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

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, $\Phi$, are sourced from both a Gaussian random field and a Gaussian-squared field, as $\Phi({\bf x}) = \phi({\bf x}) + \psi({\bf x})^2 -$, 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

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

COrE (Cosmic Origins Explorer) A White Paper

COrE (Cosmic Origins Explorer) is a fourth-generation full-sky, microwave-band satellite recently proposed to ESA within Cosmic Vision 2015-2025. COrE will provide maps of the microwave sky in polarization and temperature in 15 frequency bands, ranging from 45 GHz to 795 GHz, with an angular resolution ranging from 23 arcmin (45 GHz) and 1.3 arcmin (795 GHz) and sensitivities roughly 10 to 30 times better than PLANCK (depending on the frequency channel). The COrE mission will lead to breakthrough science in a wide range of areas, ranging from primordial cosmology to galactic and extragalactic science. COrE is designed to detect the primordial gravitational waves generated during the epoch of cosmic inflation at more than $3\sigma$ for $r=(T/S)>=10^{-3}$. It will also measure the CMB gravitational lensing deflection power spectrum to the cosmic variance limit on all linear scales, allowing us to probe absolute neutrino masses better than laboratory experiments and down to plausible values suggested by the neutrino oscillation data. COrE will also search for primordial non-Gaussianity with significant improvements over Planck in its ability to constrain the shape (and amplitude) of non-Gaussianity. In the areas of galactic and extragalactic science, in its highest frequency channels COrE will provide maps of the galactic polarized dust emission allowing us to map the galactic magnetic field in areas of diffuse emission not otherwise accessible to probe the initial conditions for star formation. COrE will also map the galactic synchrotron emission thirty times better than PLANCK. This White Paper reviews the COrE science program, our simulations on foreground subtraction, and the proposed instrumental configuration.Comment: 90 pages Latex 15 figures (revised 28 April 2011, references added, minor errors corrected

The Hierarchical Structure and Dynamics of Voids

Contrary to the common view voids have very complex internal structure and dynamics. Here we show how the hierarchy of structures in the density field inside voids is reflected by a similar hierarchy of structures in the velocity field. Voids defined by dense filaments and clusters can de described as simple expanding domains with coherent flows everywhere except at their boundaries. At scales smaller that the void radius the velocity field breaks into expanding sub-domains corresponding to sub- voids. These sub-domains break into even smaller sub-sub domains at smaller scales resulting in a nesting hierarchy of locally expanding domains. The ratio between the magnitude of the velocity field responsible for the expansion of the void and the velocity field defining the sub voids is approximately one order of magnitude. The small-scale components of the velocity field play a minor role in the shaping of the voids but they define the local dynamics directly affecting the processes of galaxy formation and evolution. The super-Hubble expansion inside voids makes them cosmic magnifiers by stretching their internal primordial density fluctuations allowing us to probe the small scales in the primordial density field. Voids also act like time machines by "freezing" the development of the medium-scale density fluctuations responsible for the formation of the tenuous web of structures seen connecting proto galaxies in computer simulations. As a result of this freezing haloes in voids can remain "connected" to this tenuous web until the present time. This may have an important effect in the formation and evolution of galaxies in voids by providing an efficient gas accretion mechanism via coherent low-velocity streams that can keep a steady inflow of matter for extended periods of time.Comment: High-res version are related media here: http://skysrv.pha.jhu.edu/~miguel/Papers/Hierarchy_voids/index.htm