Description
In this paper, we compute the inflationary trispectrum of primordial
gauge fields generated through the scalar and tensor exchanges in models with
spectator U(1) gauge fields which are kinetically coupled to the inflaton. Focusing
on the connected four-point autocorrelation function of gauge fields, we derive
exact analytical expressions for the full trispectrum of both electric and magnetic
fields using the in-in formalism and cosmological diagrammatic rules, and explore
their respective contributions in specific momentum configurations. For the scalar
exchange, we find that the trispectrum signal in the equisided configuration grows
with the exchange momentum and reaches its maximum in the flattened limit.
However, in the counter collinear limit, we show that the non-linearity parameter
associated with the trispectrum scales quadratically with the corresponding
parameter of the cross-correlation bispectrum of magnetic fields and curvature
perturbations, thereby establishing a hierarchical relation between the higher- and
lower-order correlation functions. For the tensor exchange, the trispectrum
displays a richer angular dependence, reflecting the sensitivity to the orientation of
the momentum quadrilateral with respect to the tensor polarisation, producing
characteristic angular modulations in the trispectrum. Detecting such angular
signatures in future high-precision cosmological observations would provide a
novel window into tensor-mediated interactions in the early universe.
