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

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 » 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)« less
Authors:
 [1] ;  [2] ;  [3]
  1. Dipartimento di Fisica e Astronomia ''G. Galilei'', Università degli Studi di Padova, via Marzolo 8, I-35131, Padova (Italy)
  2. Max-Planck-Institut für Astrophysik, Karl-Schwarzschild Str. 1, 85741 Garching (Germany)
  3. School of Physics and Astronomy, University of Minnesota, Minneapolis 55455 (United States)
Publication Date:
OSTI Identifier:
22373635
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Cosmology and Astroparticle Physics; Journal Volume: 2014; Journal Issue: 04; Other Information: Country of input: International Atomic Energy Agency (IAEA)
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