We compute the number density of massive Black Holes ( BHs ) at the centre of galaxies at z = 6 in different Dynamical Dark Energy ( DDE ) cosmologies , and compare it with existing observational lower limits , to derive constraints on the evolution of the Dark Energy equation of state parameter w .
Our approach only assumes the canonical scenario for structure formation from the collapse of overdense regions of the Dark Matter dominated primordial density field on progressively larger scales ; the Black Hole accretion and merging rate have been maximized in the computation so as to obtain robust constraints on w and on its look-back time derivative w _ { a } .
Our results provide independent constraints complementary to those obtained by combining Supernovae , Cosmic Microwave Background and Baryonic Acoustic Oscillations ; while the latter concern combinations of w _ { 0 } and w _ { a } leaving the time evolution of the state parameter w _ { a } highly unconstrained , the BH abundance mainly provide upper limits on w _ { a } , only weakly depending on w _ { 0 } .
Combined with the existing constraints , our results significantly restrict the allowed region in DDE parameter space , ruling out DDE models not providing cosmic time and fast growth factor large enough to allow for the building up of the observed abundance of BHs ; in particular , models with -1.2 \leq w _ { 0 } \leq - 1 and positive redshift evolution w _ { a } \gtrsim 0.8 - completely consistent with previous constraints - are strongly disfavoured by our independent constraints from BH abundance .
Such range of parameters corresponds to ” Quintom ” DDE models , with w crossing -1 starting from larger values .