bias and mass function of dark matter haloes 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 perturbatively these corrections to the standard Markovian predictions for the halo mass function and halo bias. Our model contains only two parameters: κ, which parametrizes 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 parametrizes the degree of stochasticity of the barrier. Appropriate choices of κ and a in our new model can lead to a closer match to both the halo mass function and the halo bias in the latest N-body simulations than the standard excursion set theor
Gravitational Waves from Electroweak Phase Transitions
Gravitational waves are generated during first-order phase transitions,
either by turbolence or by bubble collisions. If the transition takes place at
temperatures of the order of the electroweak scale, the frequency of these
gravitational waves is today just within the band of the planned space
interferometer LISA. We present a detailed analysis of the production of
gravitational waves during an electroweak phase transition in different
supersymmetric models where, contrary to the case of the Standard Model, the
transition can be first order. We find that the stochastic background of
gravitational waves generated by bubble nucleation can reach a maximum value
h0^2 Omega_{gw} of order 10^{-10} - 10^{-11}, which is within the reach of the
planned sensitivity of LISA, while turbolence can even produce signals at the
level h0^2 Omega_{gw} \sim 10^{-9}. These values of h0^2 Omega_{gw} are
obtained in the regions of the parameter space which can account for the
generation of the baryon asymmetry at the electroweak scale.Comment: 30 pages, 20 figure
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