Is dark matter a primordial black hole?
The latest gravitational wave observations reveal mysteriesof the early universe

How did the 13.8-billion-year-old Universe begin?

and LiteBIRD experiments [1].

If only we could observe the very farthest reaches of theIn 2020, it was reported that the GW background,

Universe, by using gravitational wa:ves (GWs), whose

which has existed since the early Universe, may havepenetrating power is much stronger than that of visible

been observed [2]. The North American Nanohertz

light, we would be able to see the birth of the Universe.

Observatory for Gravitational Waves (NANOGrav)

A primordial inflationary process caused the Universe

observed the correlation of radio signals periodicallyto expand more rapidly than that of the Big Bang. In-

emitted by multiple pulsars for 12.5 years and found aflation created the vast Universe in which we can see

significant modulation in the nanohertz band. Pulsars
are neutron stars with strong magnetic fields and, inthe same scenery everywhere we look. It also createdoquantum-mechanically on approximately the order of o= 1 in 100,000 on a large

a sense, are the lighthouses of the Universe, rotating

scale. Galaxies were created when matter gravitation-

radio signals. If a GW background exists, it would

ally coalesced to form them. Then, star systems likecause space-time to expand and contract, which in turnSolar System consisting of stars and planets were pro-would affect the period of pulsar radio-wave signals

duced within galaxies. Inflation also produced a cosmic(Fig. 1). We have not yet confirmed that the signal

GW background at the same time. Observations of theis due to GWs. However, if the signal is real, it is ancosmic microwave background (CMB) have revealedamazing discovery.

a density fluctuation

several hundred times per second and emitting periodicthat temperatme fluctuations were caused by curvaturefluctuations, and the spiral-pattern polarization in thesky (called, the B-mode polarization) caused by GWs is
1.XIO 9expectedto be observedin the future to verify inflation. To
unravel the myste1iesof the birth of the Universeby detecting the B-mode, KEK is conducting the POLARBEAR.2~

5.xm-10Jl.x ,o-tO

5.xtO·II//Hz

Fig. 1. Schematic picture showing modification of correlations for periods of pulsar's signals due to GW background.

50

I2021 at KEK Annual Report

Fig. 2. Signals of the induced GW produced by large-scalar
perturbations at the small scales (thick solid line),
which agrees with observationally allowed region(shaded region). The vertical axis shows the energydensity fraction parameter of GWs flew multiplied bya constant h2 (~0.5) as a function ofGW frequency inunits of Hz [4]. The solid lines in the upper regions
show the upper bounds from various existing observations. SKA indicates the sensitivity forecast for thefuture Square Kilometer Array (SKA) project.

t~

10-'

> 1/3

10-'~;::

I

10- 11& 10-li

BlackHole

Horizon size, H·1= (k/a)·'10- 1;
10- 11

Fig. 3. Schematic image of the fonnation of PBHs by collapsing density perturbation o> 1/3 with the horizon sizeH- 1 = (klat', wavenumber k, and the scale factor a.

GWs in the nanohertz band are thought to begenerated by collisions of supennassive black holes(SMBHs) [3]. However, the astrophysical uncertainties

10-60.01

100//HzFig. 5. San1e as Fig. 2, but for signals of GWs en1itted bymerging PBHs (diagonal solid and dashed lines) [4]with the energy fractions of PBHs to dark matter f PBHof 10-2,10-3 , 10-<,10-5 , respectively. The solid convex
lines show the expected sensitivity of various future
observational projects including LIGO-Virgo-IndlGOKAGRA (denoted to be HLVIK in the figure).

are too large to make a definite determination. Theobserved value is more than seven orders of magnitudelarger than that of the primary GWs directly produced(Fig. 5). The day is expected to come soon when future

by inflation in the early Universe.

GW experiments will be used to verify the early cosmic

On the other hand, if the small-scale (density) fluctuations 8 are large (e.g., 8"" 1/3),an extremely large num-inflation and discover PBHs as a component of darkmatter.

ber of secondary GWs can be created on small scales
via nonlinear effects. In Ref. [4], the authors pointed outReferencesthat this seconda1y GW background emission exactly[1] E. Allys, et al., the LiteBIRD collaboration, arXiv:

matches the NANOGrav 12.5-yr signal (Fig. 2). The
above large density fluctuations are expected to collapse in the early Universe to form a black hole with a

2202.02773 (2022).
[2] Z. Arzoumanian et al., the NANOGrav Collaboration, Astrophys. J. Lett. 905, L34 (2020).

solar mass (Fig. 3). This is called a primordial blackhole (PBH) to distinguish it from a black hole of astro-[3] A. Sesana, Class. Quantum Gravity 30, 224014

physical origin.
The abundance of PBHs may be as large as about 1%[4] K. Kohri and T. Terada, Phys. Lett. B 813, 136040

of dark matter. GWs with larger frequencies can be also[5] K. Somiya, the KAGRA collaboration, Class. Quan-used as a way to test this model. Those primordial black(2013).
(2021).
tum Gravity 29, 124007 (2012).

holes formed a binary star in the early Universe andare now merging (Fig. 4). The LIGO-Virgo-IndIGOKAGRA collaboration (named HLVIK) [5] may hopefully detect the GWs emitted by such systems shortly•Fig. 4. Schematic inlage of the fonnation of binary PBHs
though the three-body effect induced by another blackhole on the right side.

4 Research Highlights

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