  We consider an interacting field theory model that describes the interaction
between 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 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
the best-fit value of Hubble constant $H_0 = 69.9^{0.46}_{1.02}$ km s$^{-1}$
Mpc$^{-1}$. Thus, the interacting field theory model $\textit{alleviates the
Hubble tension}$ between Planck and these four cosmological probes. 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.
