Signatures of anisotropic sources in the trispectrum of the cosmic microwave background

Shiraishi, Maresuke; Komatsu, Eiichiro; Peloso, Marco

doi:10.1088/1475-7516/2014/04/027

Title: Signatures of anisotropic sources in the trispectrum of the cosmic microwave background

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Abstract

Soft limits of N-point correlation functions, in which one wavenumber is much smaller than the others, play a special role in constraining the physics of inflation. Anisotropic sources such as a vector field during inflation generate distinct angular dependence in all these correlators, and introduce a fix privileged direction in our sky. In this paper we focus on the four-point correlator (the trispectrum T). We adopt a parametrization motivated by models in which the inflaton φ is coupled to a vector field through a I{sup 2}(φ)F{sup 2} interaction, namely T{sub ζ}(k{sub 1},k{sub 2},k{sub 3},k{sub 4})≡∑{sub n}d{sub n}[P{sub n}( k-circumflex {sub 1}⋅ k-circumflex {sub 3})+P{sub n}( k-circumflex {sub 1}⋅ k-circumflex {sub 12})+P{sub n}( k-circumflex {sub 3}⋅ k-circumflex {sub 12})]P{sub ζ}(k{sub 1})P{sub ζ}(k{sub 3})P{sub ζ}(k{sub 12})+(23perm), where P{sub n} denotes the Legendre polynomials. This shape is enhanced when the wavenumbers of the diagonals of the quadrilateral are much smaller than the sides, k{sub i}. The coefficient of the isotropic part, d{sub 0}, is equal to τ{sub NL}/6 discussed in the literature. A I{sup 2}(φ)F{sup 2} interaction generates d{sub 2} = 2d{sub 0} which is, in turn, related to the quadrupole modulation parameter of the power spectrum, g{sub *}, as d{sub 2} ≈more »« less

Authors:

Shiraishi, Maresuke ^[1]; Komatsu, Eiichiro ^[2]; Peloso, Marco ^[3]

Dipartimento di Fisica e Astronomia ''G. Galilei'', Università degli Studi di Padova, via Marzolo 8, I-35131, Padova (Italy)
Max-Planck-Institut für Astrophysik, Karl-Schwarzschild Str. 1, 85741 Garching (Germany)
School of Physics and Astronomy, University of Minnesota, Minneapolis 55455 (United States)

Publication Date:: Tue Apr 01 00:00:00 EDT 2014

OSTI Identifier:: 22373635

Resource Type:: Journal Article

Journal Name:: Journal of Cosmology and Astroparticle Physics

Additional Journal Information:: Journal Volume: 2014; Journal Issue: 04; Other Information: Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 1475-7516

Country of Publication:: United States

Language:: English

Subject:: 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; 79 ASTROPHYSICS, COSMOLOGY AND ASTRONOMY; ANISOTROPY; CORRELATION FUNCTIONS; COSMOLOGICAL INFLATION; ERRORS; INTERACTIONS; MAPS; RELICT RADIATION; VECTOR FIELDS; YIELDS

Citation Formats


                    Shiraishi, Maresuke, Komatsu, Eiichiro, and Peloso, Marco. Signatures of anisotropic sources in the trispectrum of the cosmic microwave background.  United States: N. p., 2014. 
        Web.  doi:10.1088/1475-7516/2014/04/027.

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                    Shiraishi, Maresuke, Komatsu, Eiichiro, & Peloso, Marco. Signatures of anisotropic sources in the trispectrum of the cosmic microwave background.  United States.  https://doi.org/10.1088/1475-7516/2014/04/027

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                    Shiraishi, Maresuke, Komatsu, Eiichiro, and Peloso, Marco. 2014.  
        "Signatures of anisotropic sources in the trispectrum of the cosmic microwave background".  United States.  https://doi.org/10.1088/1475-7516/2014/04/027.

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@article{osti_22373635,

  title        = {Signatures of anisotropic sources in the trispectrum of the cosmic microwave background},

  author       = {Shiraishi, Maresuke and Komatsu, Eiichiro and Peloso, Marco},

  abstractNote = {Soft limits of N-point correlation functions, in which one wavenumber is much smaller than the others, play a special role in constraining the physics of inflation. Anisotropic sources such as a vector field during inflation generate distinct angular dependence in all these correlators, and introduce a fix privileged direction in our sky. In this paper we focus on the four-point correlator (the trispectrum T). We adopt a parametrization motivated by models in which the inflaton φ is coupled to a vector field through a I{sup 2}(φ)F{sup 2} interaction, namely T{sub ζ}(k{sub 1},k{sub 2},k{sub 3},k{sub 4})≡∑{sub n}d{sub n}[P{sub n}( k-circumflex {sub 1}⋅ k-circumflex {sub 3})+P{sub n}( k-circumflex {sub 1}⋅ k-circumflex {sub 12})+P{sub n}( k-circumflex {sub 3}⋅ k-circumflex {sub 12})]P{sub ζ}(k{sub 1})P{sub ζ}(k{sub 3})P{sub ζ}(k{sub 12})+(23perm), where P{sub n} denotes the Legendre polynomials. This shape is enhanced when the wavenumbers of the diagonals of the quadrilateral are much smaller than the sides, k{sub i}. The coefficient of the isotropic part, d{sub 0}, is equal to τ{sub NL}/6 discussed in the literature. A I{sup 2}(φ)F{sup 2} interaction generates d{sub 2} = 2d{sub 0} which is, in turn, related to the quadrupole modulation parameter of the power spectrum, g{sub *}, as d{sub 2} ≈ 14|g{sub *}|N{sup 2} with N ≈ 60. We show that d{sub 0} and d{sub 2} can be equally well-constrained: the expected 68% CL error bars on these coefficients from a cosmic-variance-limited experiment measuring temperature anisotropy of the cosmic microwave background up to ℓ{sub max} = 2000 are δd{sub 2} ≈ 4δd{sub 0} = 105. Therefore, we can reach |g{sub *}| = 10{sup −3} by measuring the angle-dependent trispectrum. The current upper limit on τ{sub NL} from the Planck temperature maps yields |g{sub *}| < 0.02 (95% CL)},

  doi          = {10.1088/1475-7516/2014/04/027},

  url          = {https://www.osti.gov/biblio/22373635},
  journal      = {Journal of Cosmology and Astroparticle Physics},

  issn         = {1475-7516},

  number       = 04,

  volume       = 2014,

  place        = {United States},

  year         = {Tue Apr 01 00:00:00 EDT 2014},

  month        = {Tue Apr 01 00:00:00 EDT 2014}

}

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