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In a variety of mechanisms generating primordial black holes, each black hole is expected to form along with a surrounding underdense region that roughly compensates the black hole mass. This region will propagate outwards and expand as a shell at the speed of sound in the homogeneous background. Dissipation of the shell due to Silk damping could lead to detectable $\mu$-distortion in the CMB spectrum. While the current bound on the average $\mu$-distortion is $\left| \bar{\mu}\right|\lesssim10^{-4}$, the standard $\Lambda$CDM model predicts $\left| \bar{\mu}\right|\sim10^{-8}$, which could possibly be detected in future missions. It is shown in this work that the non-observation of $\bar{\mu}$ beyond $\Lambda$CDM can place a new upper bound on the density of supermassive primordial black holes within the mass range $10^{6}M_{\odot}\lesssim M\lesssim10^{15}M_{\odot}$. Furthermore, black holes with initial mass $M\gtrsim10^{12}M_{\odot}$ could leave a pointlike distortion with $\mu\gtrsim10^{-8}$ at an angular scale $\sim 1^{\circ}$ in CMB, and its non-observation would impose an even more stringent bound on the population of these stupendously large primordial black holes., Comment: 21 pages in REVTeX (V.4), 3 figures

The discoveries of LIGO/Virgo black holes in recent years have revitalized the study of primordial black holes. In this work, we investigate a mechanism where primordial black holes are formed by vacuum bubbles that randomly nucleate during inflation through quantum tunneling. After inflation, these bubbles typically run into the ambient radiation fluid with a large Lorentz factor. In our previous work, we assumed the bubble fields are strongly coupled to the standard model particles so that the bubble wall is impermeable. Here we complete this picture by considering bubbles interacting with the fluid only through gravity. By studying the scenario in several limits, we found that black holes could form in either subcritical or supercritical regime. Depending on the model parameters, the resulting mass spectrum of the black holes could be wide or narrow, and may develop two peaks separated by a large mass range. With different spectra, these black holes may account for the LIGO/Virgo black holes, supermassive black holes, and may play an important role in dark matter., Comment: 28 pages, 5 figures

The LIGO-Virgo Collaboration has so far detected around 90 black holes, some of which have masses larger than what were expected from the collapse of stars. The mass distribution of LIGO-Virgo black holes appears to have a peak at $\sim30M_{\odot}$ and two tails on the ends. By assuming that they all have a primordial origin, we analyze the GWTC-1 (O1\&O2) and GWTC-2 (O3a) datasets by performing maximum likelihood estimation on a broken power law mass function $f(m)$, with the result $f\propto m^{1.2}$ for $m35M_{\odot}$. This appears to behave better than the popular log-normal mass function. Surprisingly, such a simple and unique distribution can be realized in our previously proposed mechanism of PBH formation, where the black holes are formed by vacuum bubbles that nucleate during inflation via quantum tunneling. Moreover, this mass distribution can also provide an explanation to supermassive black holes formed at high redshifts., 24 pages in revtex4, 5 figures

Vacuum bubbles may nucleate and expand during the cosmic inflation. When inflation ends, the bubbles run into the ambient plasma, producing strong shocks followed by underdensity waves, which propagate outwards. The bubbles themselves eventually form black holes with a wide distribution of masses. It has been recently suggested that such black holes may account for LIGO observations and may provide seeds for supermassive black holes observed at galactic centers. They may also provide a significant part or even the whole of the dark matter. We estimate the spectral $\mu$-distortion of the CMB induced by expanding shocks and underdensities. The predicted distortions averaged over the sky are well below the current bounds, but localized peaks due to the largest black holes impose constraints on the model parameters., Comment: 27 pages, 6 figures; v2: Added a brief discussion of PBH effect on structure formation

In theories with a broken discrete symmetry, Hubble sized spherical domain walls may spontaneously nucleate during inflation. These objects are subsequently stretched by the inflationary expansion, resulting in a broad distribution of sizes. The fate of the walls after inflation depends on their radius. Walls smaller than a critical radius fall within the cosmological horizon early on and collapse due to their own tension, forming ordinary black holes. But if a wall is large enough, its repulsive gravitational field becomes dominant much before the wall can fall within the cosmological horizon. In this ``supercritical'' case, a wormhole throat develops, connecting the ambient exterior FRW universe with an interior baby universe, where the exponential growth of the wall radius takes place. The wormhole pinches off in a time-scale comparable to its light-crossing time, and black holes are formed at its two mouths. As discussed in previous work, the resulting black hole population has a wide distribution of masses and can have significant astrophysical effects. The mechanism of black hole formation has been previously studied for a dust-dominated universe. Here we investigate the case of a radiation-dominated universe, which is more relevant cosmologically, by using numerical simulations in order to find the initial mass of a black hole as a function of the wall size at the end of inflation. For large supercritical domain walls, this mass nearly saturates the upper bound according to which the black hole cannot be larger than the cosmological horizon. We also find that the subsequent accretion of radiation satisfies a scaling relation, resulting in a mass increase by about a factor of 2.