  In a recent work [Phys. Rev. D 98, 043521 (2018)], we have investigated a
dark matter (DM)-photon coupling model in which the DM decays into photons in
the presence of dark energy (DE) with the constant equation of state (EoS)
parameter. Here, we study an extension of the DM-photon coupling model by
considering a time-varying EoS of DE via Chevalier-Polarski-Linder (CPL)
parametrization. We derive observational constraints on the model parameters by
using the data from cosmic microwave background (CMB), baryonic acoustic
oscillations (BAO), the local value of Hubble constant from Hubble Space
Telescope (HST), and large scale structure (LSS) information from the abundance
of galaxy clusters, in four different combinations. We find that in the present
DM-photon coupling scenario the mean values of $w_{\rm de0}$ are in
quintessence region ($w_{\rm de0} > -1$) whereas they were in the phantom
region ($w_{\rm de0} < -1$) in our previous study with all data combinations.
The constraints on the DM-photon coupling parameter do not reflect any
significant deviation from the previous results. Due to the decay of DM into
photons, we obtain higher values of $H_0$, consistent with the local
measurements, similar to our previous study. But, the time-varying DE leads to
lower values of $\sigma_8$ in the DM-photon coupling model with all data
combinations, in comparison to the results in our previous study. Thus,
allowing time-varying DE in the DM-photon coupling scenario is useful to
alleviate the $H_0$ and $\sigma_8$ tensions.
