Besides
particles like sterile neutrinos, axions and weakly interacting massive
particles (WIMPs), a leading candidate for the cold dark matter of the universe
are primordial black holes—black holes created from extremely dense
conglomerations of subatomic particles in the first seconds after the Big Bang.
Primordial black holes (PBHs) are
classically stable, but as shown by Stephen Hawking in 1975, they can evaporate
via quantum effects,
radiating nearly like a blackbody. Thus, they have a lifetime; it's
proportional to the cube of their initial mass. As it's been 13.8 billion years
since the Big Bang, only PBHs with an initial mass of a trillion kilograms or
more should have survived to today.
However, it has been suggested that the lifetime of a black hole might be
considerably longer than Hawking's prediction due to the memory burden effect,
where the load of information carried by a black hole stabilizes it against
evaporation.
Thus, PBHs previously thought to have
evaporated by now could still be present as cold, dark matter, lighter than about 10 million kilograms.
A research team from Japan has now
proposed detecting the hypothetical PBH dark matter by studying the
gravitational waves induced by the primordial curvature perturbations that
produced the PBHs. Their work is published in Physical
Review D.
"This research is the first in the
world to propose that evidence of PBHs being dark matter will be confirmed by
future gravitational wave observations," said Kazunori Kohri of the
National Astronomical Observatory of Japan in Tokyo and affiliated with several
other physics research organizations in the country.
Despite a large number (by now) of
experimental searches, physicists have yet to see signs of dark matter in
particle accelerators, in underground and under ice detectors and via exploring space, directly or indirectly.
"If this situation continues, the
nightmare scenario of dark matter, namely the scenario with only
gravitationally interacting dark matter, will become important," write
Kohri and his co-authors. Macroscopic dark matter might be the answer, such as
the PBH scenario if the PBHs have survived to today.
Hawking's conclusion that black holes radiate means they will
eventually evaporate completely and cease to exist. But Hawking's calculation
assumed a semiclassical black hole during its entire lifetime, ignoring the
quantum back reaction of the created particles on the evaporating black hole.
The full treatment reveals a memory
burden effect, discovered by Georgian theoretical physicist Gia Dvali in 2018. Viewing a black hole as a condensate of
gravitons, the presumed carriers of the gravitational force, micro quantum
states are responsible for the entropy of the black hole.
"Memory" refers to the information stored in the black hole; this stored information stabilizes the black hole, making it more resistant to decay. A state of the black hole becomes stabilized by the burden of its own memory. The effect becomes important when a black hole has lost about half its initial mass.
"If
we believe in the Memory Burden Effect, which is a hot topic in the field of
quantum gravity," said Kohri, "we can build a theory with extremely
little uncertainty."
It's not yet completely clear what
happens to a black hole when the memory burden becomes significant—possibly the
Hawking evaporation is suppressed, or perhaps the black hole decays into some
lumps and gravitational waves.
Kohri
and his co-authors focused on the first possibility. Dvali and his
collaborators argued that the Hawking emission rate is suppressed by some
integer power of the black hole's entropy.
Black holes have a huge amount of
entropy; a Schwarzschild black hole with a mass of the sun has an entropy of 1077 in
units of Boltzmann's constant. By comparison, the sun's entropy is 1058.
So the lifetime of a black hole is
greatly extended. Cosmological constraints put lower and upper limits on the
PBHs at play: Kohri and colleagues thus focus on PBHs with an initial mass
greater than 100 kg up to 10 million kg.
One popular PBH production mechanism is
the gravitational collapse of early cosmological patches with extremely
enhanced spacetime curvature perturbations. Significant amounts of
gravitational waves are also induced in this radiation-dominated era of the
universe, with a typical frequency in a one-to-one correspondence with the
PBH's initial mass.
Studying the observational properties of
these gravitational waves in the present universe, extensive calculations
resulted in the spectra of gravitational waves as would exist today as a
function of frequency, and also the expected signal-to-noise ratio for one-year of observations with proposed
future gravitational wave observatories.
Their calculations of the expected
induced gravitational wave spectra reveal that sufficiently heavy
memory-burdened PBH dark matter could be observable today because they induce
relatively low-frequency gravitational waves.
Future observatories are being designed
with this goal in mind, such as the space-based LISA (Laser Interferometer
Space Antenna), DECIGO (Deci-hertz Interferometer Gravitational wave
Observatory) in Japan, the Big Bang Observatory (BBO) proposed by the European
Space Agency (ESA) to replace LISA when it's run its course, and others.
Kohri and his colleagues produced graphs
of the expected spectra in terms of the waves' frequency and extend their
equations to predict the signal-to-noise ratios that would be seen in the
actual observations.
The researchers also present criteria by
which gravitational wave astronomers could confirm or exclude the scenario of
the memory-burdened PBH dark matter. Still, nonlinear dynamics of the
memory-burdened PBH dark matter will determine the detailed form of the gravitational waves.
The peak frequency of the induced waves
can be as high as 30 megahertz, 3,000 times higher than the 10 kilohertz peak
the two LIGOs in the US can detect. However, the calculations show there is an
infrared trail in the spectra that implies lower peak frequencies.
These could be detected by the proposed Cosmic Explorer, a third-generation ground-based gravitational wave observatory that would have the same L-shaped design as LIGO but with interferometer arms that are 40 km long instead of LIGO's 4 km.
Source: Detecting
the primordial black holes that could be today's dark matter
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