Year: 2014
Type: article
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 2 (ϕ) F 2 interaction, namely T ζ ( k 1 , k 2 , k 3 , k 4 )≡∑ n d n [ P n ( 1 ⋅ 3 )+ P n ( 1 ⋅ 12 )+ P n ( 3 ⋅ 12 )] P ζ ( k 1 ) P ζ ( k 3 ) P ζ ( k 12 )+(23perm), where P 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 i . The coefficient of the isotropic part, d 0 , is equal to τ NL /6 discussed in the literature. A I 2 (ϕ) F 2 interaction generates d 2 = 2 d 0 which is, in turn, related to the quadrupole modulation parameter of the power spectrum, g * , as d 2 ≈ 14| g * | N 2 with N ≈ 60. We show that d 0 and d 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 max = 2000 are δ d 2 ≈ 4δ d 0 = 105. Therefore, we can reach | g * | = 10 −3 by measuring the angle-dependent trispectrum. The current upper limit on τ NL from the Planck temperature maps yields | g * | < 0.02 (95% CL).
Authors: Maresuke Shiraishi, Eiichiro Komatsu, Marco Peloso
Language: English
Subfield: Astronomy and Astrophysics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2141501208