37 research outputs found
Moment transport equations for the primordial curvature perturbation
In a recent publication, we proposed that inflationary perturbation theory
can be reformulated in terms of a probability transport equation, whose moments
determine the correlation properties of the primordial curvature perturbation.
In this paper we generalize this formulation to an arbitrary number of fields.
We deduce ordinary differential equations for the evolution of the moments of
zeta on superhorizon scales, which can be used to obtain an evolution equation
for the dimensionless bispectrum, fNL. Our equations are covariant in field
space and allow identification of the source terms responsible for evolution of
fNL. In a model with M scalar fields, the number of numerical integrations
required to obtain solutions of these equations scales like O(M^3). The
performance of the moment transport algorithm means that numerical calculations
with M >> 1 fields are straightforward. We illustrate this performance with a
numerical calculation of fNL in Nflation models containing M ~ 10^2 fields,
finding agreement with existing analytic calculations. We comment briefly on
extensions of the method beyond the slow-roll approximation, or to calculate
higher order parameters such as gNL.Comment: 23 pages, plus appendices and references; 4 figures. v2: incorrect
statements regarding numerical delta N removed from Sec. 4.3. Minor
modifications elsewher
Primordial Non-Gaussianity and Extreme-Value Statistics of Galaxy Clusters
What is the size of the most massive object one expects to find in a survey
of a given volume? In this paper, we present a solution to this problem using
Extreme-Value Statistics, taking into account primordial non-Gaussianity and
its effects on the abundance and the clustering of rare objects. We calculate
the probability density function (pdf) of extreme-mass clusters in a survey
volume, and show how primordial non-Gaussianity shifts the peak of this pdf. We
also study the sensitivity of the extreme-value pdfs to changes in the mass
functions, survey volume, redshift coverage and the normalization of the matter
power spectrum, {\sigma}_8. For 'local' non-Gaussianity parametrized by f_NL,
our correction for the extreme-value pdf due to the bias is important when f_NL
> O(100), and becomes more significant for wider and deeper surveys. Applying
our formalism to the massive high-redshift cluster XMMUJ0044.0-2-33, we find
that its existence is consistent with f_NL = 0, although the conclusion is
sensitive to the assumed values of the survey area and {\sigma}_8. We also
discuss the convergence of the extreme-value distribution to one of the three
possible asymptotic forms, and argue that the convergence is insensitive to the
presence of non-Gaussianity.Comment: Revised version, 20 pages, 10 figures. Major improvement in the
treatment of non-Gaussian bias. Previous claim of large f_NL associated with
the cluster is no longer supporte
On the modelling of the excesses of galaxy clusters over high-mass thresholds
In this work we present for the first time an application of the Pareto
approach to the modelling of the excesses of galaxy clusters over high-mass
thresholds. The distribution of those excesses can be described by the
generalized Pareto distribution (GPD), which is closely related to the
generalized extreme value (GEV) distribution. After introducing the formalism,
we study the impact of different thresholds and redshift ranges on the
distributions, as well as the influence of the survey area on the mean excess
above a given mass threshold. We also show that both the GPD and the GEV
approach lead to identical results for rare, thus high-mass and high-redshift,
clusters. As an example, we apply the Pareto approach to ACT-CL J0102-4915 and
SPT-CL J2106-5844 and derive the respective cumulative distribution functions
of the exceedance over different mass thresholds. We also study the possibility
to use the GPD as a cosmological probe. Since in the maximum likelihood
estimation of the distribution parameters all the information from clusters
above the mass threshold is used, the GPD might offer an interesting
alternative to GEV-based methods that use only the maxima in patches. When
comparing the accuracy with which the parameters can be estimated, it turns out
that the patch-based modelling of maxima is superior to the Pareto approach. In
an ideal case, the GEV approach is capable to estimate the location parameter
with a percent level precision for less than 100 patches. This result makes the
GEV based approach potentially also interesting for cluster surveys with a
smaller area.Comment: 10 pages, 8 figures, MNRAS accepted, minor modifications to match the
accepted versio
Scale Dependence of the Halo Bias in General Local-Type Non-Gaussian Models I: Analytical Predictions and Consistency Relations
We investigate the clustering of halos in cosmological models starting with
general local-type non-Gaussian primordial fluctuations. We employ multiple
Gaussian fields and add local-type non-Gaussian corrections at arbitrary order
to cover a class of models described by frequently-discussed f_nl, g_nl and
\tau_nl parameterization. We derive a general formula for the halo power
spectrum based on the peak-background split formalism. The resultant spectrum
is characterized by only two parameters responsible for the scale-dependent
bias at large scale arising from the primordial non-Gaussianities in addition
to the Gaussian bias factor. We introduce a new inequality for testing
non-Gaussianities originating from multi fields, which is directly accessible
from the observed power spectrum. We show that this inequality is a
generalization of the Suyama-Yamaguchi inequality between f_nl and \tau_nl to
the primordial non-Gaussianities at arbitrary order. We also show that the
amplitude of the scale-dependent bias is useful to distinguish the simplest
quadratic non-Gaussianities (i.e., f_nl-type) from higher-order ones (g_nl and
higher), if one measures it from multiple species of galaxies or clusters of
galaxies. We discuss the validity and limitations of our analytic results by
comparison with numerical simulations in an accompanying paper.Comment: 25 pages, 3 figures, typo corrected, Appendix C updated, submitted to
JCA
Scale-dependent bias from the primordial non-Gaussianity with a Gaussian-squared field
We investigate the halo bias in the case where the primordial curvature
fluctuations, , are sourced from both a Gaussian random field and a
Gaussian-squared field, as , so-called "ungaussiton model". We employ the
peak-background split formula and find a new scale-dependence in the halo bias
induced from the Gaussian-squared field.Comment: 9 pages, 1 figure, comments are welcom
Primordial Black Holes, Eternal Inflation, and the Inflationary Parameter Space after WMAP5
We consider constraints on inflation driven by a single, minimally coupled
scalar field in the light of the WMAP5 dataset, as well as ACBAR and the
SuperNova Legacy Survey. We use the Slow Roll Reconstruction algorithm to
derive optimal constraints on the inflationary parameter space. The scale
dependence in the slope of the scalar spectrum permitted by WMAP5 is large
enough to lead to viable models where the small scale perturbations have a
substantial amplitude when extrapolated to the end of inflation. We find that
excluding parameter values which would cause the overproduction of primordial
black holes or even the onset of eternal inflation leads to potentially
significant constraints on the slow roll parameters. Finally, we present a more
sophisticated approach to including priors based on the total duration of
inflation, and discuss the resulting restrictions on the inflationary parameter
space.Comment: v2: version published in JCAP. Minor clarifications and references
adde
New Solutions of the Inflationary Flow Equations
The inflationary flow equations are a frequently used method of surveying the
space of inflationary models. In these applications the infinite hierarchy of
differential equations is truncated in a way which has been shown to be
equivalent to restricting the set of models considered to those characterized
by polynomial inflaton potentials. This paper explores a different method of
solving the flow equations, which does not truncate the hierarchy and in
consequence covers a much wider class of models while retaining the practical
usability of the standard approach.Comment: References added, and a couple of comment
in interacting quintessence model
A model consisting of quintessence scalar field interacting with cold dark
matter is considered. Conditions required to reach are discussed. It
is shown that depending on the potential considered for the quintessence,
reaching the phantom divide line puts some constraints on the interaction
between dark energy and dark matter. This also may determine the ratio of dark
matter to dark energy density at .Comment: 10 pages, references updated, some notes added, minor changes
applied, accepted for publication in Eur. Phys. J.
A critical analysis of high-redshift, massive galaxy clusters: I
We critically investigate current statistical tests applied to high redshift
clusters of galaxies in order to test the standard cosmological model and
describe their range of validity. We carefully compare a sample of
high-redshift, massive, galaxy clusters with realistic Poisson sample
simulations of the theoretical mass function, which include the effect of
Eddington bias. We compare the observations and simulations using the following
statistical tests: the distributions of ensemble and individual existence
probabilities (in the >M,>z sense), the redshift distributions, and the 2d
Kolmogorov-Smirnov test. Using seemingly rare clusters from Hoyle et al.
(2011), and Jee et al. (2011) and assuming the same survey geometry as in Jee
et al. (2011, which is less conservative than Hoyle et al. 2011), we find that
the (>M,>z) existence probabilities of all clusters are fully consistent with
LCDM. However assuming the same survey geometry, we use the 2d K-S test
probability to show that the observed clusters are not consistent with being
the least probable clusters from simulations at >95% confidence, and are also
not consistent with being a random selection of clusters, which may be caused
by the non-trivial selection function and survey geometry. Tension can be
removed if we examine only a X-ray selected sub sample, with simulations
performed assuming a modified survey geometry.Comment: 20 pages, 6 figures, 2 tables, modified to match accepted version
(JCAP); title changed, main analysis unchanged, additional analysi
Scale-dependent non-Gaussianity probes inflationary physics
We calculate the scale dependence of the bispectrum and trispectrum in
(quasi) local models of non-Gaussian primordial density perturbations, and
characterize this scale dependence in terms of new observable parameters. They
can help to discriminate between models of inflation, since they are sensitive
to properties of the inflationary physics that are not probed by the standard
observables. We find consistency relations between these parameters in certain
classes of models. We apply our results to a scenario of modulated reheating,
showing that the scale dependence of non-Gaussianity can be significant. We
also discuss the scale dependence of the bispectrum and trispectrum, in cases
where one varies the shape as well as the overall scale of the figure under
consideration. We conclude providing a formulation of the curvature
perturbation in real space, which generalises the standard local form by
dropping the assumption that f_NL and g_NL are constants.Comment: 27 pages, 2 figures. v2: Minor changes to match the published versio