Gravitational wave constraints on the primordial black hole dominated early universe

Abstract

We calculate the gravitational waves (GWs) induced by the density fluctuations due to the inhomogeneous distribution of primordial black holes (PBHs) in the case where PBHs eventually dominate and reheat the universe by Hawking evaporation. The initial PBH density fluctuations are isocurvature in nature. We find that most of the induced GWs are generated right after evaporation, when the universe transits from the PBH dominated era to the radiation dominated era and the curvature perturbation starts to oscillate wildly. The strongest constraint on the amount of the produced GWs comes from the big bang nucleosynthesis (BBN). We improve previous constraints on the PBH fraction and find that it cannot exceed 10-4. Furthermore, this maximum fraction decreases as the mass increases and reaches 10-12 for MPBH∼ 5×108 g, which is the largest mass allowed by the BBN constraint on the reheating temperature. Considering that PBH may cluster above a given clustering scale, we also derive a lower bound on the scale of clustering. Interestingly, the GW spectrum for MPBH∼ 104 -108 g enters the observational window of LIGO and DECIGO and could be tested in the future. Although we focus on the PBH dominated early universe in this paper, our methodology is applicable to any model with early isocurvature perturbation.

Shining Light on Dark Matter with Black Holes

“…radiation (e.g. [33,34]) as well as induced GWs associated with reheating due to PBH evaporation [35,36]. As depicted on Fig.…”

Dark matter in the time of primordial black holes

“…Additionally, stronger constraints on the amount of produced GWs comes from BBN [73]. However, this can be avoided if .…”

Dark matter from evaporating Black Holes

“…Let us define the ratio f (t) = ρ BH (t)/ρ R (t). Denoting the scale factor with a(t), since ρ BH (t) ∝ 1/a(t) 3 , while ρ R (t) ∝ 1/a(t) 4 , the ratio f (t) increases linearly in the scale factor, f (t) ∝ a(t). It is possible that PBHs dominate the energy content of the Universe before their complete evaporation: this a situation is referred to as BH domination.…”

“…Depending on β, the Universe might have been radiation or BH dominated at the evanescence of the PBHs [2]: these situations are referred to as radiation or BH domination, respectively. The range of PBHs masses between 10 −5 g and 10 9 g is quite unconstrained, apart from gravitational waves (GW) induced by second order effects [3,4], which set an upper limit on β, excluding a small portion of the region associated to BH domination.…”