Moduli constraints on primordial black holes

Abstract

Abstract. The amount of late decaying massive particles (e.g., gravitinos, moduli) produced in the evaporation of primordial black holes (PBHs) of mass M BH < ∼ 10 9 g is calculated.Limits imposed by big-bang nucleosynthesis on the abundance of these particles are used to constrain the initial PBH mass fraction β (ratio of PBH energy density to critical energy density at formation), as: β < ∼ 5 × 10 −19 (x φ /6 10 −3 ) −1 (M BH /10 9 g) −1/2 (Y φ /10 −14 ); x φ is the fraction of PBH luminosity going into gravitinos or moduli, Y φ is the upper bound imposed by nucleosynthesis on the number density to entropy density ratio of gravitinos or moduli. This notably implies that such PBHs should never come to dominate the cosmic energy density.PACS numbers: 98.80.Cq * email: Martin.Lemoine@obspm.fr 1 1. Introduction -The spectrum of locally supersymmetric theories generically contain fields whose interactions are gravitational, and whose mass m φ ∼ O(100 GeV). The Polonyi and gravitino fields of supergravity theories, or the moduli of string theories, are such examples. This leads to well-known cosmological difficulties: quite notably, such particles (hereafter generically noted φ and termed moduli) decay on a timescale τ φ ∼ M 2 Pl /m 3 φ ∼ 10 8 s (m φ /100 GeV) −3 , i.e., after big-bang nucleosynthesis (BBN), and the decay products may drastically alter the light elements abundances [1]. The success of BBN predictions provides in turn a stringent upper limit on the number density to entropy density ratio (Y φ ) of these moduli, generically Y φ < ∼ 10 −14 [2] (see Sec. 3).It is argued in this letter that these same constraints can be translated into stringent constraints on the abundance of primordial black holes (PBHs) with mass M BH < ∼ 10 9 g. In effect, moduli are expected to be part of the Hawking radiation of an evaporating black hole as soon as the temperature of the black hole exceeds (roughly speaking) the rest-mass m φ ; and indeed, the Hawking temperature of a PBH reads T BH ≡ m 2 Pl /M BH ≃ 10 4 GeV (M BH /10 9 g) −1 [3]. Primordial black holes are liable to form in the early Universe at various epochs, e.g., when a density fluctuation re-enters the horizon with an overdensity of order unity [4], or when the speed of sound vanishes [5] (as may occur in phase transitions). As a consequence, constraints on the abundance of PBHs can be translated into constraints on the structure of the very early Universe [6]. Until recently, the only existing constraint on PBHs of mass M BH < ∼ 10 9 g relied on the assumption that via evaporation, PBHs leave behind stable Planck mass relics [7]. However, recent work from the perspective of string theories seems to indicate that this is not the case [8], in particular that evaporation proceeds fully. Nevertheless, Green [9] has pointed out recently that such PBHs would also produce supersymmetric particles, and consequently, cosmological constraints on the lightest supersymmetric particle (LSP) density could be turned into constraints on the initial PBH mass fraction β (defi...

Clustering of primordial black holes: Basic results

“…While PBH reheating has been considered [29,30], it can be shown that [31,32,33] that the period of PBH domination necessary would lead to the overproduction of (supersymmetric) moduli fields and gravitinos upon their evaporation that contradict the predictions of big bang nucleosynthesis (BBN). While the authors of [28] seem to confuse the distinction between radiation perturbations and PBH perturbations (see their Equation (11)), we show later that PBH merging could be a natural consequence of clustering.…”

Grand Unification Scale Primordial Black Holes: Consequences and Constraints

“…A PBH radiates any and all particles whose rest mass is substantially less than its current temperature, including gravitons. If the PBH radiate massive, long-lived particles one obtains tight bounds on their initial population [10,11,12,13,14] but these limits are contingent upon assumptions about particle physics and quantum gravity, and other radiated particles will reach thermal equilibrium, erasing any memory of their origin. However gravitons emitted as the black hole decays cannot equilibriate and will always survive until the present day, producing a stochastic background of gravitational waves.…”

Cosmological Reflection of Particle Symmetry

“…Following References [1,2,98,180] and [183,184] (but in a different framework and using more stringent constraints), limits on the mass fraction of black holes at the time of their formation (β ≡ ρ PBH /ρ tot ) were derived in Reference [185] using the production of gravitinos during the evaporation process. Depending on whether gravitinos are expected to be stable or metastable, the limits are obtained using the requirement that they do not overclose the universe and that the formation of light nuclei by the interactions of 4 He nuclei with nonequilibrium flux of D,T, 3 He and 4 He does not contradict the observations.…”