  We consider an interacting field theory model that describes the dark energy
- dark matter interaction. Only for a specific interaction term, this
interacting field theory description has an equivalent interacting fluid
description. For inverse power law potentials and linear interaction function,
we show that the interacting dark sector model with field-fluid mapping is
consistent with \textit{four cosmological data sets} -- Hubble parameter
measurements (Hz), Baryonic Acoustic Oscillation data (BAO), Supernova Type Ia
data (SN), and High redshift HII galaxy measurements (HIIG). More specifically,
these data sets prefer a negative value of interaction strength in the dark
sector and lead to consistent best-fit values of Hubble constant and other
cosmological parameters. Having established that this interacting field theory
model is consistent with cosmological observations, we obtain quantifying tools
to distinguish between the interacting and non-interacting dark sector
scenarios. We focus on the variation of the scalar metric perturbed quantities
as a function of redshift related to structure formation, weak gravitational
lensing, and the integrated Sachs-Wolfe effect. We show that the difference in
the evolution becomes significant for $z < 20$, for all length scales, and the
difference peaks at smaller redshift values $z < 5$. We then discuss the
implications of our results for the upcoming missions.
