Reconstructing a non-linear interaction in the dark sector with
  cosmological observations
  In this work we model two non-linear directly interacting scenarios in dark
sector of the universe with the dimensionless parameter $\alpha$ and $\beta$,
which dominate the energy exchange between dark energy and dark matter. The
central goal of this investigation is to research the interacting model and
discuss the cosmological implications based on the current observational
datasets. The class of the interaction is generally characterized by a coupling
function $Q\propto H(z)\rho_x$, $x$ denotes the energy density of dark matter
or dark energy. The constrained results we obtained indicate that the direct
interaction in cosmic dark sector is favored by various observational data and
the key effects on CMB power spectrum and linear matter power spectrum appear
compared to $\Lambda$CDM standard paradigm. Finally, we discuss in depth the
effect of different neutrino mass hierarchy on matter power spectrum and the
variation of the ratio of CMB temperature power spectrum $C_{\ell}^{TT}$ and
matter power spectrum $P(k)$ when the $\Delta N_{eff}= N-3.046$ from 0.5 to 2,
respectively.
