^{1,2}

^{2,3}

^{2,4}

^{2}

^{2}

^{3}.

We propose a mechanism to generate primordial black holes (PBHs) that is independent of cosmological inflation and occurs slightly below the QCD phase transition. Our setup relies on the collapse of long-lived string-domain wall networks and is naturally realized in QCD axion models with domain wall number

The recent detection of gravitational waves emitted by the merging of relatively heavy black holes [

Several fundamental physics scenarios may explain the existence of PBHs. Arguably, the most studied proposal relies on the gravitational collapse of density fluctuations generated during inflation (see, e.g., Ref.

In this Letter we propose an alternative PBH formation mechanism, independent of inflationary physics, that relies on the collapse of axionic topological defects (see, e.g., Ref.

When the PQ symmetry is broken after inflation, the axion abundance receives comparable contributions from the (i) misalignment mechanism, (ii) radiation from string defects

The hybrid network dynamics is hard to analyze. However, for our purposes the essential features can be captured by focusing on the closed walls that arise in the network

Once the Hubble length becomes comparable to the closed wall size

Another important parameter for the formation of PBHs is the ratio of the Schwarzschild radius

The temperature behavior of

Therefore, the duration of the hybrid network has a huge impact on the likelihood of forming PBHs, as well as on their masses. The use of long-lived string-wall networks is the essential new idea of our proposal. This requires multiple DWs attached to each string

Let us embed the basic mechanism illustrated in the previous section in the QCD axion cosmology. Consider a scalar field

In Fig.

Constraints on

In Fig.

Crucially, for closed DWs collapsing at

The region around

Constraints on

Figure

Let us estimate the fraction

However, this result is sensitive to the precise numerical scaling of

Observations require

Nevertheless, to confidently estimate the actual fraction requires additional numerical studies, which we leave for future work. Let us remark that if a larger

A minimalistic option to generate Eq.

Here, we propose an alternative possibility to generate the bias term. Consider a dark gauge sector, which also breaks the

Interestingly, this naturally allows for the scale

These parameters have an important impact on PBH formation. For instance, for

We have discussed a new mechanism to generate PBHs in the context of QCD axion models. It proceeds by the late collapses of closed DWs in a long-lived string-DW network, which arises in QCD axion realizations with

Lacking accurate knowledge of the network evolution and collapse, we cannot give precise predictions for the fraction and masses of the PBHs. However, under reasonable assumptions, depending on the temperature behavior of the bias term, PBHs with masses in the range

Our proposal appears to prefer small values of the axion decay constant,

Our mechanism might be probed at gravitational wave observatories via the detection of gravitational radiation from: SMBH binaries at LISA

Finally, let us mention that considering very light generic axionlike particles, the network collapse could be delayed to

We thank J. J. Blanco-Pillado, J. Garriga, J. Redondo, K. Saikawa, G. Servant, and T. Vachaspati for useful discussions. We acknowledge support by the Spanish Ministry MEC under Grant No. FPA2014-55613-P and the Severo Ochoa excellence program of MINECO (Grants No. SO-2012- 0234, No. SEV-2016- 0588), as well as by the Generalitat de Catalunya under Grant No. 2014-SGR-1450. F. F. was also supported in part by the U.S. Department of Energy, Office of High Energy Physics, under Awards No. DE-FG02-91ER40628 and No. DE-SC0017987.

This situation can arise more generally from sequences of phase transitions in the early Universe.

The original DFSZ

See, however, Refs.

For the time being, we consider a bias term which switches on at

We have neglected angular momentum in the numerical simulation. We expect that for large

In support of this choice, numerical simulations exist

The lines of constant