Curvature-driven Molecular Demixing in the Budding and Breakup of Mixed Component Worm-like Miscelles

Amphiphilic block copolymers of suitable proportions can self-assemble into surprisingly long and stable worm-like micelles, but the intrinsic polydispersity of polymers as well as polymer blending efforts and the increasing use of degradable chains all raise basic questions of curvature–composition coupling and morphological stability of these high curvature assemblies. Molecular simulations here of polyethylene glycol (PEG) based systems show that a systematic increase in the hydrated PEG fraction, in both monodisperse and binary blends, induces budding and breakup into spherical and novel ‘dumbbell’ micelles—as seen in electron microscopy images of degradable worm-like micelles. Core dimension, d, in our large-scale, long-time dissipative particle dynamics (DPD) simulations is shown to scale with chain-length, N, as predicted theoretically by the strong segregation limit (d ≈ N2/3), but morphological transitions of binary mixtures are only crudely predicted by simple mixture rules. Here we show that for weakly demixing diblock copolymers, the coupling between local interfacial concentration and mean curvature can be described with a simple linear relationship. The computational methods developed here for PEG-based assemblies should be useful for many high curvature nanosystems

Magnification-Temperature Correlation: the Dark Side of ISW Measurements

Integrated Sachs-Wolfe (ISW) measurements, which involve cross-correlating the CMB with the foreground large-scale structure (e.g. galaxies/quasars), have proven to be an interesting probe of dark energy. We show that magnification bias, which is the inevitable modulation of the foreground number counts by gravitational lensing, alters both the shape and amplitude of the observed ISW signal. This is true especially at high redshifts because (1) the intrinsic galaxy-temperature signal diminishes greatly back in the matter dominated era, (2) the lensing efficiency increases with redshift and (3) the number count slope generally steepens with redshift in a magnitude limited sample. At z >~ 2, the magnification-temperature correlation dominates over the intrinsic galaxy-temperature correlation and causes the observed ISW signal to increase with z, despite dark energy subdominance -- a result of the fact that magnification probes structures between the observer and the sources. Ignoring magnification bias can then lead to erroneous conclusions about dark energy. While the lensing modulation opens up an interesting high z window for ISW measurements, high z measurements are not expected to add much new information to low z ones if dark energy is the cosmological constant. This is because lensing introduces significant covariance across redshifts. The most compelling reason to pursue high z ISW measurements is to look for a potential surprise such as early dark energy domination or the signature of modified gravity. We conclude with a discussion of existing measurements, the highest z of which is at the margin of being sensitive to magnification bias. We also develop a formalism which might be of general interest: to predict biases in estimating parameters when certain physical effects are ignored in interpreting data.Comment: 14 pages, 12 figures, references added, minor typos corrected, accepted for publication by PR

Local stochastic non-Gaussianity and N-body simulations

Large-scale clustering of highly biased tracers of large-scale structure has emerged as one of the best observational probes of primordial non-Gaussianity of the local type (i.e. f_{NL}^{local}). This type of non-Gaussianity can be generated in multifield models of inflation such as the curvaton model. Recently, Tseliakhovich, Hirata, and Slosar showed that the clustering statistics depend qualitatively on the ratio of inflaton to curvaton power \xi after reheating, a free parameter of the model. If \xi is significantly different from zero, so that the inflaton makes a non-negligible contribution to the primordial adiabatic curvature, then the peak-background split ansatz predicts that the halo bias will be stochastic on large scales. In this paper, we test this prediction in N-body simulations. We find that large-scale stochasticity is generated, in qualitative agreement with the prediction, but that the level of stochasticity is overpredicted by ~30%. Other predictions, such as \xi independence of the halo bias, are confirmed by the simulations. Surprisingly, even in the Gaussian case we do not find that halo model predictions for stochasticity agree consistently with simulations, suggesting that semi-analytic modeling of stochasticity is generally more difficult than modeling halo bias.Comment: v3: minor changes matching published versio

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

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

3D Photometric Cosmic Shear

Here we present a number of improvements to weak lensing 3D power spectrum analysis, 3D cosmic shear, that uses the shape and redshift information of every galaxy to constrain cosmological parameters. We show how photometric redshift probability distributions for individual galaxies can be directly included in this statistic with no averaging. We also include the Limber approximation, considerably simplifying full 3D cosmic shear analysis, and we investigate its range of applicability. Finally we show the relationship between weak lensing tomography and the 3D cosmic shear field itself; the steps connecting them being the Limber approximation, a harmonic-space transform and a discretisation in wavenumber. Each method has its advantages: 3D cosmic shear analysis allows straightforward inclusion of all relevant modes, thus ensuring minimum error bars, and direct control of the range of physical wavenumbers probed, to avoid the uncertain highly nonlinear regime. On the other hand, tomography is more convenient for checking systematics through direct investigation of the redshift dependence of the signal. Finally, for tomography, we suggest that the angular modes probed should be redshift-dependent, to recover some of the 3D advantages.Comment: Accepted to MNRAS. 15 pages, 7 figure

Effects and Detectability of Quasi-Single Field Inflation in the Large-Scale Structure and Cosmic Microwave Background

Quasi-single field inflation predicts a peculiar momentum dependence in the squeezed limit of the primordial bispectrum which smoothly interpolates between the local and equilateral models. This dependence is directly related to the mass of the isocurvatons in the theory which is determined by the supersymmetry. Therefore, in the event of detection of a non-zero primordial bispectrum, additional constraints on the parameter controlling the momentum-dependence in the squeezed limit becomes an important question. We explore the effects of these non-Gaussian initial conditions on large-scale structure and the cosmic microwave background, with particular attention to the galaxy power spectrum at large scales and scale-dependence corrections to galaxy bias. We determine the simultaneous constraints on the two parameters describing the QSF bispectrum that we can expect from upcoming large-scale structure and cosmic microwave background observations. We find that for relatively large values of the non-Gaussian amplitude parameters, but still well within current uncertainties, galaxy power spectrum measurements will be able to distinguish the QSF scenario from the predictions of the local model. A CMB likelihood analysis, as well as Fisher matrix analysis, shows that there is also a range of parameter values for which Planck data may be able distinguish between QSF models and the related local and equilateral shapes. Given the different observational weightings of the CMB and LSS results, degeneracies can be significantly reduced in a joint analysis.Comment: 27 pages, 14 figure

Relativistic effects and primordial non-Gaussianity in the galaxy bias

When dealing with observables, one needs to generalize the bias relation between the observed galaxy fluctuation field to the underlying matter distribution in a gauge-invariant way. We provide such relation at second-order in perturbation theory adopting the local Eulerian bias model and starting from the observationally motivated uniform-redshift gauge. Our computation includes the presence of primordial non-Gaussianity. We show that large scale-dependent relativistic effects in the Eulerian bias arise independently from the presence of some primordial non-Gaussianity. Furthermore, the Eulerian bias inherits from the primordial non-Gaussianity not only a scale-dependence, but also a modulation with the angle of observation when sources with different biases are correlated.Comment: 12 pages, LaTeX file; version accepted for publication in JCA

An Improved Calculation of the Non-Gaussian Halo Mass Function

The abundance of collapsed objects in the universe, or halo mass function, is an important theoretical tool in studying the effects of primordially generated non-Gaussianities on the large scale structure. The non-Gaussian mass function has been calculated by several authors in different ways, typically by exploiting the smallness of certain parameters which naturally appear in the calculation, to set up a perturbative expansion. We improve upon the existing results for the mass function by combining path integral methods and saddle point techniques (which have been separately applied in previous approaches). Additionally, we carefully account for the various scale dependent combinations of small parameters which appear. Some of these combinations in fact become of order unity for large mass scales and at high redshifts, and must therefore be treated non-perturbatively. Our approach allows us to do this, and to also account for multi-scale density correlations which appear in the calculation. We thus derive an accurate expression for the mass function which is based on approximations that are valid over a larger range of mass scales and redshifts than those of other authors. By tracking the terms ignored in the analysis, we estimate theoretical errors for our result and also for the results of others. We also discuss the complications introduced by the choice of smoothing filter function, which we take to be a top-hat in real space, and which leads to the dominant errors in our expression. Finally, we present a detailed comparison between the various expressions for the mass functions, exploring the accuracy and range of validity of each.Comment: 28 pages, 13 figures; v2: text reorganized and some figured modified for clarity, results unchanged, references added. Matches version published in JCA