Spins of primordial black holes formed in the matter-dominated phase of the Universe

Abstract

Angular momentum plays very important roles in the formation of primordial black holes in the matter-dominated phase of the Universe if it lasts sufficiently long. In fact, most collapsing masses are bounced back due to centrifugal force, since angular momentum significantly grows before collapse. For masses with q ≤ q c ≃ 2.4I 1/3 σ 1/3 H , where q is a nondimensional parameter of initial reduced quadrupole moment, σ H is the density fluctuation at horizon entry t = t H , and I is a parameter of the order of unity, angular momentum gives a suppression factor ∼ exp(−0.15I 4/3 σ −2/3 H ) to the production rate. As for masses with q > q c , the suppression factor is even stronger as ∼ exp(−0.0046q 4 /σ 2 H ). We derive the spin distribution of primordial black holes and find that most of the primordial black holes are rapidly rotating near the extreme value a * = 1, where a * is the nondimensional Kerr parameter at their formation. The smaller σ H is, the stronger the tendency towards the extreme rotation. Combining this result with the effect of anisotropy, we numerically and semianalytically estimate the production rate β 0 of primordial black holes. Then we find that β 0 ≃ 1.9 × 10 −6 f q (q c )I 6 σ 2is the fraction of masses whose q is smaller than q c and we assume f q (q c ) is not too small. We argue that matter domination significantly enhances the production of primordial black holes despite the suppression factor. If the end time t end of the matter-dominated phase satisfies t end (0.4Iσ H ) −1 t H , the effect of the finite duration significantly suppresses primordial black hole formation and weakens the tendency towards large spins.

Sensitivity of primordial black hole abundance on the reheating phase

“…We illustrate this reheating sensitivity in a simplest model of single-field inflation with a quasi-inflection point, which we believe is also manifest itself in other generation models of PBH, for example, double inflation model [61][62][63], double inflection-point model [64], to name just a few. It is worth noting that the reheating sensitivity shown in this paper is different from those interesting discussions where PBHs are formed during slow reheating after inflation [65] or during matter-dominated epoch after inflation but before reheating [66][67][68].…”

Primordial black hole remnants as dark matter produced in thermal, matter, and runaway-quintessence postinflationary scenarios

“…If the collapsing region has angular momentum the formation rate is further suppressed and reads [60],…”

“…Benchmark values are q c = √ 2, I = 1, f q ∼ 1. According to [60] the expression (3.19) applies for σ 0.005 whereas Eq. (3.18) applies for 0.005 σ 0.2.…”

“…Ref. [60] concluded that the finite duration of the PBH formation can be neglected if the reheating time t rh satisfies t rh > 2 5 I σ −1 t k where t k is the time of the horizon entry of the scale k −1 (it does not coincide with the formation time t form ). In terms of temperatures this condition rewrites T rh < 2 5 I σ 1/2 T k where T k the temperature that the scale k −1 would enter the horizon during RD.…”

Unraveling the origin of black holes from effective spin measurements with LIGO-Virgo

“…As a result, a generic prediction of the picture where the LIGO-Virgo BBH events are in part or all PBH mergers is that the effective spin parameter (to be defined below, and which depends among other things on the intrinsic black hole spin magnitudes) is very low. Incidentally, it is important to point out that this fact (that binary mergers of PBH should have a low effective spin parameter) does depend on cosmology: it has been shown, for instance, that if the universe went through a matter-domination phase during PBH formation, then in fact the intrinsic spin of the resulting PBHs is generically close to maximal [13]. Furthermore, other possibilities might arise for cosmologies where the early universe was neither matter-nor radiation-dominated at early times, as we explored recently [14,15].…”