We investigate the cosmic evolution of the ratio between black hole mass ( M _ { BH } ) and host galaxy total stellar mass ( M _ { stellar } ) out to z \sim 2.5 for a sample of 100 X-ray-selected moderate-luminosity , broad-line active galactic nuclei ( AGNs ) in the Chandra -COSMOS Legacy Survey .
By taking advantage of the deep multi-wavelength photometry and spectroscopy in the COSMOS field , we measure in a uniform way the galaxy total stellar mass using a SED decomposition technique and the black hole mass based on broad emission line measurements and single-epoch virial estimates .
Our sample of AGN host galaxies has total stellar masses of 10 ^ { 10 - 12 } M _ { \odot } , and black hole masses of 10 ^ { 7.0 - 9.5 } M _ { \odot } .
Combining our sample with the relatively bright AGN samples from the literature , we find no significant evolution of the M _ { BH } - M _ { stellar } relation with black hole-to-host total stellar mass ratio of M _ { BH } / M _ { stellar } \sim 0.3 \% at all redshifts probed .
We conclude that the average black hole-to-host stellar mass ratio appears to be consistent with the local value within the uncertainties , suggesting a lack of evolution of the M _ { BH } - M _ { stellar } relation up to z \sim 2.5 .