Mass spectrum of primordial black holes from inflationary perturbation in the Randall–Sundrum braneworld: a limit on blue spectra

Abstract

The mass spectrum of the primordial black holes formed by density perturbation in the radiationdominated era of the Randall-Sundrum type-2 cosmology is given. The spectrum coincides with standard four-dimensional one on large scales but the deviation is apparent on smaller scales. The mass spectrum is initially softer than standard four-dimensional one, while after accretion during the earliest era it becomes harder than that. We also show expected extragalactic diffuse photon background spectra varying the initial perturbation power-law power spectrum and give constraints on the blue spectra and/or the reheating temperature. The most recent observations on the small scale density perturbation from WMAP, SDSS and Lyman-α Forest are used. What we get are interpreted as constraints on the smaller-scale inflation on the brane connected to the larger one at the scale of Lyman-α Forest. If we set the bulk curvature radius to be 0.1 mm and assume the reheating temperature is higher than 10 6 GeV, the scalar spectral index from the smaller scale inflation is constrained to be n 1.3. Typically, the constraints are tighter than the standard four-dimensional one, which is also revised by us using the most recent observations.

Scalar perturbations in braneworld cosmology

“…the greater gravitational force of attraction in the early universe will create more of these objects than in GR (different aspects of primordial black holes in RS cosmology in the context of various effective theories have been considered in Refs. [41,42,43,44,45,46,47]). We know that the abundance of primordial black holes can be constrained by big bang nucleosythesis and observations of high-energy cosmic rays, so it would be interesting to see if the kind of enhancement of density perturbations predicted in this paper can be used to derive new limits on Randall-Sundrum cosmology.…”

Accuracy of slow-roll formulae for inflationary perturbations: implications for primordial black hole formation

“…Previous work [42,43,44] has used the Press-Schechter formalism, in which P (δ) is a Gaussian function, yielding…”

Efficient electroweak baryogenesis by black holes

“…However, as Carr notes [55], initial density pertur bations in FRW cosmologies that produce primordial black holes suggest values in the range 2 < n < 3. In RS cosmology similar ranges for the power law apply [50].…”

“…These constraints refer to the fraction at formation time of the mass of the Universe going into PBHs, namely they refer to the quantity «,■ = -it \ye summarize the possibly relevant observational constraints in relation to the very small PBH masses that appeared in our scenario [31,[47][48][49][50][51]. PBHs with lifetime smaller than 10_25 are free from big bang nucleosynthesis (BBN) constraints because they evaporate well before weak freeze-out and leave no trace.…”