Power spectrum of density fluctuations, halo abundances and clustering with primordial black holes

Abstract

We calculate the effect of dark matter (DM) being encapsulated in primordial black holes (PBHs) on the power spectrum of density fluctuations P (k); we also look at its effect on the abundance of haloes and their clustering. We adopt a growth of Poisson fluctuations that starts only after the moment of matter and radiation equality and study both monochromatic and extended Press-Schechter distributions. We present updated monochromatic black hole mass constraints by demanding < 10% deviations from the Λ cold dark matter power spectrum at a scale of k = 1hMpc −1 . Our results show that PBHs with masses > 10 4 h −1 M are excluded from conforming all of the dark matter in the Universe; they would, however, be able to act as seeds for super massive black holes if they conform a small fraction of the DM. We also apply this condition to our extended Press-Schechter (PS) mass functions, and find that the Poisson power is scale dependent even before applying evolution, due to the change of the mass density in PBHs with redshift, and therefore with scale, as they start affecting the gravitational potential at different times. We find that characteristic masses M * ≤ 10 2 h −1 M are allowed, leaving only two characteristic PBH mass windows of PS mass functions when combining with previous constraints, at M * ∼ 10 2 h −1 M and ∼ 10 −8 h −1 M where all of the DM can be in PBHs. The resulting dark matter halo mass functions within these windows are similar to those resulting from cold dark matter made of fundamental particles, but as soon as the parameters produce unrealistic P (k), the resulting halo mass functions and their bias as a function of halo mass deviate strongly from the behaviour measured in the real Universe.

Detecting Planetary-mass Primordial Black Holes with Resonant Electromagnetic Gravitational Wave Detectors

“…For more realistic extended mass functions, the abundance, size and evolution of DM halos, partially or entirely made of PBHs, is impacted by several effects, see e.g. [59][60][61][62][63][64][65][66][67][68][69]. Let us mention a Poissonian noise from the discrete nature of PBHs, a seeding effect from heavy PBHs, the enhancement of the primordial power spectrum at the origin of PBH formation, the dynamical heating and evaporation of clusters, etc.…”

Magnetic field generation from primordial black hole distributions

“…Finally, as dark matter is (posited to be) made of discrete massive entities (i.e., primordial black holes), there is a further effect that has to be accounted for in the power spectrum. This last effect corresponds to the Poisson sampling noise, which is currently being studied (Padilla et al 2020). All in all, the matter power spectrum is given by…”

Horizons and Correlation Functions in 2D Schwarzschild-de Sitter Spacetime

“…Recently, LIGO detections of gravitational waves have introduced another potential source of information about the early universe, and have lead to renewed interest in the possibility of primordial black holes [5] [6] [7] [8]. See [9] for an analysis based on quantum gravity considerations, and [10] for an analysis based on ΛCDM phenomenology, plus compilations of references relevant to these different perspectives. If black holes existed in the early universe it is possible that the effects could be observed in the CMBR.…”