Anisotropic trispectrum of curvature perturbations induced by primordial non-Abelian vector fields

Abstract

Motivated by the interest in models of the early universe where statistical isotropy is broken and can be revealed in cosmological observations, we consider an SU (2) theory of gauge interactions in a single scalar field inflationary scenario. We calculate the trispectrum of curvature perturbations, as a natural follow up to a previous paper of ours, where we studied the bispectrum in the same kind of models. The choice of a non-Abelian set-up turns out to be very convenient: on one hand, gauge boson self-interactions can be very interesting being responsible for extra non-trivial terms (naturally absent in the Abelian case) appearing in the cosmological correlation functions; on the other hand, its results can be easily reduced to the U (1) case. As expected from the presence of the vector bosons, preferred spatial directions arise and the trispectrum reveals anisotropic signatures. We evaluate its amplitude τ N L , which receives contributions both from scalar and vector fields, and verify that, in a large subset of its parameter space, the latter contributions can be larger than the former. We carry out a shape analysis of the trispectrum; in particular we discuss, with some examples, how the anisotropy parameters appearing in the analytic expression of the trispectrum can modulate its profile and we show that the amplitude of the anisotropic part of the trispectrum can be of the same order of magnitude as the isotropic part.

Anisotropic power spectrum and bispectrum in thef(ϕ)F2mechanism

“…In fact, the two results (41) and (51) have been first obtained in [39] for I ∝ a 2 . Although the mechanism (2) was first introduced with this motivation, the magnetogenesis application suffers a strong coupling problem [26].…”

“…In Section III we study how these modes δA are coupled to the modes of ζ through (2). The power spectrum and bispectrum of ζ are computed respectively in Sections IV and V. There, we show explicitly how the sum of the long-wavelength modes adds up with the solution of the classical equations of motion to determine the 3 For previous works on anisotropic non-gaussianity, see [28][29][30][31][32][49][50][51][52][53][54][55].…”

Measuring primordial anisotropic correlators with CMB spectral distortions

“…On the other hand, a connected anisotropic contribution to the curvature trispectrum is expected to create some non-vanishing off-diagonal signals, as well as diagonal ones due to τ NL . It is known that anisotropic trispectrum signals can also be produced in vector inflation models [40][41][42][43][44], while there may exist other possible models where unknown anisotropic signals are realized. The trispectrum parametrization is still nontrivial and the resultant µ-µ signatures need to be analyzed on a case-by-case basis.…”

Stability analysis of inflation with an SU(2) gauge field

“…The initial interests in inflaton-gauge interactions rooted from the quest to generating anomalous features during inflation, e.g. statistical anisotropy of CMBR [16][17][18][19][20][21][22][23][24][25][26][27][28][29][30], primordial gravitational waves that potentially break the Lyth bound [31,32], large scale seed magnetic fields [33][34][35], and primordial non-Gaussianity [31,[36][37][38][39][40][41][42][43]. Eventually, it has been found that the back reaction of the generated gauge fields slows down the inflaton and alleviates the necessity of flat potential [44][45][46].…”