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Title: Squeezed bispectrum in the δ N formalism: local observer effect in field space

Abstract

The prospects of future galaxy surveys for non-Gaussianity measurements call for the development of robust techniques for computing the bispectrum of primordial cosmological perturbations. In this paper, we propose a novel approach to the calculation of the squeezed bispectrum in multiple-field inflation. With use of the δ N formalism, our framework sheds new light on the recently pointed out difference between the squeezed bispectrum for global observers and that for local observers, while allowing one to calculate both. For local observers in particular, the squeezed bispectrum is found to vanish in single-field inflation. Furthermore, our framework allows one to go beyond the near-equilateral ('small hierarchy') limit, and to automatically include intrinsic non-Gaussianities that do not need to be calculated separately. The explicit computational programme of our method is given and illustrated with a few examples.

Authors:
 [1];  [2]
  1. Kavli Institute for the Physics and Mathematics of the Universe (WPI), UTIAS, The University of Tokyo, 5-1-5 Kashiwanoha, Kashiwa, Chiba 277-8583 (Japan)
  2. Institute of Cosmology and Gravitation, University of Portsmouth, Dennis Sciama Building, Burnaby Road, Portsmouth, PO1 3FX (United Kingdom)
Publication Date:
OSTI Identifier:
22680032
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Cosmology and Astroparticle Physics; Journal Volume: 2017; Journal Issue: 02; Other Information: Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
79 ASTROPHYSICS, COSMOLOGY AND ASTRONOMY; DISTURBANCES; GALAXIES; INFLATIONARY UNIVERSE; PERTURBATION THEORY; SPACE; VISIBLE RADIATION

Citation Formats

Tada, Yuichiro, and Vennin, Vincent, E-mail: yuichiro.tada@ipmu.jp, E-mail: vincent.vennin@port.ac.uk. Squeezed bispectrum in the δ N formalism: local observer effect in field space. United States: N. p., 2017. Web. doi:10.1088/1475-7516/2017/02/021.
Tada, Yuichiro, & Vennin, Vincent, E-mail: yuichiro.tada@ipmu.jp, E-mail: vincent.vennin@port.ac.uk. Squeezed bispectrum in the δ N formalism: local observer effect in field space. United States. doi:10.1088/1475-7516/2017/02/021.
Tada, Yuichiro, and Vennin, Vincent, E-mail: yuichiro.tada@ipmu.jp, E-mail: vincent.vennin@port.ac.uk. Wed . "Squeezed bispectrum in the δ N formalism: local observer effect in field space". United States. doi:10.1088/1475-7516/2017/02/021.
@article{osti_22680032,
title = {Squeezed bispectrum in the δ N formalism: local observer effect in field space},
author = {Tada, Yuichiro and Vennin, Vincent, E-mail: yuichiro.tada@ipmu.jp, E-mail: vincent.vennin@port.ac.uk},
abstractNote = {The prospects of future galaxy surveys for non-Gaussianity measurements call for the development of robust techniques for computing the bispectrum of primordial cosmological perturbations. In this paper, we propose a novel approach to the calculation of the squeezed bispectrum in multiple-field inflation. With use of the δ N formalism, our framework sheds new light on the recently pointed out difference between the squeezed bispectrum for global observers and that for local observers, while allowing one to calculate both. For local observers in particular, the squeezed bispectrum is found to vanish in single-field inflation. Furthermore, our framework allows one to go beyond the near-equilateral ('small hierarchy') limit, and to automatically include intrinsic non-Gaussianities that do not need to be calculated separately. The explicit computational programme of our method is given and illustrated with a few examples.},
doi = {10.1088/1475-7516/2017/02/021},
journal = {Journal of Cosmology and Astroparticle Physics},
number = 02,
volume = 2017,
place = {United States},
year = {Wed Feb 01 00:00:00 EST 2017},
month = {Wed Feb 01 00:00:00 EST 2017}
}
  • We investigate the consistency relation relating the squeezed limit of the bispectrum to the scalar spectral index in single field models of inflation. We give a simple integral formula for the bispectrum in the squeezed limit in terms of the free mode functions of the primordial curvature perturbation, in any Lorentz invariant single field model of inflation and without resorting to any approximation, generalizing a recent result obtained by Ganc and Komatsu in the case of canonical kinetic terms. We use our result to verify the consistency relation in an exactly solvable class of models with a non-trivial speed ofmore » sound. We then verify the consistency relation at the first non-trivial order in the slow-varying approximation in general single field inflation (a known result) and at second order in this approximation in canonical single field inflation.« less
  • We calculate the squeezed limit of the bispectrum produced by inflation with multiple light fields. To achieve this we allow for different horizon exit times for each mode and calculate the intrinsic field-space three-point function in the squeezed limit using soft-limit techniques. We then use the δ N formalism from the time the last mode exits the horizon to calculate the bispectrum of the primordial curvature perturbation. We apply our results to calculate the spectral index of the halo bias, n{sub δ b}, an important observational probe of the squeezed limit of the primordial bispectrum and compare our results with previous formulae.more » We give an example of a curvaton model with n{sub δ b} ∼ O(n{sub s}−1) for which we find a 20% correction to observable parameters for squeezings relevant to future experiments. For completeness, we also calculate the squeezed limit of three-point correlation functions involving gravitons for multiple field models.« less
  • We compute the matter bispectrum in the presence of primordial local non-Gaussianity over a wide range of scales, including the very small nonlinear ones. We use the Halo Model approach, considering non-Gaussian corrections to the halo profiles, the halo mass function and the bias functions. We compare our results in the linear and mildly nonlinear scales to a large ensemble of Gaussian and non-Gaussian numerical simulations. We consider both squeezed and equilateral configurations, at redshift z = 0 and z = 1. For z = 0, the deviations between the Halo Model and the simulations are smaller than 10% inmore » the squeezed limit, both in the Gaussian and non-Gaussian cases. The Halo Model allows to make predictions on scales much smaller than those reached by numerical simulations. For local non-Gaussian initial conditions with a parameter f{sub NL} = 100, we find an enhancement of the bispectrum in the squeezed configuration k = k{sub 3} = k{sub 2} >> k{sub 1} ∼ 0.01h{sup −1}Mpc, of ∼ 15% and ∼ 25% on scales k ∼ 1h{sup −1}Mpc, at z = 0 and z = 1 respectively. This is mainly due to the non-Gaussian corrections in the linear bias. Finally we provide a very simple expression valid for any scenario, i.e. for any choice of the halo profile, mass and bias functions, which allow for a fast evaluation of the bispectrum on squeezed configurations.« less
  • We develop a theory of nonlinear cosmological perturbations on superhorizon scales for a single scalar field with a general kinetic term and a general form of the potential. We employ the ADM formalism and the spatial gradient expansion approach, characterised by O(ε{sup m}), where ε = 1/(HL) is a small parameter representing the ratio of the Hubble radius to the characteristic length scale L of perturbations. We obtain the general solution for a full nonlinear version of the curvature perturbation valid up through second-order in ε (m = 2). We find the solution satisfies a nonlinear second-order differential equation asmore » an extension of the equation for the linear curvature perturbation on the comoving hypersurface. Then we formulate a general method to match a perturbative solution accurate to n-th-order in perturbation inside the horizon to our nonlinear solution accurate to second-order (m = 2) in the gradient expansion on scales slightly greater than the Hubble radius. The formalism developed in this paper allows us to calculate the superhorizon evolution of a primordial non-Gaussianity beyond the so-called δN formalism or separate universe approach which is equivalent to leading order (m = 0) in the gradient expansion. In particular, it can deal with the case when there is a temporary violation of slow-roll conditions. As an application of our formalism, we consider Starobinsky's model, which is a single field model having a temporary non-slow-roll stage due to a sharp change in the potential slope. We find that a large non-Gaussianity can be generated even on superhorizon scales due to this temporary suspension of slow-roll inflation.« less
  • In our previous paper [1], we have proposed a new algorithm to calculate the power spectrum of the curvature perturbations generated in inflationary universe with use of the stochastic approach. Since this algorithm does not need the perturbative expansion with respect to the inflaton fields on super-horizon scale, it works even in highly stochastic cases. For example, when the curvature perturbations are very large or the non-Gaussianities of the curvature perturbations are sizable, the perturbative expansion may break down but our algorithm enables to calculate the curvature perturbations. We apply it to two well-known inflation models, chaotic and hybrid inflation,more » in this paper. Especially for hybrid inflation, while the potential is very flat around the critical point and the standard perturbative computation is problematic, we successfully calculate the curvature perturbations.« less