Scalar-Assisted Growth of Supermassive Black Holes: Boson-Mass Windows and Observational Constraints

We study a phenomenological cosmological model of black-hole growth in which a finite baryonic reservoir and a bosonic scalar cloud feed the black hole simultaneously. The baryonic component accretes through an Eddington-like channel, while the scalar cloud transfers mass through an effective quasibound-state decay rate. Evolving the system directly in redshift within a flat Λ CDM background, we scan over μ, M 0, M c,0, and M b,0 to assess whether scalar-assisted accretion can accelerate the formation of 10 9M supermassive black holes. We find that the scalar contribution is highly selective in parameter space. For the mass scales explored here, scalar transfer is most efficient for μ about10-19-10-16 eV, producing rapid cloud depletion and significantly earlier black-hole growth, while outside this interval the evolution remains mainly baryonic. More generally, this efficient window reflects a preferred range of the dimensionless coupling α=μM BH and therefore shifts approximately as μ proportional to M BH-1. Comparison with observed quasar masses and luminosities instead favors lower boson masses, broadly around μ about10-21-10-20 eV. These results are not necessarily in tension, since the boson mass that maximizes early growth depends on the characteristic black-hole mass and evolutionary stage. This separation between dynamical efficiency and observational compatibility leaves open complementary roles for different bosonic mass scales in supermassive black hole growth and dark-matter phenomenology.