We study a sample of 1,604 moderate-to-high radiative luminosity active galactic nuclei (HLAGN) selected at 3 GHz within the VLA-COSMOS 3 GHz Large Project. These were classified by combining multiple AGN diagnostics: X-ray data, mid-infrared data and broad-band spectral energy distribution fitting. We decompose the total radio 1.4 GHz luminosity ($mathrm{L_{1.4 GHz,TOT}}$) into the emission originating from star formation and AGN activity by measuring the excess in $mathrm{L_{1.4 GHz,TOT}}$ relative to the infrared-radio correlation of star-forming galaxies. To quantify the excess, for each source we calculate the AGN fraction ($mathrm{f_{AGN}}$), the fractional contribution of AGN activity to $mathrm{L_{1.4 GHz,TOT}}$. The majority of the HLAGN, $(68.0pm1.5)%$, are dominated by star-forming processes ($f_{AGN}leq0.5$), while $(32.0pm1.5)%$ are dominated by AGN-related radio emission ($0.5<f_{AGN}leq1$). We use the AGN-related 1.4 GHz emission to derive the 1.4 GHz AGN luminosity functions of HLAGN. By assuming pure density and pure luminosity evolution models we constrain their cosmic evolution out to $zsim6$, finding $mathrm{Phi^* (z) propto (1+z)^{(2.64pm0.10)+(-0.61pm0.04) z}}$ and $mathrm{L^* (z) propto (1+z)^{(3.97pm0.15) + (-0.92pm0.06)z}}$. These evolutionary laws show that the number and luminosity density of HLAGN increased from higher redshifts ($zsim6$) up to a maximum in the redshift range $ 1<z<2.5$, followed by a decline towards local values. By scaling the 1.4 GHz AGN luminosity to kinetic luminosity using the standard conversion, we estimate the kinetic luminosity density as a function of redshift. We compare our result to the semi-analytic models of radio mode feedback finding that this feedback could have played an important role in the context of AGN-host coevolution in HLAGN which show evidence of AGN-related radio emission ($f_{AGN}>0$).
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