  This paper investigates the cosmological dynamics arising from the
interaction between a 2-form field and cold dark matter within a Bianchi I
background. Employing a dynamical system analysis, we identify two attractors
yielding to exponential expansion of the Universe, i.e., de-Sitter solutions.
Notably, these solutions exhibit a pivotal distinction: one is
indistinguishable from the cosmological constant scenario, while the other
corresponds to an \emph{anisotropic de-Sitter} expansion sourced by the 2-form
field. To validate the asymptotic behavior of our model, we conduct a numerical
exploration of its expansion history. Our analysis reveals that the coupling
between the dark sectors amplifies the shear during the matter-dominated epoch,
offering a potential avenue to address certain observational discrepancies
related to the structure formation process. Then, we constrain the parameter
space of the model using recent observational datasets. Remarkably, we find
that the current shear is precisely constrained to be approximately $\Sigma_0
\approx - 10^{-4}$. We also discuss some key differences in the expansionary
dynamics sourced by the 2-form field compared to a 1-form field, i.e., a vector
field, offering insights into their respective impacts on the support they
provide to late-time anisotropy.
