Tag Archives: #primordialblackholes

How Primordial Black Holes Forms From Inflation With Solo or Multiple Bumps? (Cosmology / Quantum Physics)

Ruifeng Zheng and colleagues investigated the formation of primordial black holes (PBHs) from inflation model with bumpy potential, which has multiple bumps. They found that, the potential can give rise to power spectrum with single or multiple peaks in small scales, which can in turn predict the production of primordial black holes. Their study recently appeared in Arxiv.

There are several inflation models which discuss the possibility of the production of primordial black holes in inflation process of the early universe. But, the production of PBHs requires the violation of slow-roll condition. For this reason, slow-roll violating models become an interesting alternative, including ultra-slow-roll (USR) inflation, inflation with inflection points or bumps and others.

Previous studies have already discussed the case of potential with one bump. Now, Ruifeng and colleagues discussed the extended case of multiple bumps, which can generate PBHs at different mass ranges.

Fig 1: The evolution of φ with the parameter N, which enters the USR-like stage three times near N = 20, N = 35 and N = 50. © Zheng et al.

Specifically, they considered the power-law potential as the basic potential, and add one or several bumps of Gaussian type which makes the inflaton roll from the slow-roll stage to USR-like stage.

“These multiple bumps are quite different from the solo-bumpy ones, we have to take care of not only the shape of each bump like height, width, etc., but also the relative distance of the bumps. This is important because, when the inflaton field passes through one bump, it will lose kinetic energy, and if the bumps are far from each other, it may not have enough energy to pass through the next ones. For this reason, we set the bumps close to each other.”

With the potential, they constructed the power spectrum with single or multiple peaks in small scales, while keeping the large scale power spectrum consistent with CMB data. Later, they numerically calculated the abundances of PBHs (fraction to dark matter) at the mass range given by the solo-bumpy potential, as well as three mass ranges given by the multi-bumpy potential. Finally, they found that, PBHs can be formed at different mass ranges, including asteroid mass range (10¯16 − 10¯14M), planet mass range (10¯6 − 10¯3M) and solar mass range (around 1M), some of which can reach significant abundance.

FIG. 2: They plot fP BH for potential (21) given in paper with p = 2 using different threshold densities δc, where the yellow line corresponds to δc = 0.41, the purple line corresponds to δc = 0.46, and the blue line corresponds to δc = 0.486. Their results are consistent with the constraints from current observations. © Zheng et al.

They also found that, the larger threshold energy density (δc) is, the smaller the abundance will be, and this is easy understanding: the larger the threshold energy is, the more difficult it is to form black holes. For the small value of threshold energy density, the abundance of PBHs can reach around 10% of dark matter. The mass range of the PBHs formed is around 10¯15 M, namely the asteroid mass.

Moreover, they also considered the possibility of formation of primordial black holes (PBHs) in the early universe, through ellipsoidal collapse instead of spherical collapse. The difference between these two collapse models is that the threshold density for forming PBH is different. Because compared with the spherical collapse, the PBHs formed by the ellipsoidal collapse will increase the ellipticity of the formed PBHs, which will lead to the correction of the threshold density. Thus, abudance of ellipsoidal PBHs is lower than that of spherical PBHs, due to difference in their threshold densities.

FIG. 3: The figures above show the constraints on primordial black holes acting as dark matter, in which the colored region is excluded by various observations. The blue line correspond to fPBH, and the red line correspond to fe-PBH. The plot is for potential and δc = 0.465. From left to right, the masses of PBHs are 3.6975 × 10¯27 M, 5.8601 × 10¯16 M and 3.6975 × 10¯3 M respectively. Constraints are obtained from the publicly available Python code PBHbounds. © Zheng et al.

Finally, it has been suggested that, considering the age of the universe, PBHs with initial mass less than 1015g (∼ 10¯18 M) has been completely evaporated today. But, the PBHs of mass 3.6975 × 10¯27 (as shown in figure 3 above) may actually be vanishing, and cannot explain the dark matter today. But, although they can’t explain today’s dark matter they may still have a significant impact on the early universe, such as the process of Big Bang Nucleosynthesis, reheating, baryogenesis and so on.

Ruifeng and colleagues suggested that, we can be able to detect the traces left by such PBHs with future observation techniques, to find more evidence of their existence. Meanwhile, for other mass ranges, the PBHs are hardly evaporated till now and thus can act as dark matter.

“We will explore further details on the influences of the PBHs in our model in the future work.”

— concluded authors of the study

Reference: Ruifeng Zheng, Jiaming Shi, Taotao Qiu, “On Primordial Black Holes generated from inflation with solo/multi-bumpy potential”, Arxiv, pp. 1-14, 2021. https://arxiv.org/abs/2106.04303

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How To Confirm The Existence of Primordial Black Holes? (Cosmology / Physics)

Primordial black holes (PBH’s) are a hypothetical type of black hole that formed soon after the Big Bang. In the early universe, high densities and heterogeneous conditions could have led sufficiently dense regions to undergo gravitational collapse, forming black holes. They are non-baryonic and as such are plausible dark matter (DM) candidates. PBH’s emit Hawking radiation and evaporation process can give rise to observable signals. Now, Antonio Palazzo and colleagues for the first time proposed a possibility that, PBHs with masses in the range of [5 × 1014 − 5 × 1015]g, emit neutrinos during evaporation and these neutrinos can interact through the coherent elastic neutrino nucleus scattering process, producing an observable signals in the dark matter (DM) direct detection experiments (like XENONnT, DARWIN etc.) Their study recently appeared in Arxiv.

Coherent elastic neutrino-nucleus scattering (“CEvNS”) is a process involving the neutral-current scattering of a neutrino with an entire nucleus. It is only recently that, CEvNS process has been successfully observed by COHERENT, where a few kilograms of detector was exposed to an intense neutrino flux of artificial origin. The very same process involving neutrinos of natural origin, such as, from the Sun, diffuse supernovae and Earth’s atmosphere, constitute an irreducible background in DM direct searches. This background gives rise to the so-called “neutrino floor”, which applies only to direct detection experiments. These experiments search for the scattering of a dark matter particle like WIMP’s, off of a nucleus.

Fig 1: Impact of PBHs on the Neutrino floor. The black contour delimiting the yellow region represents the ordinary neutrino floor, while the upper border of the colored bands correspond to the modifications induced by neutrinos from PBHs with masses and DM fractions in the legend. These benchmark values lie on the 90% C.L. exclusion curve obtainable from a liquid xenon experiment with 200 t yr exposure © Antonio Palazzo et al.

Antonio Palazzo and colleagues, showed that, PBHs with masses in the range, I mentioned above, emit neutrinos with peak energy 10 MeV and 100 MeV, which may emerge as a signal on such a familiar background. As a result, it is possible to set prospective bounds on the PBHs fraction of dark matter (DM) in this mass range, by improving the existing neutrino limits obtained with Super-Kamiokande.

“We have shown that with the high exposures envisaged for the next-generation facilities, it will be possible to set bounds on the fraction of dark matter (DM) composed of PBHs, improving the existing neutrino limits obtained with Super-Kamiokande.”

— wrote authors of the study

Finally, they showed how the neutrino floor gets modified by the presence of a hypothetical signal from PBHs. The neutrinos emitted by PBHs would lie on top of an irreducible background. Therefore, the existence of even a minute fraction of PBHs in the DM content would modify the neutrino floor, making it higher.

“In the context of PBHs searches, the direct DM experiments would rather operate as indirect DM observatories. From this perspective, our study lends further support to the emerging role of such underground facilities as multi-purpose low-energy neutrino telescopes complementary to their high-energy “ordinary” counterparts, IceCube and KM3NeT.”

— concluded authors of the study

Reference: Roberta Calabrese, Damiano F.G. Fiorillo, Gennaro Miele, Stefano Morisi, Antonio Palazzo, “Primordial Black Hole Dark Matter evaporating on the Neutrino Floor”, Arxiv, pp. 1-8, 2021. https://arxiv.org/abs/2106.02492

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How Primordial Black Hole Forms? (Quantum / Cosmology)

Michael Baker and colleagues discussed the new mechanism of formation of primordial black holes (PBH’s) during a first-order phase transition in the early Universe. Their study recently appeared in Arxiv.

Primordial black holes are a hypothetical type of black hole that formed soon after the Big Bang. There are several possible formation mechanisms of primordial black holes (PBH’s): the most widely studied is collapse of density perturbations generated during inflation, while the collapse of topological defects, the dynamics of scalar condensates, or collisions of bubble walls during a first-order phase transition are viable alternatives.

Now, Michael Baker and colleagues, proposed a new mechanism of PBH production during a first-order cosmological phase transition.

“While previous papers on this topic have only considered the energy density stored in the bubble wall, we focused on a population of particles that interact with the bubble wall and showed that during a first-order phase transition, the energy density of the reflected particles can reach sufficient densities to trigger collapse into PBHs.”

— wrote M. Baker and his collaborators

They considered a particle species that interact/collides with the bubble wall. The mass of these particles may increase significantly during phase transitions due to either confinement or a Higgs mechanism. High-momentum particles can pass through the bubble wall into the true vacuum and gain a large mass, while low-momentum χ particles are reflected due to energy conservation (as shown in fig 1 below). The build-up of reflected particles (in front of the walls) creates a density perturbation which may lead to PBH formation.

(article continues below image)

A cartoon picture of the late stage of a first-order cosmological phase transition: regions of true vacuum (blue) are expanding with speed vw and coalescing, leaving an approximately spherical bubble of false vacuum (light red). High-momentum χ particles can pass through the bubble wall into the true vacuum and gain a large mass, while low-momentum χ particles are reflected due to energy conservation. The build-up of χ particles creates a density perturbation which may lead to PBH formation. The local coordinate system is also shown, along with the bubble wall thickness, lw. © M. Baker et al.

They track this process quantitatively by solving a Boltzmann equation, and demonstrated that the mass and density of the PBHs depend on the temperature at which the phase transition occurs and the probability that a black hole will form in a given volume.

Reference: Michael J. Baker, Moritz Breitbach, Joachim Kopp, Lukas Mittnacht, “Primordial Black Holes from First-Order Cosmological Phase Transitions”, Arxiv, pp. 1-7, 2021. https://arxiv.org/abs/2105.07481

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Does Fall Of Inflaton Give Rise To Primordial Black Holes (PBH’s)? (Quantum Physics / Cosmology)


  • According to physicists, e-folding is simply the amount of time it takes for space to expand by approximately 2.71828 times its original size. The number 2.71828 is eulers number.
  • In order to produce primordial black holes (PBH’s) from inflationary fluctuations, large deceleration of inflation is required.
  • Now, Inamoto and colleagues showed that a large enhancement of perturbations results when the inflation crosses a downward step in its potential in less than an e-fold.
  • In simple terms, during this step, inflation loses extra kinetic energy due to hubble friction and there are large enhancement of perturbations which produces primordial black holes and ultra-compact minihalos.

Primordial black holes (PBHs) are one of the most intriguing topics in modern cosmology, owing to their potential to explain dark matter (DM) and the BHs detected by the LIGO-Virgo collaboration. Also, PBHs might be related to other observational results, such as the existence of supermassive black holes, the OGLE results, the recent NANOGrav results, and the anomalous excess of 511 keV photons. PBHs can be produced when very large density perturbations enter the horizon in the early universe. In particular, the PBH scenarios for DM or LIGO-Virgo events can be associated with the large power spectrum of primordial curvature perturbations, PR ∼ 10¯2, on small scales.

Now, Inomata and colleagues, focused on single-field inflation models that can realize the large power spectrum on small scales for the PBH scenarios. Under the slow-roll approximation, the power spectrum is given by

where the subscript “∗” denotes evaluation at the horizon exit of the perturbation and

where N ≡ ∫ Hdt is the number of e-folds of inflationary expansion. From this relation, at first glance, the large power spectrum on small scales needed for the PBH scenarios seems to require a substantial decrease in ϵ, and hence the kinetic energy of the inflaton, from the horizon exit of CMB scales. This decrease is realized by a large negative value of η ≡ d ln ϵ/dN which violates the slow-roll assumption. This can be achieved with a very flat potential in a period of so called “ultra slow roll (USR)” when Hubble friction dominates over the potential slope. On the other hand since the slow-roll approximation must be violated, this invalidates the naive expectation of a decreased and leaves the possibility of alternative mechanisms.

“In our paper, we show that a decrease in the kinetic energy of the inflaton relative to that at CMB scales is not necessary for the large enhancement of perturbations required for the PBH scenarios. Equivalently, the inflation potential need not have a region that is flatter than it is at CMB scales. If the inflaton instead gains kinetic energy by rolling down a sufficiently sharp feature that it crosses in less than an e-fold, non-adiabatic particle production occurs.”

— told Inomata, first author of the study.

They showed that a large enhancement of perturbations results when the inflaton crosses a downward step in its potential in less than an e-fold, which counter-intuitively allows a sizable amount of PBHs to form in a model wherein the inflaton always possesses a velocity higher than its value at the horizon exit of CMB scales. The enhancement can be interpreted as particle production due to the non-adiabatic transition whose curvature fluctuations are then adiabatically enhanced to large values as the inflaton loses the extra kinetic energy from the step due to Hubble friction.

Finally, they mentioned that, depending on the height and the location of the downward step, their enhancement mechanism can generate seeds not only for PBHs with a variety of masses, but also for ultra-compact minihalos. Additionally, the enhancement can be probed (constrained or discovered) by a range of complementary observables, such as the gravitational waves induced by the scalar perturbations, and CMB spectral distortions.

“Future observations of PBHs and these varied observable probes will enable us to probe this characteristic feature in the inflaton potential.”

— told Inomata, first author of the study

Featured image: The inflaton potential of Eq. (14) given in paper that realizes the large enhancement of perturbations, with the steplike transition at φ1 ≤ φ ≤ φ2 highlighted and an inset for the full range. The parameters are ns = 0.97, ϵ1 = 7.43 × 10¯10, ϵ2 = 0.01, ϵ3 = 10¯9, and ∆Nstep = 0.5. φend denotes the end of inflation (red vertical dotted line) and corresponds to 50 e-folds from φCMB. © Inomata et al.

Reference: Keisuke Inomata, Evan McDonough, Wayne Hu, “Primordial Black Holes Arise When The Inflaton Falls”, Arxiv, pp. 1-6, 2021. https://arxiv.org/abs/2104.03972

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Does Something Prevents Primordial Black Holes To Evaporate Completely? PART 2: The Truth (Quantum)

Previously on “Does something prevents primordial black holes to evaporate completely: PART 1”, we saw that in 2003, Chen and Adler argued that primordial black hole doesn’t evaporate completely,. Instead, it exists in the form of Planck-mass remnant with a cross-section on the order of 10¯70 m² which makes direct detection nearly impossible. Such black hole remnants have been identified as possible cold dark matter candidates.

But now, in a recently published paper in Astronomical Journal, Samuel Kovacik argued that it’s not completely true, instead, the final stage of the evaporation has a recoil effect which would give the microscopic black hole velocity on the order of 10¯1 c which is in disagreement with the cold dark matter cosmological model.

Samuel Kovacik et al.

Yeah friends, the temperature as a function of mass, grows very rapidly in the vicinity of m0. This means that, when the black hole has the mass mTmax for which it reaches the maximal temperature, the radiation is so energetic that the mass difference ∆m = mTmax – m0 is radiated in a relatively small amount of quanta, Nq ≈ ∆m / Tmax ≤ 10². Each quantum carries momentum on the order of p ≈ ∆m/√Nq and due to the conservation law the black hole receives the opposite momentum. As the radiation is random so are the momentum impulses the black hole receives. As a result, it performs a random walk in the momentum space, and after radiating Nq quanta will carry momentum of magnitude pr ≈ ∆m/√Nq. As a result, its final recoiled velocity will be on the order of:

This is the recoil effect due to thermal Hawking radiation of Planck-size black holes.

For the considered cases of matter density, they have ∆m / m0 = 0.33/0.26/0.22 and Nαq = 88/8.4/3.8; therefore recoil velocity = 0.03/0.09/0.11. In all three cases, this is a considerable fraction of speed of light (recall that they used units in which c = 1).

Samuel Kovacik et al.

The recoil effect due to the Hawking radiation modified by the quantum structure of space discussed by us makes the Planck-size black holes improbable dark matter candidates as during the last moments of radiation they would obtain velocities large enough to be incompatible as cold dark matter. Velocities of the Planck-size black holes would also exceed escape velocities from most astronomical objects.

— told Samuel Kovacik, lead author of the study

However, their discussion has not been very detailed as they do not have a detailed description of the quantum gravity and the behaviour of the Hawking radiation on this scale. But, at least under current assumptions they think that the recoil effect due to thermal radiation of microscopic black holes should be taken into consideration.

This research was supported by VEGA 1/0703/20 and the MUNI Award for Science and Humanities funded by the Grant Agency of Masaryk University.

Reference: Samuel Kováčik et al., “Hawking-Radiation Recoil of Microscopic Black Holes”, Astronomical Journal, pp. 1-5, 2021. https://arxiv.org/abs/2102.06517

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Does Something Prevents Primordial Black Holes To Evaporate Completely?: PART 1 (Quantum / Cosmology)


Hawking radiation would make microscopic black holes evaporate rapidly which excludes them from many astrophysical considerations. However, Chen and Adler in their paper argued that the quantum nature of space would alter this behaviour: the temperature of a Planck-size black hole vanishes and what is left behind is a Planck-mass remnant with a cross-section on the order of 10¯70 m² which makes direct detection nearly impossible. Such black hole remnants have been identified as possible dark matter candidates.

In 2003, Chen and Adler argued that, when the gravity effect is included, the generalized uncertainty principle (GUP) may prevent black holes from total evaporation in a similar way that the standard uncertainty principle prevents the hydrogen atom from total collapse.

In the standard view of black hole thermodynamics, based on the entropy expression of Bekenstein and the temperature expression of Hawking, a small black hole should emit black body radiation, thereby becoming lighter and hotter, leading to an explosive end when the mass approaches zero. However Hawking’s calculation assumes a classical background metric and ignores the radiation reaction, assumptions which must break down as the black hole becomes very small and light. Thus it does not provide an answer as to whether a small black hole should evaporate entirely, or leave something else behind, which we refer to as a black hole remnant (BHR).

Numerous calculations of black hole radiation properties have been made from different points of view, and some hint at the existence of remnants, but in the absence of a well-defined quantum gravity theory none appears to give a definitive answer.

A cogent argument against the existence of BHRs can be made: since there is no evident symmetry or quantum number preventing it, a black hole should radiate entirely away to photons and other ordinary stable particles and vacuum, just like any unstable quantum system.

Chen and Alder, in their paper, argued that, when the gravity effect is included, the generalized uncertainty principle (GUP) may prevent black holes from total evaporation in a similar way that the standard uncertainty principle prevents the hydrogen atom from total collapse.

Specifically, they derived the GUP to obtain a modified Hawking temperature, which indicated that there should exist non-radiating Planck-size remnants (BHR) with a cross-section on the order of 10¯70 m² which makes direct detection nearly impossible.

The temperature of such Planck-size black hole vanishes and what is left behind is a Planck-mass remnant with a cross-section on the order. In the ordinary space, small black holes evaporate rapidly. In quantum space, they can be eternal and are very difficult to detect due to their miniscule cross-section. If they contributed significantly to the overall dark matter density, proving it would be difficult as direct detection seems to be impossible.

— told Chen, Lead author of the study.

BHRs are an attractive candidate for cold dark matter since they are a form of weakly massive interacting particles. They also investigated an alternative cosmology in which primordial BHRs are the primary source of dark matter. Their study indicated that their scenario is not inconsistent with basic cosmological facts, but more scrutiny is required before it can become a viable option.

To be continued in next part..

Reference: Pisin Chen, Ronald J. Adler, “Black hole remnants and dark matter”, Nuclear Physics B – Proceedings Supplements, Volume 124, 2003, Pages 103-106, ISSN 0920-5632, https://doi.org/10.1016/S0920-5632(03)02088-7.

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A Technique to Sift Out The Universe’s First Gravitational Waves (Astronomy)

Identifying primordial ripples would be key to understanding the conditions of the early universe.

In the moments immediately following the Big Bang, the very first gravitational waves rang out. The product of quantum fluctuations in the new soup of primordial matter, these earliest ripples through the fabric of space-time were quickly amplified by inflationary processes that drove the universe to explosively expand.

Primordial gravitational waves, produced nearly 13.8 billion years ago in the moments following the Big Bang, still echo through the universe today. Credits: MIT News

Primordial gravitational waves, produced nearly 13.8 billion years ago, still echo through the universe today. But they are drowned out by the crackle of gravitational waves produced by more recent events, such as colliding black holes and neutron stars.

Now a team led by an MIT graduate student has developed a method to tease out the very faint signals of primordial ripples from gravitational-wave data. Their results are published this week in Physical Review Letters.

Gravitational waves are being detected on an almost daily basis by LIGO and other gravitational-wave detectors, but primordial gravitational signals are several orders of magnitude fainter than what these detectors can register. It’s expected that the next generation of detectors will be sensitive enough to pick up these earliest ripples.

In the next decade, as more sensitive instruments come online, the new method could be applied to dig up hidden signals of the universe’s first gravitational waves. The pattern and properties of these primordial waves could then reveal clues about the early universe, such as the conditions that drove inflation.

“If the strength of the primordial signal is within the range of what next-generation detectors can detect, which it might be, then it would be a matter of more or less just turning the crank on the data, using this method we’ve developed,” says Sylvia Biscoveanu, a graduate student in MIT’s Kavli Institute for Astrophysics and Space Research. “These primordial gravitational waves can then tell us about processes in the early universe that are otherwise impossible to probe.”

Biscoveanu’s co-authors are Colm Talbot of Caltech, and Eric Thrane and Rory Smith of Monash University.

A concert hum

The hunt for primordial gravitational waves has concentrated mainly on the cosmic microwave background, or CMB, which is thought to be radiation that is leftover from the Big Bang. Today this radiation permeates the universe as energy that is most visible in the microwave band of the electromagnetic spectrum. Scientists believe that when primordial gravitational waves rippled out, they left an imprint on the CMB, in the form of B-modes, a type of subtle polarization pattern.

A team led by an MIT graduate student has developed a method to tease out the very faint signals of primordial ripples from gravitational-wave data produced by more recent events, such as colliding black holes and neutron stars. Credits: Image: Carl Knox, OzGrav/ Swinburne

Physicists have looked for signs of B-modes, most famously with the BICEP Array, a series of experiments including BICEP2, which in 2014 scientists believed had detected B-modes. The signal turned out to be due to galactic dust, however.

As scientists continue to look for primordial gravitational waves in the CMB, others are hunting the ripples directly in gravitational-wave data. The general idea has been to try and subtract away the “astrophysical foreground” — any gravitational-wave signal that arises from an astrophysical source, such as colliding black holes, neutron stars, and exploding supernovae. Only after subtracting this astrophysical foreground can physicists get an estimate of the quieter, nonastrophysical signals that may contain primordial waves.

The problem with these methods, Biscoveanu says, is that the astrophysical foreground contains weaker signals, for instance from farther-off mergers, that are too faint to discern and difficult to estimate in the final subtraction.

“The analogy I like to make is, if you’re at a rock concert, the primordial background is like the hum of the lights on stage, and the astrophysical foreground is like all the conversations of all the people around you,” Biscoveanu explains. “You can subtract out the individual conversations up to a certain distance, but then the ones that are really far away or really faint are still happening, but you can’t distinguish them. When you go to measure how loud the stagelights are humming, you’ll get this contamination from these extra conversations that you can’t get rid of because you can’t actually tease them out.”

A primordial injection

For their new approach, the researchers relied on a model to describe the more obvious “conversations” of the astrophysical foreground. The model predicts the pattern of gravitational wave signals that would be produced by the merging of astrophysical objects of different masses and spins. The team used this model to create simulated data of gravitational wave patterns, of both strong and weak astrophysical sources such as merging black holes.

The team then tried to characterize every astrophysical signal lurking in these simulated data, for instance to identify the masses and spins of binary black holes. As is, these parameters are easier to identify for louder signals, and only weakly constrained for the softest signals. While previous methods only use a “best guess” for the parameters of each signal in order to subtract it out of the data, the new method accounts for the uncertainty in each pattern characterization, and is thus able to discern the presence of the weakest signals, even if they are not well-characterized. Biscoveanu says this ability to quantify uncertainty helps the researchers to avoid any bias in their measurement of the primordial background.

Once they identified such distinct, nonrandom patterns in gravitational-wave data, they were left with more random primordial gravitational-wave signals and instrumental noise specific to each detector.

Primordial gravitational waves are believed to permeate the universe as a diffuse, persistent hum, which the researchers hypothesized should look the same, and thus be correlated, in any two detectors.

In contrast, the rest of the random noise received in a detector should be specific to that detector, and uncorrelated with other detectors. For instance, noise generated from nearby traffic should be different depending on the location of a given detector. By comparing the data in two detectors after accounting for the model-dependent astrophysical sources, the parameters of the primordial background could be teased out.

The researchers tested the new method by first simulating 400 seconds of gravitational-wave data, which they scattered with wave patterns representing astrophysical sources such as merging black holes. They also injected a signal throughout the data, similar to the persistent hum of a primordial gravitational wave.

They then split this data into four-second segments and applied their method to each segment, to see if they could accurately identify any black hole mergers as well as the pattern of the wave that they injected. After analyzing each segment of data over many simulation runs, and under varying initial conditions, they were successful in extracting the buried, primordial background.

“We were able to fit both the foreground and the background at the same time, so the background signal we get isn’t contaminated by the residual foreground,” Biscoveanu says.

She hopes that once more sensitive, next-generation detectors come online, the new method can be used to cross-correlate and analyze data from two different detectors, to sift out the primordial signal. Then, scientists may have a useful thread they can trace back to the conditions of the early universe.

Paper: “Measuring the Primordial Gravitational-Wave Background in the Presence of Astrophysical Foregrounds

Provided by MIT

Cusps On Cosmic String Loops Collapse To Form Primordial Black Holes (Quantum)

Jenkins and colleagues, demonstrated using the hoop conjecture, that cusps on cosmic string loops must inevitably collapse to form PBHs.

Primordial black holes (PBHs) have held a prominent place in theoretical cosmology and astrophysics for more than 50 years, playing a wide variety of possible phenomenological roles. Their original motivation was as a source of Hawking radiation, and this remains an important line of research today. They are natural and well-motivated dark matter (DM) candidates, being massive, nonbaryonic, nonrelativistic, and interacting only through gravity. Binary PBHs are interesting potential sources of gravitational waves (GWs), and are a possible formation channel for the unexpectedly massive BH binaries observed by Advanced LIGO and Advanced Virgo in their first two observing runs (O1 and O2). PBHs could also act as the seeds for the formation of cosmic structures, particularly the supermassive black holes (SMBHs) observed at the centres of most galaxies.

Fig 1: A collapsing circular cosmic string loop (in blue) forms a PBH (in grey) once its Lorentz factor satisfies. ©JENKINS ET AL.

The most commonly-invoked mechanism for PBH formation is the collapse of large overdensities in the early Universe. However, this is only possible if the primordial power spectrum has a very large amplitude at small scales, which typically requires a certain degree of inflationary model building and fine tuning —either in terms of the inflationary field content, or in terms of adding features to the inflation potential—and is subject to constraints from CMB measurements of the power spectrum at large scales by the Planck satellite. These constraints become much stronger in the presence of primordial non-Gaussianity, as PBH formation then sources large isocurvature modes which are ruled out by Planck. Given a generic inflationary theory, there is therefore no guarantee of PBH formation. It is thus of great interest to find alternative PBH formation mechanisms that are as generic as possible.

One such alternative is the gravitational collapse of cosmic strings: 1+1-dimensional topological defects which are generic predictions of many extensions to the Standard Model. On macroscopic scales, cosmic strings are effectively described by a single parameter—their tension µ, which is conventionally written in the dimensionless combination Gµ, and is linked to the energy scale η at which the cosmic strings are formed by the relation Gµ ≤ (η/mP)<<1, where mP is the Planck mass. This tension characterises the gravitational influence of the strings, and is subject to constraints of order Gµ ≤ 10^-7 from CMB observations and of order Gµ ≤ 10^-11 from GW searches. Hawking first showed that PBH formation is the inevitable endpoint of the evolution of circular cosmic string loops, and PBH formation from circular loop collapse has remained an active research topic ever since. However (quasi)circular collapse is only possible if all three components of the loop’s angular momentum are smaller than those of a typical loop by a factor of ∼ Gµ. This mechanism is thus finely-tuned, and only a very small fraction of the cosmic loop population is expected to collapse in this way.

In this new study, Jenkins and colleagues showed that circular loop collapse is not the dominant mechanism for PBH formation from cosmic strings. They demonstrated, using the hoop conjecture, that cusps on cosmic string loops must inevitably collapse to form PBHs. Since cusps are generic features of cosmic string loops, and do not rely on finely-tuned loop configurations like circular collapse, this implies that the rate of PBH formation from cosmic strings has been drastically underestimated in the prior literature.

Figure 2. A segment of a cosmic string loop (in blue) becomes more compact as it develops a cusp. Once it satisfies the hoop condition it collapses to form a PBH (in grey). ©JENKINS et al.

If you dont know about, hoop conjecture, let me tell you, it is a powerful diagnostic for the formation of Black Hole horizons, which circumvents the need to solve the full nonlinear Einstein equation. The conjecture states that “horizons form when, and only when, a mass M gets compacted into a region whose circumference in every direction is C ≤ 4πGM. In other words, if a sphere containing mass M fits inside its own Schwarzschild radius rS ≡ 2GM, it must form a black hole.

Figure 3. An illustration of the PBH (in grey) immediately after formation. The cusp acceleration X¨ , cusp velocity nˆ, and PBH angular momentum J are all orthogonal to each other. The cosmic string (in blue) punctures the horizon at two points separated by a small angle ∼ Gµ, with its cusp hidden behind the horizon. ©JENKINS et al.

Their analysis is based on the flat-space equations of motion,

they have argued that gravitational backreaction acts far too slowly to prevent the collapse. (meaning that backreaction is unlikely to prevent PBH formation).

They also argued that, due to the unstable configuration of the parent loop near the horizon, large cusp-collapse PBHs are likely to be rapidly cut off from the loop network by string self-intersection. The majority of cusp-collapse PBHs, however, are extremely small, and evaporate on short timescales. These evaporating PBHs are constrained by their damping of small-scale CMB anisotropies, which leads to a nearly model-independent bound on the string tension, Gµ ≤ 10^-6. This in turn implies that cusp-collapse PBHs can only make up a small fraction of the dark matter, DM.

By calculating the angular momentum of the string segment captured behind the horizon, they have shown that cusp-collapse PBHs are highly spinning, with dimensionless spin parameter equal to two-thirds of the extremal Kerr value, χ = 2/3. This spin is a universal property of the formation mechanism, and is independent of the loop size, l and string tension, Gµ. To the best of their knowledge, cusp collapse is the only known primordial or astrophysical mechanism for generating subsolar-mass BHs with large but sub-extremal spins. The observation of such a black hole would therefore be a “smoking gun” signal of cusp collapse, and of cosmic strings more generally.

Cusps emit strong burst of gravitational waves, and are promising potential sources for ground-based gravitational waves interferometers like LIGO/Virgo and future space-based interferometers like LISA. It is therefore important to understand how Primordial black hole formation affects the gravitational waves emission from the cusp.

For that, they have developed a simple approximation for the expected gravitational waves (GW) signal, based on the standard cusp waveform. At low frequencies, the radiated GW energy spectrum is reduced by a factor of 1/4 compared to the standard cusp waveform, due to the truncation of the signal at, or just before, the peak of the cusp (as shown in below equation) .

At very high frequencies, there is a strong contribution due to the quasi normal mode (Quasinormal modes (QNM) are the modes of energy dissipation of a perturbed object or field, i.e. they describe perturbations of a field that decay in time.) ringing of the newly-formed primordial black hole, PBH. Integrating this GW emission over the cosmic string loop distribution, they have obtained updated predictions for the SGWB spectrum. The reduction of the SGWB intensity at frequencies probed by LIGO/Virgo and PTAs relaxes existing constraints on Gµ by as much as an order of magnitude, depending on the GW frequency band and the loop network model. However, for sufficiently small values of Gµ the SGWB spectrum is unchanged at observable frequencies, and the corresponding constraints are unaffected—this is the case for LISA, as well as for the LIGO constraint on model 3.

Figure 4. The SGWB spectrum from cusps on cosmic string loops. Solid lines include the effects of cusp collapse, while dotted lines correspond to the standard case without collapse. The magenta curve shows the power-law integrated (PI) sensitivity curve from the LIGO O1+O2 isotropic stochastic search. The green curve shows the Parkes Pulsar Timing ARray (PPTA) PI curve. The cyan curve shows the projected LISA power-law-integrated sensitivity curve. They use model 3 of the loop network with Gµ = 3 × 10^-¹¹, illustrating how the PPTA bound is weakened due to cusp collapse. At high frequencies the spectra with and without cusp collapse become identical; the frequency at which this changeover occurs decreases for smaller values of Gµ, meaning that the LIGO bound on model 3 is the same in both cases.

Future work is needed to calculate the merger rate of cusp-collapse PBH binaries, as well as the corresponding SGWB spectrum, as consistency with LIGO/Virgo observations (in particular the subsolar-mass search would provide another independent constraint on the string tension.

References : Alexander C. Jenkins, Mairi Sakellariadou, “Primordial black holes from cusp collapse on cosmic strings”, ArXiv, pp. 1-20, 2020. https://arxiv.org/abs/2006.16249

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Gravitational Waves From The Universe Filled With Primordial Black Holes (Astronomy)

Friends, primordial black holes (PBHs) are attracting increasing attention since they may play a number of important roles in Cosmology. They may indeed constitute part or all of the dark matter, they may explain the generation of large-scale structures through Poisson fluctuations, they may provide seeds for supermassive black holes in galactic nuclei, and they may account for the progenitors of the black-hole merging events recently detected by the LIGO/VIRGO collaboration through their gravitational wave emission.

There are several constraints on the abundance of PBHs, ranging from microlensing constraints, dynamical constraints (such as constraints from the abundance of wide dwarfs in our local galaxy, or from the existence of a star cluster near the centres of ultra-faint dwarf galaxies), constraints from the cosmic microwave background due to
the radiation released in PBH accretion, and constraints from the extragalactic gamma-ray background to which Hawking evaporation of PBHs contributes. However, all these constraints are restricted to certain mass ranges for the black holes, and no constraint applies to black holes with masses smaller than ∼ 10^9g, since those would Hawking evaporate before big-bang nucleosynthesis.

Nonetheless, various scenarios have been proposed where ultra-light black holes are abundantly produced in the early universe, so abundantly that they might even dominate the energy budget of the universe for a transient period. By Hawking evaporating before big-bang nucleosynthesis takes place, those PBHs would leave no direct imprint. It thus seems rather frustrating that such a drastic change in the cosmological standard model, where an additional matter-dominated epoch driven by PBHs is introduced, and where reheating proceeds from PBH evaporation, cannot be constrained by the above-mentioned probes. This situation could however be improved by noting that a gas of gravitationally interacting PBHs is expected to emit gravitational waves, & that these gravitational waves would propagate in the universe until today, leaving an indirect imprint of the PBHs past existence.

In the present work, Theodoros Papanikolaou and colleagues have studied the gravitational waves induced at second order by the gravitational potential of a gas of primordial black holes. In particular, they have considered scenarios where ultralight PBHs, with masses < 10^9g, dominate the universe content during a transient period, before Hawking evaporating.

There are several ways PBHs can be involved in the production of gravitational waves. First, the induction of gravitational waves can proceed from the primordial, large curvature perturbations that must have preceded and given rise to the existence of PBHs in the very early universe. Second, the relic Hawking-radiated gravitons may also contribute to the stochastic gravitational-wave background. Third, gravitational waves are expected to be emitted by PBHs mergers. But in the current paper, researchers investigated a fourth effect, namely the production of gravitational waves induced by the large-scale density perturbations underlain by PBHs themselves.

Contrary to the first effect which I mentioned above, more commonly studied, where PBHs and gravitational waves have a common origin (namely the existence of a large primordial curvature perturbation), in the problem at hand the gravitational waves are produced by the PBHs, via the curvature perturbation they underlie. They also notice that since they make use of cosmological perturbations theory, they would restrict their analysis to those scales where the density field remains linear, while the inclusion of smaller scales would require to resolve non-linear mechanisms such as merging, described in the third effect I mentioned above.

This fourth route is a very powerful one to constrain scenarios where the universe is transiently dominated by PBHs, since the mere requirement that the energy contained in the emitted gravitational waves does not overtake the one of the background after PBHs have evaporated (which would lead to an obvious backreaction problem), leads to tight constraints on the abundance of PBHs at the time they form. In particular, it excludes the possibility that PBHs dominate the universe upon their time of formation, independently of their mass.

In practice, they considered that PBHs are initially randomly distributed in space, since recent works suggest that initial clustering is indeed negligible. They also assume that the mass distribution of PBHs is monochromatic, since it was shown to be the case in most formation mechanisms. If PBHs form during the radiation era, their contribution to the total energy density increases as an effect of the expansion. Therefore, if their initial abundance is sufficiently large, they dominate the universe content before they evaporate, and researchers compute the amount of gravitational waves produced during the PBH-dominated era.

By neglecting clustering at formation, they found that the Poissonian fluctuations in their (PBH) number density underlay small-scale density perturbations, which in turn induce the production of gravitational waves at second order. In practice, they have computed the gravitational-wave energy spectrum, as well as the integrated energy density of gravitational waves, as a function of the two parameters of the problem, namely the mass of the PBHs, mPBH (assuming that all black holes form with roughly the same mass), and their relative abundance at formation ΩPBH,f. This calculation was performed by researchers both numerically and by means of well-tested analytical approximations. They have found that the amount of gravitational waves increases with mass of primordial black holes i.e. mPBH, since heavier black holes take longer to evaporate, hence dominate the universe for a longer period; and with ΩPBH,f, since more abundant black holes dominate the universe earlier, hence for a longer period too.

Requiring that the energy contained in gravitational waves never overtakes the one of the background universe led them to the constraint:

Equation 5.1.

Let them stress that since PBHs with masses smaller than 10^9g evaporate before big-bang nucleosynthesis, they cannot be directly constrained (at least without making further assumption). To their knowledge, the above constraint is therefore the first one ever derived on ultra-light PBHs. In particular, it shows that scenarios where PBHs dominate from their formation time on, ΩPBH,f ≈ 1, are excluded (given that m > 10g for inflation to proceed at less than 10^16GeV).

They also mentioned that the condition (equation given above) simply comes from avoiding a backreaction problem, and does not implement observational constraints. However, even if the above condition is satisfied, gravitational waves induced by a dominating gas of PBHs might still be detectable in the future with gravitational-waves experiments. Since they have found that the energy spectrum peaks at the Hubble scale at the time black holes start dominating, this corresponds to a frequency f = Hd/(2πa0), where a0 is the value of the scale factor today and Hd is the comoving Hubble scale at domination time. This
leads to

Equation 5.2

where, H0 is the value of the Hubble parameter today and zeq is the redshift at matter radiation equality. In Fig. given below, this frequency is shown in the region of parameter space that satisfies the condition. Covering 14 orders of magnitude, one can see that it intersects the detection bands of the einstein telescope (ET), the Laser Interferometer Space Antenna (LISA) and the Square Kilometre Array (SKA) facility.

Frequency at which the gravitational waves induced by a dominating gas of primordial black holes peak, as a function of their energy density fraction at the time they form, ΩPBH,f (horizontal axis), and their mass mPBH (colour coding). The region of parameter space that is displayed corresponds to values of mPBH and ΩPBH,f such that black holes dominate the universe content for a transient period, that they form after inflation and Hawking evaporate before big-bang nucleosynthesis, & that the induced gravitational waves do not lead to a backreaction problem. In practice, Eq. (5.2) is displayed with geff = 100, zeq = 3387 and H0 = 70 kms–¹ Mpc–¹. For comparison, the detection bands of ET, LISA and SKA are also shown by researchers.

This may help to further constrain ultra-light primordial black holes, and set potential targets for these experiments.

References: Theodoros Papanikolaou, Vincent Vennin, David Langlois, “Gravitational waves from a universe filled with primordial black holes”, ArXiv, pp. 1-18, 2020. arXiv:2010.11573 link: https://arxiv.org/abs/2010.11573

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