2015.09.13 12th icrp dialog seminar presentation
TRANSCRIPT
hayano
Measure & Communicate 4.5 years, and beyond 測って伝える これまでの歩み、そしてこれから Ryugo S. Hayano 早野 龍五Physics department, The University of Tokyo
Sep 13, 2015, ICRP 12th dialogue seminar, Date City
“antimatter” at CERN Team leader since 1997
ジュネーブのCERN研究所で「反物質」を研究
No past experience in Radiation Protection nor Risk Communication - School lunch measurement - large-scale WBC surveys - BABYSCAN - “D-shuttle”
Photo CERN
2011年3月以前に放射線防護 リスクコミュニケーションの経験皆無 - 給食の放射能検査 - WBCによる内部被ばく測定と論文 - BABYSCANの開発・測定・論文 - “D-shuttle”による外部被ばく測定
The No. of my twitter followers 僕のツイッターフォロワー数
←M
arch
201
1
←M
arch
201
2
←M
arch
201
3
←M
arch
201
4
←M
arch
201
5
one summer day in 2011, I stepped out with my right foot, and stumbled upon Dr. Miyazaki
2011年夏のある日右足を出したところに宮崎先生がおられた
1. 測る:最近の進展 measurement: recent developments
Courtesy, NHK World
1. BABYSCAN
Whole-body counter surveys of over 2700 babies and small children in and around Fukushima
Prefecture 33 to 49 months after the Fukushima Daiichi NPP accident
福島第一原発事故後33-49ヶ月間に実施した 福島県及び周辺県における
2700名以上の乳幼児・小児のホールボディーカウンターによる内部被ばく検査
Hayano et al., to be published in Proc. Japan Acad. B
早野ほか,日本学士院紀要10月号掲載
BABYSCANで昨年は2700人以上測定 → 論文来月公表 > 2700 babies scanned last year → to be published in Oct.
セシウム検出者は一人もなし. Nobody had detectable level of radiocaesium
3台のBABYSCANと 2700人の地理的分布 3 BABYSCANs were used to measure 2700 babies
= =%水
avoid tap Water米
avoid Fukushima rice
野菜avoid Fukushima
vegetables
= =%
三春町南相馬市
←WHY?→
しかし内部被ばくに対する家庭のリスク認知には大きな地域差 Differences in risk perception in Minamisoma vs Miharu
57%
4%
2. D-shuttle
フランスの高校生がD-shuttleを着けて来福 French students came to Fukushima with D-shuttle
Jul 31 Aug 01 Aug 02 Aug 03 Aug 04 Aug 05 Aug 06 Aug 070.0
0.2
0.4
0.6
0.8
1.0
µSv/h (含自然放射線:追加線量ではない)
← 福島 Fukushima →← パリ Paris → ←東京 Tokyo→←いわき Iwaki
←富岡駅 Tomioka
CDG security→
French embassy security→
生徒8人引率者4人:データを重ねると D-shuttle data, 8 students, 4 teachers&experts
Jul 31 Aug 01 Aug 02 Aug 03 Aug 04 Aug 05 Aug 06 Aug 070.0
0.2
0.4
0.6
0.8
1.0
µSv/h (含自然放射線:追加線量ではない)
← 福島 Fukushima →← パリ Paris → ←東京 Tokyo→
生徒8人引率者4人:データを重ねると D-shuttle data, 8 students, 4 teachers&experts
←都路(Miyakoji)
Jul 31 Aug 01 Aug 02 Aug 03 Aug 04 Aug 05 Aug 06 Aug 070.0
0.2
0.4
0.6
0.8
1.0
µSv/h (含自然放射線:追加線量ではない)
← 福島 Fukushima →← パリ Paris → ←東京 Tokyo→
生徒8人引率者4人:データを重ねると D-shuttle data, 8 students, 4 teachers&experts
←会津 Aizu
←国見 Kunimi
Jul 31 Aug 01 Aug 02 Aug 03 Aug 04 Aug 05 Aug 06 Aug 070.0
0.2
0.4
0.6
0.8
1.0
µSv/h (含自然放射線:追加線量ではない)
← 福島 Fukushima →← パリ Paris → ←東京 Tokyo→
生徒8人引率者4人:データを重ねると D-shuttle data, 8 students, 4 teachers&experts
変わらないじゃん Not much difference
2. 伝える:いつ 誰に どうやって communicate: when, to whom, how?
1. 時間とともに Time factor
人々はいつ何を知りたがったか? google 検索キーワードから見る傾向
goole search keyword trends reveal…
全世界で World-wide trend
2011 2015
Germany
Austria
Switzerland
Luxembourg
Singapore
France
Belgium
Fukushima, TEPCOドイツ語圏で関心高い 半減期2か月ぐらい 時々ぶり返す German media coverage Half-life ~2mo, but recurs
日本では Japanese trend
2011 2015
Fukushima Daiichi accident
Bq, Sv
ICRP ECRR
Internal & external exposures
2011 2015
26
Thyroid cancer & screening
mostly from Fukushima
Fukushima
2.空間:さまざまなレイヤー/レベル/対象でのコミュニケーションの必要性
2. Space:Need for communication at various layers, levels and audience
28
Difficult to communicate
コミュニケートすることが非常に困難な方々
Convinced, unperturbed
動じない方々
unconvinced majority
揺れ動く世の中の「空気」
public-serviceresources行政のリソース
media
Expert?
social media
← リスクの考え方 risk perception →
3. HOPE
Measurement and comparison of individual external doses of high-school
students
living in Japan, France, Poland and Belarus
– the “D-shuttle” project –
Adachi, N.,1 Adamovitch, V.,2 Adjovi, Y.,3 Aida, K.,4 Akamatsu, H.,5 Akiyama, S.,6 Akli, A.,7
Ando, A.,8 Andrault, T.,9 Antonietti, H.,3 Anzai, S.,10 Arkoun, G.,3 Avenoso, C.,11 Ayrault, D.,9
Banasiewicz, M.,12 Banaskiewicz, M.,13 Bernandini, L.,11 Bernard, E.,7 Berthet, E.,11
Blanchard, M.,3 Boreyko, D.,14 Boros, K.,15 Charron, S.,16 Cornette, P.,9 Czerkas, K.,15
Dameron, M.,11 Date, I.,17 De Pontbriand, M.,3 Demangeau, F.,9 Dobaczewski, L.,18
Dobrzynski, L.,19 Ducouret, A.,3 Dziedzic, M.,20 Ecalle, A.,9 Edon, V.,9 Endo, K.,21 Endo, T.,21
Endo, Y.,21 Etryk, D.,12 Fabiszewska, M.,18 Fang, S.,4 Fauchier, D.,9 Felici, F.,7 Fujiwara, Y.,10
Gardais, C.,9 Gaul, W.,20 Gurin, L.,9 Hakoda, R.,22 Hamamatsu, I.,6 Handa, K.,10 Haneda, H.,10
Hara, T.,10 Hashimoto, M.,1 Hashimoto, T.,8 Hashimoto, K.,21 Hata, D.,1 Hattori, M.,10
Hayano, R.,23, Hayashi, R.,22 Higasi, H.,5 Hiruta, M.,6 Honda, A.,6 Horikawa, Y.,8
Horiuchi, H.,24 Hozumi, Y.,17 Ide, M.,25 Ihara, S.,8 Ikoma, T.,24 Inohara, Y.,22 Itazu, M.,24
Ito, A.,8 Janvrin, J.,9 Jout, I.,11 Kanda, H.,5 Kanemori, G.,5 Kanno, M.,10 Kanomata, N.,10
Kato, T.,24 Kato, S.,24 Katsu, J.,5 Kawasaki, Y.,21 Kikuchi, K.,4 Kilian, P.,26 Kimura, N.,25
Kiya, M.,10 Klepuszewski, M.,15 Kluchnikov, E.,14 Kodama, Y.,5 Kokubun, R.,10 Konishi, F.,22
Konno, A.,6 Kontsevoy, V.,2 Koori, A.,6 Koutaka, A.,6 Kowol, A.,27 Koyama, Y.,4 Kozio l, M.,13
Kozue, M.,1 Kravtchenko, O.,14 Krucza la, W.,12 Kud la, M.,28 Kudo, H.,29 Kumagai, R.,24
Kurogome, K.,25 Kurosu, A.,29 Kuse, M.,25 Lacombe, A.,3 Lefaillet, E.,3 Magara, M.,17
Malinowska, J.,26 Malinowski, M.,18 Maroselli, V.,7 Masui, Y.,29 Matsukawa, K.,29
Matsuya, K.,17 Matusik, B.,20 Maulny, M.,9 Mazur, P.,27 Miyake, C.,29 Miyamoto, Y.,4
Miyata, K.,1 Miyata, K.,5 Miyazaki, M.,30 Moleda, M.,20 Morioka, T.,1 Morita, E.,24 Muto, K.,1
Nadamoto, H.,5 Nadzikiewicz, M.,28 Nagashima, K.,29 Nakade, M.,22 Nakayama, C.,25
Nakazawa, H.,17 Nihei, Y.,4 Nikul, R.,2 Niwa, S.,8 Niwa, O.,30 Nogi, M.,6 Nomura, K.,29
Ogata, D.,8 Ohguchi, H.,31 Ohno, J.,24 Okabe, M.,17 Okada, M.,22 Okada, Y.,6 Omi, N.,25
Onodera, H.,10 Onodera, K.,25 Ooki, S.,21 Oonishi, K.,29 Oonuma, H.,10 Ooshima, H.,8
Oouchi, H.,1 Orsucci, M.,11 Paoli, M.,11 Penaud, M.,9 Perdrisot, C.,9 Petit, M.,9 Piskowski, A.,15
P locharski, A.,15 Polis, A.,13 Polti, L.,3 Potsepnia, T.,14 Przybylski, D.,12 Pytel, M.,28
Quillet, W.,9 Remy, A.,3 Robert, C.,9 Sadowski, M.,19 Saito, M.,10 Sakuma, D.,1 Sano, K.,5
arX
iv:1
506.
0636
4v1
[phy
sics.m
ed-p
h] 2
1 Ju
n 20
15
2
Sasaki, Y.,24 Sato, N.,4 Schneider, T.,32 Schneider, C.,3 Schwartzman, K.,2 Selivanov, E.,14
Sezaki, M.,25 Shiroishi, K.,21 Shustava, I.,14 Sniecinska, A.,28 Stalchenko, E.,14 Staron, A.,27
Stromboni, M.,7 Studzinska, W.,26 Sugisaki, H.,17 Sukegawa, T.,21 Sumida, M.,22 Suzuki, Y.,17
Suzuki, K.,10 Suzuki, R.,10 Suzuki, H.,10 Suzuki, K.,6 Swiderski, W.,18 Szudejko, M.,33
Szymaszek, M.,27 Tada, J.,34 Taguchi, H.,22 Takahashi, K.,4 Tanaka, D.,5 Tanaka, G.,29
Tanaka, S.,24 Tanino, K.,4 Tazbir, K.,13 Tcesnokova, N.,14 Tgawa, N.,5 Toda, N.,6 Tsuchiya, H.,17
Tsukamoto, H.,8 Tsushima, T.,1 Tsutsumi, K.,25 Umemura, H.,8 Uno, M.,24 Usui, A.,25
Utsumi, H.,29 Vaucelle, M.,9 Wada, Y.,17 Watanabe, K.,4 Watanabe, S.,22 Watase, K.,29
Witkowski, M.,26 Yamaki, T.,21 Yamamoto, J.,4 Yamamoto, T.,17 Yamashita, M.,22 Yanai, M.,21
Yasuda, K.,22 Yoshida, Y.,1 Yoshida, A.,21 Yoshimura, K.,25 Zmijewska, M.,15 and Zuclarelli, E.7
1Adachi High School, 2-347 Kakunai, Nihonmatsu, Fukushima 964-0904, Japan
2Bragin High School, Bragin, Gomel region, Belarus
3Notre Dame High School, 1 Avenue Charles de Gaulle, 92100 Boulogne-Billancourt, France
4Aizu Gakuho High School, Ikkimachi Oaza Yahata,
Yahata-1-1, Aizuwakamatsu, Fukushima 965-0003, Japan
5Nada High Shool, 8-5-1 Uozakikitamachi,
Higashinada-ku, Kobe, Hyogo 658-0082, Japan
6Iwaki High School, Taira Aza Takatsuki 7, Iwaki, Fukushima 970-8026, Japan
7Giocante de Casabianca High School, Avenue Jean Zuccarelli, 20200 Bastia, France
8Ena High School, 1023-1 Ohi-cho, Ena, Gifu 509-7201, Japan
9Bois d’Amour High School, 9 Rue de la Garenne, 86000 Poitiers, France
10Fukushima High School, 5-72 Moriaicho, Fukushima, Fukushima 960-8002, Japan
11Paul Vincensini High School, Rue de la Quatrieme Division Marocaine de Montagne, 20600 Bastia, France
12ZS nr 2 im. Marii Sk lodowskiej-Curie, Otwock, Poland
13I LO im. J. S lowackiego, Czestochowa, Poland
14Blaise Pascal High School n46, 14, rue de Clermont-Ferrand, 246027 Gomel, Belarus
15ZS nr 5 im. Unii Europejskiej, III LO, Ostroleka, Poland
16Institute for Protection and Nuclear Safety (IPSN) BP 6, 92265 Fontenay-aux-Roses, France
17Asaka High School, 5-25-63 Kaisei, Koriyama, Fukushima 963-8851, Japan
18ZS Centrum Edukacji im. Ignacego lukasiewicza, Plock, Poland
19National Centre for Nuclear Research, 05-400 Otwock, A.So ltana 7, Poland
20Publiczne Gimnazjum nr 1 im. Jana Paw la II, Zabki, Poland
21Tamura High School, Mochiaibata 8,Tamuragun Miharumachi, Fukushima 963-7763, Japan
22Fukuyama High School Attached to Hiroshima University,
5-14-1 Kasugacho, Fukuyama, Hiroshima 721-0907, Japan
日本フランスポーランドベラルーシ 高校生200人以上が著者となって英国の専門誌に投稿した 世界の高校生の個人線量比較論文
Japan-France-Poland-Belarus, >200 high school students co-authored a paper comparing personal dose (J. Radiol. Prot., under review)
0
0.5
1
1.5
2
1 (Fukuyama)
2 (Nada)
3 (Nara)
4 (Tajimi)
5 (Ena)
6 (Kanagawa)
7 (Asaka)
8 (Iwaki)
9 (Aizu)
10 (Tamura)
11 (Adachi)
12 (Fukushima)
Poitiers (France)
Boulogne (France)
Bastia (France)
Belarus
Poland
mSv/y
Outside of Fukushima
EuropeInside of Fukushima
Comparison of the individual doses (annual basis)
同じ線量計で自然放射線を含む個人線量を世界比較 Same dosimeter, incl. natural background
ミラノ万博 日本館 認定イベント 福島高校生徒さんと Milano EXPO, official event (with high school students)
FOOD SAFETY CONFERENCEMILANO | 22 SETTEMBRE 2015
Sala Pirelli Consiglio Regionale della Lombardia Via Fabio Filzi 22
FUKUSHIMA
SICUREZZA ALIMENTARE E IMPATTO MEDIATICO ESPERIENZE TRA GIAPPONE E ITALIAA distanza di 4 anni dal disastro di Fukushima molte questioni rimangono aperte: che cosa è importante sapere sulla radioattività? I prodotti alimentari provenienti dalla zona dell’incidente sono nocivi? L’obiettivo della conferenza è di esaminare la percezione del consumatore in termini di sicurezza alimentare, come viene condizionata e come può cambiare, tema strettamente collegato alla fiducia del consumatore.Sarà l’occasione per parlare di sicurezza alimentare in modo approfondito ed esaminare le similitudini tra l’approccio giapponese e quello italiano.
PROGRAMMA14.30 Registrazione15.00 Saluto delle Autorità15.10 Introduzione Prof. Claudia Sorlini | Presidente Comitato Scientifico del Comune di Milano - Le università per Expo 2015 Dott. Ettore Prandini | Presidente Coldiretti Lombardia15.40 Radioactive data both in Fukushima and Europe Presentazione della ricerca di alcuni studenti di un liceo di Fukushima16.00 Fukushima dopo il 2011 Prof. Ryugo Hayano | Dip. di Fisica, Università di Tokyo16.30 Fukushima #nofilter Prof. Stefano Maria Iacus | Dip. di Economia, Management e Metodi Quantitativi, Università degli Studi di Milano Dott.sa Tiziana Carpi | Dip. di Scienze della Mediazione Linguistica e di Studi Interculturali, Università degli Studi di Milano17.00 Food Safety in Italia e in Giappone Intervengono: Mara Soffientini | Responsabile Servizio Consulenza - Food Safety, ChemService Controlli e Ricerche
One more thing (for Date city) 伊達市用特別付録
140.45 140.50 140.55 140.60 140.65 140.70 140.7537.65
37.70
37.75
37.80
37.85
37.90
37.952011/11/5
0
1
2
3
4
µSv/h432101
Airborne monitoring 2011/11
How can I contribute? (may be, not much any more…)
僕にできることは何?(あまりないような気がするが…)
22. Big-Bang cosmology 3
22.1.3. The Friedmann-Lemaıtre equations of motion :
The cosmological equations of motion are derived from Einstein’s equations
Rµν − 12gµνR = 8πGNTµν + Λgµν . (22.6)
Gliner [17] and Zeldovich [18] have pioneered the modern view, in which the Λ termis taken to the rhs and interpreted as an effective energy–momentum tensor Tµν for thevacuum of Λgµν/8πGN. It is common to assume that the matter content of the Universeis a perfect fluid, for which
Tµν = −pgµν + (p + ρ)uµuν , (22.7)
where gµν is the space-time metric described by Eq. (22.1), p is the isotropic pressure,ρ is the energy density and u = (1, 0, 0, 0) is the velocity vector for the isotropic fluid inco-moving coordinates. With the perfect fluid source, Einstein’s equations lead to theFriedmann-Lemaıtre equations
H2 ≡
!
R
R
"2
=8π GN ρ
3−
k
R2 +Λ
3, (22.8)
andR
R=
Λ
3−
4πGN
3(ρ + 3p) , (22.9)
where H(t) is the Hubble parameter and Λ is the cosmological constant. The first of theseis sometimes called the Friedmann equation. Energy conservation via Tµν
;µ = 0, leads to a
third useful equation [which can also be derived from Eq. (22.8) and Eq. (22.9)]
ρ = −3H (ρ + p) . (22.10)
Eq. (22.10) can also be simply derived as a consequence of the first law of thermodynamics.
Eq. (22.8) has a simple classical mechanical analog if we neglect (for the moment) thecosmological term Λ. By interpreting −k/R2 Newtonianly as a ‘total energy’, then wesee that the evolution of the Universe is governed by a competition between the potentialenergy, 8πGNρ/3, and the kinetic term (R/R)2. For Λ = 0, it is clear that the Universemust be expanding or contracting (except at the turning point prior to collapse in a closedUniverse). The ultimate fate of the Universe is determined by the curvature constantk. For k = +1, the Universe will recollapse in a finite time, whereas for k = 0,−1, theUniverse will expand indefinitely. These simple conclusions can be altered when Λ = 0 ormore generally with some component with (ρ + 3p) < 0.
August 21, 2014 13:17
26. Dark energy3
More generally, one can search for signatures of modified gravity by comparing the
history of cosmic structure growth to the history of cosmic expansion. Within GR, these
two are linked by a consistency relation, as described below (Eq. (26.2)). Modifying
gravity can change the predicted rate of structure growth, and it can make the growth
rate dependent on scale or environment. In some circumstances, modifying gravity alters
the combinations of potentials responsible for gravitational lensing and the dynamics of
non-relativistic tracers (such as galaxies or stars) in different ways (see Sec. 22.4.7 in this
Review), leading to order unity mismatches between the masses of objects inferred from
lensing and those inferred from dynamics in unscreened environments.
At present there are no fully realized and empirically viable modified gravity theories
that explain the observed level of cosmic acceleration. The constraints on f(R) models
now force them so close to GR that they cannot produce acceleration without introducing
a separate dark energy component [18]. The DGP model is empirically ruled out by
several tests, including the expansion history, the integrated Sachs-Wolfe effect, and
redshift-space distortion measurements of the structure growth rate [19]. The elimination
of these models should be considered an important success of the program to empirically
test theories of cosmic acceleration. However, it is worth recalling that there was no
fully realized gravitational explanation for the precession of Mercury’s orbit prior to the
completion of GR in 1915, and the fact that no complete and viable modified gravity
theory exists today does not mean that one will not arise in the future. In the meantime,
we can continue empirical investigations that can tighten restrictions on such theories or
perhaps point towards the gravitational sector as the origin of accelerating expansion.
26.2.2.Expansion History and Growth of Structure :
The main line of empirical attack on dark energy is to measure the history of cosmic
expansion and the history of matter clustering with the greatest achievable precision
over a wide range of redshift. Within GR, the expansion rate H(z) is governed by
the Friedmann equation (see the articles on Big Bang Cosmology and Cosmological
Parameters—Secs. 22 and 24 in this Review). For dark energy with an equation of state
w(z), the cosmological constant contribution to the expansion, ΩΛ , is replaced by a
redshift-dependent contribution with the evolution of the dark energy density following
from Eq. (22.10),ΩDE ρDE (z)ρDE(z = 0) = Ω
DE exp!
3"
z
0[1 + w(z ′)] dz ′
1 + z ′
#
=Ω
DE (1 + z) 3(1+w),(26.1)
where the second equality holds for constant w. If Ωm , Ωr , and the present value of Ωtot
are known, then measuring H(z) pins down w(z). (Note that ΩDE is the same quantity
denoted Ωv in Sec. 22, but we have adopted the DE subscript to avoid implying that dark
energy is necessarily a vacuum effect.)
While some observations can probe H(z) directly, others measure the distance-redshift
relation. The basic relations between angular diameter distance or luminosity distance
and H(z) are given in Ch. 22 —and these are generally unaltered in time-dependent dark
energy or modified gravity models. For convenience, in later sections, we will sometimes
refer to the comoving angular distance, DA,c (z) = (1 + z)D
A (z).
August 21, 201413:17
(as a physicist)Space-time perspective
(物理学者としては)
時空を考えねば
22.Big-B
ang cosmolog
y 1
22.BIG-BANG COSMOLOGY
RevisedSeptember 2013
by K.A. Olive(Univers
ity of Minnesota) and J.A. Peaco
ck
(University of Edinburgh).
22.1. Introductio
n to Standard
Big-Bang Model
The observed expansion
of the Universe [1–3
] is a natural (almost inevitable) resu
lt of
anyhomogen
eous and isotropic cosm
ological
model basedon general
relativity.
However,
by itself, the Hubble expansion
does not provide sufficientevidence for what we generall
y
referto as the Big-B
ang model of cosmolog
y. While generalrelat
ivity is in principle
capable of describing the cosm
ology of any
givendistrib
utionof matter
, it is extremely
fortunate
that our Universe appears
to be homogeneous and isotr
opic on largescale
s.
Together, homogen
eityand isotr
opyallow
us to extend the CopernicanPrinciple to the
Cosmological
Principle, stating that all spatial
positions in the Univers
e are essentially
equivalent.
The formulatio
n of the Big-Bang model began
in the 1940s with the work
of George
Gamow and his collaborat
ors,Alpher and Herman. In order to acco
unt for the possibility
that the abundancesof the elem
entshad a cosm
ological
origin, they proposed
that
the earlyUnivers
e which was once veryhot and dense (enough so as to allow
for the
nucleosynthetic
processing of hydroge
n), and has expanded and cooledto its presen
t
state[4,5]
. In 1948, Alpher and Herman predicted
that a directconsequence of this
model is the presence of a relic
background radiatio
n with a temperature of order a few
K [6,7]. Of course this radiatio
n was observed 16 year
s lateras the microw
ave background
radiation [8].
Indeed, it was the observation
of the 3 K background radiatio
n that singled
out the Big-Bang model as the prime candidate
to describe our Univers
e. Subsequent
workon Big-B
ang nucleosynthesis
further confirmed the necessity of our hot and dense
past.(See the review
on BBN—Sec. 23 of this Review for a detail
ed discussionof BBN.)
These relativistic
cosmolog
icalmodels face
severe problems with their initial
conditions,
to which the best modernsolution
is inflationary
cosmolog
y, discussedin Sec. 22.3
.5. If
correct, these ideas
would strictly render the term
‘Big Bang’ redundant,since it was
first coined by Hoyle to represen
t a criticism
of the lackof understa
nding of the initial
conditions.
22.1.1.
The Robertson
-Walker Univer
se :
The observed homogen
eityand isotr
opyenable us to descri
be the overall geom
etry
and evolution
of the Universe in term
s of two cosmolog
icalparam
etersacco
unting for
the spatialcurvat
ure and the overall expansion
(or contracti
on) of the Universe. These
two quantities appear in the most general
expression for a space-t
ime metricwhich has a
(3D) maximallysymmetric
subspace of a 4D space-time, known as the Robertso
n-Walker
metric: ds
2 = dt2 − R
2 (t)
! dr2
1 − kr2+ r
2 (dθ2 + sin
2 θ dφ2 )
"
.
(22.1)
Note that we adopt c = 1 throughout. By rescaling the radial coordinate,
we canchoose
the curvature constan
t k to takeonly the discre
te values +1, −1, or 0 corre
sponding
to closed, open, or spatial
ly flat geometrie
s. In this case, it is often
more convenient
to
re-express
the metricas
K.A. Oliveet al. (PDG), Chin. Phys. C38, 0900
01 (2014) (http
://pdg.lbl.gov
)
August 21,201
413:1
7
知ろうとすること。
新潮文庫
早野龍五
東京大学大学院
理学系研究科教授
糸井重里
十万部超 >100,000 copies printed so far (also in e-book)
英語版も出ました English Kindle version now available