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Title: Reduced bispectrum seeded by helical primordial magnetic fields

Abstract

In this paper, we investigate the effects of helical primordial magnetic fields (PMFs) on the cosmic microwave background (CMB) reduced bispectrum. We derive the full three-point statistics of helical magnetic fields and numerically calculate the even contribution in the collinear configuration. We then numerically compute the CMB reduced bispectrum induced by passive and compensated PMF modes on large angular scales. There is a negative signal on the bispectrum due to the helical terms of the fields and we also observe that the biggest contribution to the bispectrum comes from the non-zero IR cut-off for causal fields, unlike the two-point correlation case. For negative spectral indices, the reduced bispectrum is enhanced by the passive modes. This gives a lower value of the upper limit for the mean amplitude of the magnetic field on a given characteristic scale. However, high values of IR cut-off in the bispectrum, and the helical terms of the magnetic field relaxes this bound. This demonstrates the importance of the IR cut-off and helicity in the study of the nature of PMFs from CMB observations.

Authors:
 [1];  [2]
  1. Universidad Nacional de Colombia-Bogotá, Facultad de Ciencias, Departamento de Física, Carrera 30 Calle 45-03, C.P. 111321 Bogotá (Colombia)
  2. Grupo de Gravitación y Cosmología, Observatorio Astronómico Nacional, Universidad Nacional de Colombia, cra 45 No 26-85, Edificio Uriel Gutierréz, Bogotá, D.C. (Colombia)
Publication Date:
OSTI Identifier:
22676166
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Cosmology and Astroparticle Physics; Journal Volume: 2017; Journal Issue: 06; Other Information: Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
79 ASTROPHYSICS, COSMOLOGY AND ASTRONOMY; AMPLITUDES; COMPUTERIZED SIMULATION; CORRELATIONS; HELICITY; MAGNETIC FIELDS; RELICT RADIATION; STATISTICS

Citation Formats

Hortúa, Héctor Javier, and Castañeda, Leonardo, E-mail: hjhortuao@unal.edu.co, E-mail: lcastanedac@unal.edu.co. Reduced bispectrum seeded by helical primordial magnetic fields. United States: N. p., 2017. Web. doi:10.1088/1475-7516/2017/06/020.
Hortúa, Héctor Javier, & Castañeda, Leonardo, E-mail: hjhortuao@unal.edu.co, E-mail: lcastanedac@unal.edu.co. Reduced bispectrum seeded by helical primordial magnetic fields. United States. doi:10.1088/1475-7516/2017/06/020.
Hortúa, Héctor Javier, and Castañeda, Leonardo, E-mail: hjhortuao@unal.edu.co, E-mail: lcastanedac@unal.edu.co. Thu . "Reduced bispectrum seeded by helical primordial magnetic fields". United States. doi:10.1088/1475-7516/2017/06/020.
@article{osti_22676166,
title = {Reduced bispectrum seeded by helical primordial magnetic fields},
author = {Hortúa, Héctor Javier and Castañeda, Leonardo, E-mail: hjhortuao@unal.edu.co, E-mail: lcastanedac@unal.edu.co},
abstractNote = {In this paper, we investigate the effects of helical primordial magnetic fields (PMFs) on the cosmic microwave background (CMB) reduced bispectrum. We derive the full three-point statistics of helical magnetic fields and numerically calculate the even contribution in the collinear configuration. We then numerically compute the CMB reduced bispectrum induced by passive and compensated PMF modes on large angular scales. There is a negative signal on the bispectrum due to the helical terms of the fields and we also observe that the biggest contribution to the bispectrum comes from the non-zero IR cut-off for causal fields, unlike the two-point correlation case. For negative spectral indices, the reduced bispectrum is enhanced by the passive modes. This gives a lower value of the upper limit for the mean amplitude of the magnetic field on a given characteristic scale. However, high values of IR cut-off in the bispectrum, and the helical terms of the magnetic field relaxes this bound. This demonstrates the importance of the IR cut-off and helicity in the study of the nature of PMFs from CMB observations.},
doi = {10.1088/1475-7516/2017/06/020},
journal = {Journal of Cosmology and Astroparticle Physics},
number = 06,
volume = 2017,
place = {United States},
year = {Thu Jun 01 00:00:00 EDT 2017},
month = {Thu Jun 01 00:00:00 EDT 2017}
}
  • Gravitational wave production induces a strong constraint on the amplitude of a primordial magnetic field. It has been shown that the nucleosynthesis bound for a stochastic gravitational wave background implies that causally generated fields cannot have enough power on large scales to provide the seeds necessary for the observed magnetic fields in galaxies and clusters, even by the most optimistic dynamo amplification. Magnetic fields generated at inflation can have high enough amplitude only if their spectrum is very red. Here we show that helicity, which leads to an inverse cascade, can mitigate these limits. In particular, we find that helicalmore » fields generated at the QCD phase transition or at inflation with red spectrum are possible seeds for the dynamo. Helical fields generated at the electroweak phase transition are instead excluded as seeds at large scales. We also calculate the spectrum of gravitational waves generated by helical magnetic fields.« less
  • No abstract prepared.
  • Using the full radiation transfer function, we numerically calculate the CMB angular bispectrum seeded by the compensated magnetic scalar density mode. We find that, for the string inspired primordial magnetic fields characterized by index n{sub B} = −2.9 and mean-field amplitude B{sub λ} = 9nG, the angular bispectrum is dominated by two primordial magnetic shapes. The first magnetic shape looks similar to the one from local-type primordial curvature perturbations, so both the amplitude and profile of the Komatsu-Spergel estimator (reduced bispectrum) seeded by this shape are almost the same as those of the primary CMB anisotropies. However, for different parametermore » sets (l{sub 1},l{sub 2}), this ''local-type'' reduced bispectrum oscillates around different asymptotic values in the high-l{sub 3} regime because of the effect of the Lorentz force, which is exerted by the primordial magnetic fields on the charged baryons. This feature is different from the standard case where all modes approach to zero asymptotically in the high-l limit. On the other hand, the second magnetic shape appears only in the primordial magnetic field model. The amplitude of the Komatsu-Spergel estimator sourced by the second shape diverges in the low-l regime because of the negative slope of shape. In the high-l regime, this amplitude is approximately equal to that of the first estimator, but with a reversal phase.« less
  • We evaluate the angular bispectrum of the CMB temperature anisotropy at large angular scale due to a stochastic background of primordial magnetic fields. The shape of non-Gaussianity depends on the spectral index of the magnetic field power spectrum and is peaked in the squeezed configuration for a scale-invariant magnetic spectrum. By using the large angular part of the bispectrum generated by magnetic fields, the present bounds on non-Gaussianity set a limit on the amplitude of the primordial magnetic field of the order of O(10) nGauss for the scale-invariant case and O(20) nGauss for the other spectral indexes.
  • We study the parity violation in the cosmic microwave background (CMB) bispectrum induced by primordial magnetic fields (PMFs). Deriving a general formula for the CMB bispectrum generated from not only non-helical but also helical PMFs, we find that helical PMFs produce characteristic signals, which disappear in parity-conserving cases, such as the intensity-intensity-intensity bispectra arising from Σ{sup 3}{sub n=1}l{sub n} = odd. For fast numerical calculation of the CMB bispectrum, we reduce the one-loop formula to the tree-level one by using the so-called pole approximation. Then, we show that the magnetic anisotropic stress, which depends quadratically on non-helical and helical PMFsmore » and acts as a source of the CMB fluctuation, produces the local-type non-Gaussianity. Comparing the CMB bispectra composed of the scalar and tensor modes with the noise spectra, we find that assuming the generation of the nearly scale-invariant non-helical and helical PMFs from the grand unification energy scale (10{sup 14}GeV) to the electroweak one (10{sup 3}GeV), the intensity-intensity-intensity bispectrum for Σ{sup 3}{sub n=1}l{sub n} = odd can be observed by the WMAP experiment under the condition that B{sub 1Mpc;}{sup 2/3}B{sub 1Mpc;}{sup 1/3} > 2.7−4.5nG with B{sub 1Mpc;} and B{sub 1Mpc;} being the non-helical and helical PMF strengths smoothed on 1 Mpc, respectively.« less