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Title: Non-Gaussianity and large-scale structure in a two-field inflationary model

Abstract

Single-field inflationary models predict nearly Gaussian initial conditions, and hence a detection of non-Gaussianity would be a signature of the more complex inflationary scenarios. In this paper we study the effect on the cosmic microwave background and on large-scale structure from primordial non-Gaussianity in a two-field inflationary model in which both the inflaton and curvaton contribute to the density perturbations. We show that in addition to the previously described enhancement of the galaxy bias on large scales, this setup results in large-scale stochasticity. We provide joint constraints on the local non-Gaussianity parameter f-tilde{sub NL} and the ratio {xi} of the amplitude of primordial perturbations due to the inflaton and curvaton using WMAP and Sloan Digital Sky Survey data.

Authors:
;  [1];  [2]
  1. Caltech M/C 350-17, Pasadena, California 91125 (United States)
  2. Brookhaven National Laboratory, Upton, New York 11973 (United States)
Publication Date:
OSTI Identifier:
21420936
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physical Review. D, Particles Fields; Journal Volume: 82; Journal Issue: 4; Other Information: DOI: 10.1103/PhysRevD.82.043531; (c) 2010 American Institute of Physics
Country of Publication:
United States
Language:
English
Subject:
79 ASTROPHYSICS, COSMOLOGY AND ASTRONOMY; AMPLITUDES; DENSITY; DETECTION; DISTURBANCES; GALAXIES; GAUSSIAN PROCESSES; INFLATIONARY UNIVERSE; PERTURBATION THEORY; RELICT RADIATION; COSMOLOGICAL MODELS; ELECTROMAGNETIC RADIATION; MATHEMATICAL MODELS; MICROWAVE RADIATION; PHYSICAL PROPERTIES; RADIATIONS

Citation Formats

Tseliakhovich, Dmitriy, Hirata, Christopher, and Slosar, Anze. Non-Gaussianity and large-scale structure in a two-field inflationary model. United States: N. p., 2010. Web. doi:10.1103/PHYSREVD.82.043531.
Tseliakhovich, Dmitriy, Hirata, Christopher, & Slosar, Anze. Non-Gaussianity and large-scale structure in a two-field inflationary model. United States. doi:10.1103/PHYSREVD.82.043531.
Tseliakhovich, Dmitriy, Hirata, Christopher, and Slosar, Anze. 2010. "Non-Gaussianity and large-scale structure in a two-field inflationary model". United States. doi:10.1103/PHYSREVD.82.043531.
@article{osti_21420936,
title = {Non-Gaussianity and large-scale structure in a two-field inflationary model},
author = {Tseliakhovich, Dmitriy and Hirata, Christopher and Slosar, Anze},
abstractNote = {Single-field inflationary models predict nearly Gaussian initial conditions, and hence a detection of non-Gaussianity would be a signature of the more complex inflationary scenarios. In this paper we study the effect on the cosmic microwave background and on large-scale structure from primordial non-Gaussianity in a two-field inflationary model in which both the inflaton and curvaton contribute to the density perturbations. We show that in addition to the previously described enhancement of the galaxy bias on large scales, this setup results in large-scale stochasticity. We provide joint constraints on the local non-Gaussianity parameter f-tilde{sub NL} and the ratio {xi} of the amplitude of primordial perturbations due to the inflaton and curvaton using WMAP and Sloan Digital Sky Survey data.},
doi = {10.1103/PHYSREVD.82.043531},
journal = {Physical Review. D, Particles Fields},
number = 4,
volume = 82,
place = {United States},
year = 2010,
month = 8
}
  • Single-field inflationary models predict nearly Gaussian initial conditions, and hence a detection of non-Gaussianity would be a signature of the more complex inflationary scenarios. In this paper we study the effect on the cosmic microwave background and on large-scale structure from primordial non-Gaussianity in a two-field inflationary model in which both the inflaton and curvaton contribute to the density perturbations. We show that in addition to the previously described enhancement of the galaxy bias on large scales, this setup results in large-scale stochasticity. We provide joint constraints on the local non-Gaussianity parameter f*{sub NL} and the ratio {zeta} of themore » amplitude of primordial perturbations due to the inflaton and curvaton using WMAP and Sloan Digital Sky Survey data.« less
  • I compute the effect on the power spectrum of tracers of the large-scale mass-density field (e.g., galaxies) of primordial non-Gaussianity of the form {phi}={phi}+f{sub NL}({phi}{sup 2}-<{phi}{sup 2}>)+g{sub NL}{phi}{sup 3}+..., where {phi} is proportional to the initial potential fluctuations and {phi} is a Gaussian field, using beyond-linear-order perturbation theory. I find that the need to eliminate large higher-order corrections necessitates the addition of a new term to the bias model, proportional to {phi}, i.e., {delta}{sub g}=b{sub {delta}}{delta}+b{sub {phi}}f{sub NL}{phi}+..., with all the consequences this implies for clustering statistics, e.g., P{sub gg}(k)=b{sub {delta}}{sup 2}P{sub {delta}}{sub {delta}}(k)+2b{sub {delta}}b{sub {phi}}f{sub NL}P{sub {phi}}{sub {delta}}(k)+b{sub {phi}}{supmore » 2}f{sub NL}{sup 2}P{sub {phi}}{sub {phi}}(k)+.... This result is consistent with calculations based on a model for dark matter halo clustering, showing that the form is quite general, not requiring assumptions about peaks, or the formation or existence of halos. The halo model plays the same role it does in the usual bias picture, giving a prediction for b{sub {phi}} for galaxies known to sit in a certain type of halo. Previous projections for future constraints based on this effect have been very conservative--there is enough volume at z < or approx. 2 to measure f{sub NL} to {approx}{+-}1, with much more volume at higher z. As a prelude to the bias calculation, I point out that the beyond-linear (in {phi}) corrections to the power spectrum of mass-density perturbations are naively infinite, so it is dangerous to assume they are negligible; however, the infinite part can be removed by a renormalization of the fluctuation amplitude, with the residual k-dependent corrections negligible for models allowed by current constraints.« less
  • We forecast combined future constraints from the cosmic microwave background and large-scale structure on the models of primordial non-Gaussianity. We study the generalized local model of non-Gaussianity, where the parameter f{sub NL} is promoted to a function of scale, and present the principal component analysis applicable to an arbitrary form of f{sub NL}(k). We emphasize the complementarity between the CMB and LSS by using Planck, DES and BigBOSS surveys as examples, forecast constraints on the power-law f{sub NL}(k) model, and introduce the figure of merit for measurements of scale-dependent non-Gaussianity.
  • One of the main signatures of primordial non-Gaussianity of the local type is a scale-dependent correction to the bias of large-scale structure tracers such as galaxies or clusters, whose amplitude depends on the bias of the tracers itself. The dominant source of noise in the power spectrum of the tracers is caused by sampling variance on large scales (where the non-Gaussian signal is strongest) and shot noise arising from their discrete nature. Recent work has argued that one can avoid sampling variance by comparing multiple tracers of different bias, and suppress shot noise by optimally weighting halos of different mass.more » Here we combine these ideas and investigate how well the signatures of non-Gaussian fluctuations in the primordial potential can be extracted from the two-point correlations of halos and dark matter. On the basis of large N-body simulations with local non-Gaussian initial conditions and their halo catalogs we perform a Fisher matrix analysis of the two-point statistics. Compared to the standard analysis, optimal weighting and multiple-tracer techniques applied to halos can yield up to 1 order of magnitude improvements in f{sub NL}-constraints, even if the underlying dark matter density field is not known. In this case one needs to resolve all halos down to 10{sup 10}h{sup -1}M{sub sun} at z=0, while with the dark matter this is already achieved at a mass threshold of 10{sup 12}h{sup -1}M{sub sun}. We compare our numerical results to the halo model and find satisfactory agreement. Forecasting the optimal f{sub NL}-constraints that can be achieved with our methods when applied to existing and future survey data, we find that a survey of 50h{sup -3} Gpc{sup 3} volume resolving all halos down to 10{sup 11}h{sup -1}M{sub sun} at z=1 will be able to obtain {sigma}{sub f{sub N{sub L}}}{approx}1 (68% cl), a factor of {approx}20 improvement over the current limits. Decreasing the minimum mass of resolved halos, increasing the survey volume or obtaining the dark matter maps can further improve these limits, potentially reaching the level of {sigma}{sub f{sub N{sub L}}}{approx}0.1. This precision opens up the possibility to distinguish different types of primordial non-Gaussianity and to probe inflationary physics of the very early Universe.« less
  • Recent work has shown that the local non-Gaussianity parameter f{sub NL} induces a scale dependent bias, whose amplitude is growing with scale. Here we first rederive this result within the context of the peak-background split formalism and show that it only depends on the assumption of universality of the mass function, assuming that the halo bias only depends on the mass. We then use the extended Press-Schechter formalism to argue that this assumption may be violated and that the scale dependent bias will depend on other properties, such as the merging history of halos. In particular, in the limit ofmore » recent mergers we find that the effect is suppressed. Next we use these predictions in conjunction with a compendium of large scale data to put a limit on the value of f{sub NL}. When combining all data assuming that the halo occupation depends only on the halo mass, we get a limit of -29 (-65)« less