Xing Zh., Zhou Sh. Neutrinos in Particle Physics, Astronomy and Cosmology

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366 10 Neutrinos and
C
osmological
S
tructures
Ω
ν
≡
ρ
ν
ρ
c
=
8
π
G
N
3
H
2
i
m
i
n
ν
i
+
n
ν
i
≈
1
9
4
h
2
eV
i
m
i
,
(
10.21
)
w
h
ere
n
ν
i
=
n
ν
i
≈
56
cm
−
3
is today’s number density of reli
c
ν
i
n
eutrinos or
ν
i
antineutrinos as given in Eq.
(
8.27
)
or Eq.
(
9.40
)
.Thesmallvalueso
f
m
i
yield a small value of Ω
ν
,
typically of
O
(
10
−
2
)
or smaller if the sum of
m
i
is
of
O
(
1
)
eV or smaller. But small effects of neutrino masses may still leave an
i
mprint in the measurable amount of clusterin
g
of
g
alaxies
.
T
able 10.1 lists today’s energy densities of neutrinos, photons, baryon
s
a
nd total matter as compared with the vacuum energy density
(
or equiva
-
l
ently, the cosmological constant
)
.Infact,ρ
ν
,
ρ
γ
,
ρ
B
an
d
ρ
C
DM
all decrease
d
with the expansion of the Universe. The evolution of these energy densi
-
ties is shown in Fig. 10.4
(
Strumia and Vissani, 2006
)
, from which one ca
n
c
learl
y
see the transition from the radiation-dominated epoch to the matter
-
d
ominate
d
epoc
h
aroun
d
T
∼
O
(
1
)
eV. As discussed before, gravity amplifie
d
the primordial density
fl
uctuations o
f
cold dark matter. This
g
ravitational
c
lustering process finally led to the formation of galaxies and other LSS that
we have observed today. Relativistic particles with a mean
f
ree path lar
g
e
r
than the horizon, such as relativistic neutrinos, could
f
reel
y
stream in the
U
niverse and thus suppress the gravitational clustering process. However,
n
eutrino masses should more or less hinder the
f
ree streamin
g
o
f
neutrinos
because their velocities were smaller than the speed of li
g
ht such that the
y
c
ould only travel in a fraction of the horizon within the Hubble time. On th
e
other hand, the contribution o
f
massive neutrinos to the total ener
g
y density
of the Universe tended to increase the cosmolo
g
ical expansion which woul
d
weaken gravitational interactions and slow down the formation of structures
.
A
careful stud
y
of the formation rate of structures in the recent past of the
niverse should therefore provide us with a unique opportunit
to measure
the absolute
n
eut
rin
o
m
ass scale.
S
imilar to Eq.
(
10.18
)
, small fluctuations in the density of cold dark matter
c
an be described b
y
δ
C
DM
(
x
)
≡
[
ρ
C
D
M
(
x
)
−
ρ
C
DM
]
/
ρ
C
D
M
. The evolutio
n
of this parameter obeys
(
Bon
d
et al.
,
1980; Kolb and Turner, 1990
)
¨
δ
C
DM
+
2
H
˙
δ
C
DM
=4
π
G
N
Δ
ρ,
(
10.22
)
whe
r
e
Δ
ρ
≡
ρ
(
x
)
−
ρ
d
enotes t
h
epertur
b
ations to t
h
e tota
l
ener
g
y
d
ensit
y
ρ
.
To examine the role of neutrinos with res
p
ect to that of cold dark matter
i
ntheL
SS
, we simply take
ρ
≈
ρ
C
DM
+
ρ
ν
by ne
g
lectin
g
other components o
f
ρ
.A
slon
g
as
T
m
i
, neutrinos would be relativistic and have little chanc
e
to cluster. In this case we take
Δ
ρ
ν
= 0 and rewrite Eq.
(
10.22
)
a
s
¨
δ
C
D
M
+2
H
˙
δ
C
DM
=
4
π
G
N
ρ
(1
−
f
ν
ff
)
δ
C
D
M
,
(
10.23
)
whe
r
e
f
ν
ff
≡
ρ
ν
/ρ
.
G
iven a spatially
fl
at Universe with
k
=0
o
r
ρ
=
ρ
c
=
3
H
2
/
(8
π
G
N
)
, an analytical solution to Eq.
(
10.23
)
can be found in th
e
m
atter-
d
ominate
d
era wit
h
H
=2
/
(3
t
)
.Oneobtain
s
δ
C
D
M
∝
t
2
/
3
∝
a
(
t
)
∝
10.2 Large-scale
S
tructures and Dark Matter 36
7









_1*  #







3 - #




(


)



^  ` * + -
Λf
γ
&f
.- 
ν
Fig. 10.4 Evolution o
f
the energy densities o
f
photons, neutrinos, baryons and cold
dark matter
(
CDM
)
between
T
∼
10
2
eV an
d
T
0
TT
≈
2
.
73 K to
d
a
y
, as compare
d
wit
h
the cosmological constan
t
Λ
,
based on the standard
Λ
C
DM model (Strumia an
d
Vissani, 2006
)
. Note that neutrinos were relativistic at
T
m
i
(
wher
e
ρ
ν
∝
T
4
)
an
d
non-re
l
ativistic at
T
m
i
(
wher
e
ρ
ν
∝
m
i
T
3
)
. For simplicity, different neutrino
species are assumed to have the degenerate mass of
O
(
0
.
1
) eV. The shaded are
a
covers the epoch be
f
ore the decoupling o
f
photons
f
rom matte
r
T
−
1
b
y takin
g
f
ν
ff
=
0
,
where
a
(
t
)
≡
R
(
t
)
/
R
(
t
0
)
is the dimensionless scale
parameter and satisfies Hubble’s law ˙
a
(
t
)=
Ha
(
t
)
. During the period fro
m
T
∼
1eVto
T
0
TT
=
2
.
7
25 K, the primordial
fl
uctuations were enhanced b
y
a
l
arge facto
r
T/T
0
TT
∼
4
300 and thus
p
roduced the LSS as one has observed to-
d
ay
(
Strumia and Vissani, 2006
)
. Of course,
f
ν
ff
= 0 would somewhat suppress

the
g
rowth o
f
the dark matter
fl
uctuations.
O
ne may obtai
n
δ
C
D
M
∝
a
p
(
t
)
w
i
th
p
=[
1
+24
(1
−
f
ν
f
f
)
−
1]
/
4
in the assumption of a constant
f
ν
ff
.It
i
s
obvious that the primordial fluctuations would have never grown
(
i.e.
,
p
=0
)
i
f the Universe had been dominated b
y
relativistic particles with
f
ν
ff
=1
(
i.e.,
ρ
=
ρ
ν
)
. That is why only the matter-dominated epoch was relevant to th
e
f
ormation of the LSS. Note that the cosmological constant
(
or vacuum energy
)
gradually dominated the energy density of the Universe after the temperature
was below
T
10
−
3
e
Vass
h
owninFi
g
. 10.4. It wou
ld
re
d
uce t
h
e
l
ate-time
g
rowth o
f
the dark matter
fl
uctuations by a
f
acto
r
∼
1
/
4(
Strumia and Vis
-
ani, 2006; Lesgourgues and Pastor, 2006
. Neutrinos became non-relativisti
afte
r
T
∼
m
i
.O
ne ha
s
f
ν
ff
=
Ω
ν
/Ω
∼
Ω
ν
f
or non-relativistic neutrinos, a
s
given in Eq.
(
10.21
)
.Evensuchasmal
l
f
ν
f
f
c
ould make the
g
rowth o
f
struc
-
ture a bit slow from the tim
e
T
∼
m
i
u
ntil today. Since the matter power
s
pectrum
P
(
k
)
defined in Eq.
(
10.20
)
is proportional t
o
|
δ
C
DM
|
2
,
we
fi
n
d
368 10 Neutrinos and
C
osmological
S
tructures
Fig. 10.5 The matter power spectru
m
P
(
k
)
predicted by the standard
Λ
C
DM
model
(
solid curve
)
and its dependence on neutrino masses
(
dashed curves
)
.Mea-
surements at di
ff
erent cosmolo
g
ical scales are per
f
ormed with di
ff
erent techniques,
which slightly overlap. The data points do not show the overall uncertainty that
plagues galaxy surveys
(
SDSS and 2dF
)
at intermediate scales and especially
L
y
man
-
α
data at smaller scales with larger wavenumbers
(
Strumia and Vissani
,
2006
)
P
(
k
)
f
ν
=0
P
(
k
)
f
ν
=0
∼
|
a
(
t
)
|
2
(
p
−
1
)
∼|
a
(
t
)
|
−
6
f
ν
/
5
(
10.24
)
d
uring the aforementioned period.
A
simple numerical interpolation yield
s
P
(
k
)
f
ν
=0

/P
(
k
)
f
ν
=0
∼
e
−
8
f
ν
≈
1
−
8
f
ν
ff
(
Strumia and Vissani, 2006; Lesgour-
gues and Pastor, 2006
)
, and thus the matter power spectrum is modified up
to
Δ
P
(
k
)
/
P
(
k
)
∼
−
8
f
ν
ff
on sma
ll
cosmo
l
o
g
ica
l
sca
l
es.
A
com
p
lete descri
p
tion of the effect of massive neutrinos on the matte
r
power spec
t
rum
P
(
k
)
is technically complicated
(
Lesgourgues and Pastor
,
2
006
)
. For simplicity, here we only illustrate the shape o
f
P
(
k
)
and its depen
-
d
ence on neutrino masses in Fi
g
. 10.5, wher
e
m
ν
s
tands for nearly de
g
enerate
m
i
(
Strumia and Vissani, 2006
)
. One can see that it is possible to probe neu-
trino masses via a precision measurement o
f
P
(
k
)
,if
m
ν
0
.
1
e
Vh
o
ld
s
.
F
uture cosmological measurements of the LSS might even be sensitive to th
e
m
ass sp
l
ittin
g
Δ
m
2
3
2
≈
0
.
05 eV for atmospheric neutrino oscillations.
I
t is wort
h
mentionin
g
t
h
at a very ti
gh
t upper
b
oun
d
on neutrino masse
s
h
as recently been obtained from a new mapping of the matter density distri
-
bution of surrounding galaxies based on the standard
Λ
C
DM model
(
Thomas
et al
., 2010
)
. In this analysis the authors used the SDSS data and photometri
c
redshift estimates to reconstruct a three-dimensional map of galaxies on muc
h
l
ar
g
er cosmolo
g
ical scales than be
f
ore, providin
g
an important indication o
f
10.2 Large-scale
S
tructures and Dark Matter 36
9
the distribution o
f
structures not onl
y
in a recent past but also a
f
ew billion
years a
g
o when most remote
g
alaxies in this map emitted the li
g
ht that w
e
h
ave observed today
(
Lesgourgues, 2010
)
. Such an approach is particularly
uitable
or probin
the e
ect o
neutrino masses on the rate o
structur
ormation, on both smaller and larger cosmological scales as compared wit
the neutrino free-streaming scale. In combination with the WMAP data and
ot
h
er cosmo
l
o
g
ica
l
measurements, it yie
lds
>
m
i
0
.
2
8eVatthe95
%
con
-
fidence level
(
Thoma
s
et al
.
, 2010
)
. Of course, this and other cosmological
c
onstraints on neutrino masses are strongly dependent upon specific mode
l
parameters an
d
ot
h
er t
h
eoretica
l
assumptions. But t
h
e
y
can a
l
wa
y
s
b
ecom
-
plementary to the laboratory measurements of neutrino masses, which prob
e
d
i
ff
erent quantities and have independent systematic errors.
1
0
.2.4
S
terile Neutrinos as Dark Matter
The term “sterile neutrino” was coined b
y
Bruno Pontecorvo in one of his
s
eminal papers
(
Pontecorvo, 1968
)
. A sterile neutrino is by definition a neu-
trino t
h
at
d
oes not ta
k
epartint
h
estan
d
ar
d
wea
k
interactions. In some
l
iterature th
e
SU
(
2
)
L
singlet neutrinos or right-handed neutrinos are sim-
ply referred to as sterile neutrinos. Such hypothetical particles may not be
c
omp
l
ete
l
y “steri
l
e
”
in t
h
e sense t
h
at t
h
ey can s
l
i
gh
t
l
ymixwit
h
or
d
inar
y
n
eutrinos and thus indirectly take part in weak interactions
(
see, e.g., the
type-I seesaw mechanism discussed in Section 3.2.3 and Section 4.1.2
)
.Th
e
existence o
f
completel
y
or almost sterile neutrinos has not been experimen
-
tally established, although they are favored in some models to understand the
ori
g
in o
f
tiny masses o
f
three active neutrinos, to interpret the cosmolo
g
ica
l
m
atter-antimatter as
y
mmetr
y
and to describe dark matter. In this sectio
n
we are going to briefly discuss warm dark matter in the form of keV steril
e
neut
rin
os
.
T
o be specific, we assume the existence of a sin
g
le sterile neutrin
o
ν
s
whose
mass eigenstate ˜
ν
s
h
as an eigenva
l
u
e
m
s
.
Its mixing wit
h
active neutrino
s
c
an be described by an e
ff
ective mixin
g
an
g
le
θ
as fo
ll
ows:
ν
s
˜
ν
s
cos
θ
+
ν
L
sin
θ
,
where
|
θ
|
1 holds and
ν
L
d
enotes a linear combination of the mass
eigenstates of three active neutrino
s
6
. For this kind of sterile neutrinos to be
a
via
bl
e
d
ar
k
matter can
d
i
d
ate
,
m
s
sh
ou
ld
most
l
i
k
e
l
y
l
ie in t
h
e
k
eV ran
g
ean
d
θ
m
ust be extremel
y
small. Such keV sterile neutrinos were never in therma
l
equi
l
i
b
rium at
h
ig
h
temperatures in t
h
eear
l
y Universe,
b
ut t
h
ey cou
ld b
e
produced in several ways
(
Kusenko, 2009
)
. For instance, light sterile neutrino
s
c
ould be
p
roduced from neutrino oscillations at a tem
p
eratur
e
T
∼
100 MeV
(
Dodelson and Widrow, 1994
)
. An estimate of the relic population of keV
s
terile neutrinos
y
ield
s
6
I
n a self-consistent parametrization of the four-neutrino mixing matrix
(
Guo
and Xing, 2002
)
, one approximately ha
s
ν
s
˜
ν
s
cos
θ
+(
ν
1
ˆ
s
∗
14
+
ν
2
ˆ
s
∗
24
+
ν
3
ˆ
s
∗
34
)
with
ˆ
s
i
4
≡
e
i
δ
i
4
sin
θ
i
4
(
for
i
=1, 2, 3). Hence sin
2
θ
s
2
1
4
+
s
2
2
4
+
s
2
34
(
Li and Xing, 2010)
.
370 10 Neutrinos and
C
osmological
S
tructures
Fi
g
. 10.6
A
llowed re
g
ions of sin
2
2
θ
a
n
d
m
s
f
or sterile neutrinos to be dark matte
r
(
Abazajian and Koushiappas, 2006). The contour labeled with
L
= 0 correspond
s
to the
p
roduction scenario o
f
sterile neutrinos wit
h
Ω
s
≈
0
.
24
,
an
d
t
h
ose
l
a
b
e
l
e
d
wit
h
L =0
.
0
03
,
0
.
01 an
d0
.
1
corres
p
on
d
to
Ω
s
≈
0
.
3. T
h
e
g
rey re
g
ion to t
h
eri
ght
o
f
t
h
e
L = 0 contour is excluded to avoid overproduction of sterile neutrinos a
s
dark matter, and the “X-ray back
g
round” and “
C
luster X-ray” re
g
ions are excluded
because the X-ray signals arising from ˜
ν
s
→
ν
i
+
γ
decays
(
fo
r
i
=
1
,
2
,
3)
have neve
r
been seen. The diagonal wide-hatched region is the claimed potential constraint
f
rom
f
uture X-ra
y
searches. The horizontal band with
m
s
<
0
.
4k
e
V
is ru
l
e
d
out
b
y
a conservative application of the Tremaine-Gunn bound, whereas the one with
0
.
5
ke
V
m
s
1 keV is consistent with the production of a core in the Fornax
dwar
fg
alaxy and pulsar kicks. The re
g
ions labeled with L
y
α
(
1
)
,
(
2
)
and
(
3
)
are
constrained by the amplitude and slope of the matter power spectrum inferred from
some high-resolution data on the SDSS Lyman
-
α
f
o
r
est
Ω
s
∼
0
.
2
×
s
i
n
2
2
θ
10
−
8
m
s
3k
e
V
1
.
8
,
(
10.25
)
provided the Universe has a ne
g
li
g
ibly small lepton number asymmetry
L
(
Feng, 2010
)
.Her
e
L
is de
fin
ed as
L
≡
(
n
ν
−
n
ν
)
/n
γ
w
i
th
n
ν
(
or
n
ν
)
being
the number density of neutrinos
(
or antineutrinos
)
an
d
n
γ
b
ein
g
t
h
enum
b
e
r
d
ensity of photons
(
Abazajian and Koushiappas, 2006
)
. Fig. 10.6 shows the
a
llowed parameter space of sin
2
2
θ
a
n
d
m
s
fo
r
ste
ril
e
n
eut
rin
os to be t
h
e
10.2 Large-scale
S
tructures and Dark Matter 37
1
c
andidate o
f
dark matter.
G
iven a preexistin
g
lepton number asymmetry
L
1
0
−
3
, which remains small enou
g
h to be consistent with the current BB
N
d
ata, steri
l
e neutrinos wit
h
sma
ll
masses an
d
mixing ang
l
es may constitute a
ll
of dark matter in the Universe
(
Shi and Fuller, 1999; Asak
a
et al.
,
2007; Fen
g
,
2
010
)
. Sterile neutrinos could also be produced at much higher temperatures,
f
or example, in the decays of heavy particles in the early Universe. Allowin
g
ag
au
g
e-sin
gl
et sca
l
ar
Φ
to coup
l
etori
gh
t-
h
an
d
e
d
neutrinos an
d
t
h
eir c
h
ar
g
e
-
c
onjugate fields, one may obtain a Majorana mass term similar to the
M
μ
M
term in Eq.
(
4.48
)
after
Φ
a
cquires its vacuum expectation va
l
ue. T
h
e
l
epton
-
n
um
b
er-vio
l
atin
gd
eca
y
Φ
→
ν
s
+
ν
s
m
i
g
ht there
f
ore produce sterile neutrinos
a
s dark matter at a tem
p
eratur
e
T
∼
m
Φ
(
Shaposhnikov and Tkachev, 2006
;
K
usenko, 2006, 2009; Feng, 2010
).
Dark matter in the
f
orm o
f
keV sterile neutrinos is re
f
erred to as war
m
d
ark matter, which should have little small-scale su
pp
ression in the matte
r
power spectrum. In
f
act, both warm dark matter and cold dark matter can
fi
t
the observed structures on lar
g
e scales, but their predictions on small scales
a
re different. A potential problem associated with cold dark matter is th
e
d
iscrepanc
y
between the number o
f
satellites predicted in the
N
-b
o
dy
simu
-
l
ations and the one observed in galaxies such as the Milky Way
(
Kauffman
n
et a
l.
,
1993
;M
oor
e
e
ta
l.
, 1999
)
. This discrepancy can be ameliorated if dark
m
atter is warm, because warm dark matter ma
y
suppress the
f
ormation o
f
d
warf galaxies and other small-scale structures
(
Bod
e
et al.
,
2001
;
Kusenko
,
2
009
)
. How warm sterile neutrinos could be depends on their productio
n
m
ec
h
anism. Fi
g
. 10.6 s
h
ows t
h
at
m
s
m
a
y
var
yf
rom
O
(
1
)
keV to
O
(
10
)
keV
.
B
esides its im
p
act on small-scale structures, dark matter in the form
of sterile neutrinos may have some other astrophysical effects, for instance
,
on the X-ra
y
spectrum, on the velocit
y
distribution o
f
pulsars and on the
f
ormation of the first stars
(
Kusenko, 2009; Feng, 2010
)
. The search for a
n
X-ray line from the radiative decay ˜
ν
s
→
ν
i
+
γ
(
fo
r
i
=
1
,
2
,
3
)
is expecte
d
to o
ff
er the best chance to detect relic sterile neutrinos i
f
the
y
exist as war
m
d
ark matter. In view of Fig. 10.6 together with the widths of the dominant
and subdominant decay modes of ˜
ν
s
(
Li and Xing, 2010
)
3
i
,
j
=
1
Γ
(˜
ν
s
→
ν
i
+
ν
j
ν
+
ν
j
)
C
ν
G
2
F
192
π
3
m
5
s
si
n
2
θ
C
ν
sin
2
2
θ
1
.
2 ×
10
2
0
s
m
s
ke
V
5
(
10.26
)
a
nd
(
Pal and Wolfenstein, 1982; Shrock, 1982; Li and Xing, 2010
)
3
i
=
1
Γ
(˜
ν
s
→
ν
i
+
γ
)
9
α
em
C
ν
G
2
F
512
π
4
m
5
s
s
i
n
2
θ
C
ν
s
in
2
2
θ
1
.
5
×
10
22
s
m
s
k
e
V
5
(
10.27
)
wit
h
α
em
≈
1
/
1
37 being the fine-structure constant an
d
C
ν
=
1
(
Dira
c
n
eutrinos
)
o
r
C
ν
=
2
(
Majorana neutrinos
)
, one concludes that the lifetime
of sterile neutrinos can be much longer than the age of the Universe
(
i.e.,
t
0
≈
1
3
.
7
Gy
r
∼
10
1
7
s
)
and thus satisfy one of the requirements for dark
372 10 Neutrinos and
C
osmolo
g
ical
S
tructure
s
matter candidates. The signature of the two-body radiative decay ˜
ν
s
→
ν
i
+
γ
i
s a monoener
g
etic flux of X-rays with ener
g
y
E
γ
E
≈
m
s
/
2
.Itisin
p
rinci
p
le
possible to observe this signature of sterile neutrinos in the XMN-Newton
,
Chandra X-ray and Suzaku observatories
(
Loewenstein and Kusenko, 2010;
P
rokhorov and Silk, 2010; Chan and Chu, 2010
).
Finally, it is worth mentioning that a laboratory search for keV sterile
n
eutrinos would require a care
f
ul anal
y
sis o
f
kinematics o
f
the beta deca
ys
of different isotopes
(
Trincze
k
e
tal
.
, 2003; Shaposhnikov, 2007
)
. Because of
the mixing between active and sterile neutrinos, one may study the details of
kinematics o
f
the tritium beta deca
y
3
H
→
3
H
e
+
e
−
+
ν
e
in
wh
i
ch
ν
e
co
n
tai
n
s
a
tin
y
contribution from sterile antineutrinos. On the other hand, one ma
y
probe the existence o
f
keV sterile neutrinos by detectin
g
the neutrino capture
processes like ˜
ν
s
+
3
H
→
3
H
e
+
e
−
and ˜
ν
s
+
106
R
u
→
106
R
h
+
e
−
ag
ainst the
β
-
decay backgrounds
(
Li and Xing, 2010; Liao, 2010
)
in a way similar to th
e
d
etection o
f
the sterile component o
f
the
C
ν
B(
Li
et al
.
,
2010
)
. Although such
d
irect laborator
y
searches
f
or dark matter in the
f
orm o
f
sterile neutrinos ar
e
extreme
l
yc
h
a
ll
enging, t
h
ey mig
h
tnot
b
e
h
ope
l
ess in t
h
e
l
ong term
.
R
e
f
erence
s
A
bazajian, K., and Koushiappas, S. M., 2006, Phys. Rev.
D
7
4, 02352
7.
A
lbrecht,
A
., and Steinhardt, P. J., 1982, Ph
y
s. Rev. Lett
.
48
, 1220
.
A
saka, T., Laine, M., and Shaposhnikov, M., 2007, JHE
P
0701
, 091.
B
arto
l
o
,
N.
,
et al
., 2004, P
hy
s. Rept.
40
2
, 103
.
B
ennett
,C
.L.
,
et a
l.
(
WMAP Collaboration
)
, 2003, Astrophys. J. Supp
.
1
4
8
,
1.
B
ode, P., Ostriker, J. P., and Turok, N., 2001,
A
stroph
y
s. J
.
556
,93
.
B
ond, J. R., E
f
stathiou,
G
., and
S
ilk, J., 1980, Ph
y
s. Rev. Lett
.
45
,
1980
.
C
han, M. H., and Chu, M. C., 2010, arXiv:1009.5872
.
C
lowe
,
D.
,
et al
.
,
2006,
A
stroph
y
s. J
.
648
,L
109.
C
ourteau
,S
.
,
e
ta
l
.
,
2000,
A
stroph
y
s. J
.
5
4
4
,
636
.
D
irac, P. A. M., 1931, Proc. Roy. Soc.
A
133, 60.
D
odelson,
S
., and Widrow, L. M., 1994, Ph
y
s. Rev. Lett.
7
2
,
1
7.
D
unkley, J.
,
e
ta
l
.
(
WMAP Collaboration
)
, 2009, Astrophys. J. Supp
.
180
,
306.
F
eng, J. L., 2010, arXiv:1003.0904
.
F
ixsen
,D
.
J
.
,
et al
.
,
1994,
A
stroph
y
s. J
.
4
2
0
,44
5
.
G
ru
p
en, C.
,
et a
l.
,
2005
,
A
stroparticle Ph
y
sic
s
(
Springer-Verlag
)
.
G
uo, W. L., and Xing, Z. Z., 2002, Phys. Rev.
D
65
, 073020.
G
uth,
A
. H., 1981, Ph
y
s. Rev. D
23
,
3
4
7.
H
amann
,
J.
,
et a
l.
,
2010a
,
JCA
P
1007
,
022
.
H
amann, J.
,
et al.
, 2010b, Phys. Rev. Lett
.
105
, 181301.
H
annestad,
S
., and Ra
ff
elt,
G
.
G
., 1999, Ph
y
s. Rev.
D
59
,
0
4
3001.
H
inshaw, G., et a
l
.
(
WMAP Collaboration
)
, 2009, Astrophys. J. Supp
.
18
0
,
225
.
H
u, W., and Dodelson, S., 2002, Ann. Rev. Astron. Astrophys
.
40
,
1
7
1
.
J
arosi
k,
N.
,
et a
l.
(
WMAP Collaboration
)
, 2007, Astrophys. J. Supp
.
170
, 263.
K
ainulainen, K., 1990, Phys. Lett.
B
2
4
4
,
191
.
R
e
f
erences 37
3
K
amionkowski, M., and Kinkhabwala,
A
., 1998, Ph
y
s. Rev.
D
57
, 3256.
K
auffmann, G., White, S. D. M., and Guiderdoni, B., 1993, Mon. Not. Ro
y
.
A
stron.
S
oc
.
264
,
201
.
K
ohri, K., L
y
th, D. H., and Melchiorri,
A
., 2008, JC
AP
0804
, 038.
K
olb, E. W., and Turner, M. S., 1990
,
T
h
eEar
l
y Univers
e
(
Addison-Wesley,
R
edwood City
)
.
K
omatsu
,
E.
,
e
ta
l
.
(
WMAP Collaboration
)
, 2009, Astrophys. J. Supp.
1
8
0
,
3
30.
K
omatsu, E.,
et al
.
(
WMAP Collaboration
)
, 2010, arXiv:1001.4538
.
K
usenko,
A
., 2006, Ph
y
s. Rev. Lett
.
9
7
,
2
4
1301.
K
usenko, A., 2009, Phys. Rept
.
48
1
,
1.
L
esgourgues, J., 2010, P
h
ysic
s
3
,
5
7
.
L
es
g
our
g
ues, J., and Pastor,
S
., 2006, Phys. Rept
.
4
2
9
,
30
7.
L
ewis, A., Challinor, A., and Lasenby, A., 2000, Astrophys. J
.
538, 473.
L
i, Y. F., an
d
Xin
g
, Z. Z., 2010, arXiv:1009.5870
.
L
i, Y. F., Xin
g
, Z. Z., and Luo,
S
., 2010, Phys. Lett.
B
692
,
261.
L
iao, W., 2010, Phys. Rev.
D
8
2, 073001.
L
iddle,
A
. R., and L
y
th, D., 2000
,
C
osmolo
g
ical In
fl
ation and Lar
g
e-
S
cale
S
truc-
t
ur
e
(
Cambridge University Press
).
L
inde, A. D., 1982, Phys. Lett. B 10
8
,
389
.
L
oewenstein, M., and Kusenko,
A
., 2010,
A
stroph
y
s. J.
7
14
, 652
.
M
ather
,
J.
C
.
,
et a
l.
, 1999,
A
stroph
y
s. J. 512
,
511.
M
oore, B.
,
et al
., 1999, Astrophys. J
.
52
4
,
L19.
N
a
k
amura
,
K.
,
et al.
(
Particle Data Group
)
, 2010, J. Phys. G
37
,
0
7
5021
.
P
al, P., and Wol
f
enstein, L., 1982, Ph
y
s. Rev.
D
2
5
,
766.
P
eacock, J. A., 1999,
C
osmological Physics
(
Cambridge University Press
).
P
eccei, R. D., and
Q
uinn, H. R., 1977, Ph
y
s. Rev. Lett.
38
,
1
44
0
.
P
eebles, P. J. E., and Wilkinson, D. T., 1968, Ph
y
s. Rev
.
174
,
2168.
P
enzias, A., and Wilson, R., 1965, Astrophys. J
.
142
, 419.
P
erciva
l,
W. J.
,
et al.
, 2010, Mon. Not. Ro
y
.
A
stron. Soc.
401
,
21
4
8
.
P
erkins
,
D. H.
,
2009
,
P
article Astroph
y
sic
s
(
Oxford University Press
).
P
ontecorvo, B., 1968, Sov. Phys. JETP
26
, 984.
P
rokhorov
,
D.
A
.
,
and Silk
,
J.
,
2010
,
arXiv:1001.0215.
R
iess
,
A. G.
,
e
ta
l
.
,
2009, Astroph
y
s. J
.
6
9
9
,
539
.
R
ubin, V. C., and Ford, W. K., Jr., 1970, Astrophys. J.
159
,
379
.
R
ubin, V. C., Thonnard, N., and Ford, W. K., Jr., 1980,
A
stroph
y
s. J
.
2
3
8
,
471.
S
achs, R. K., and Wolfe, A. M., 1967, Astrophys. J
.
1
4
7
,
7
3.
S
aha, M. N., 1921, Proc. Ro
y
. Soc. Lond.
A
9
9
, 135.
S
eljak, U., and Zaldarriaga, M., 1996, Astrophys. J
.
469, 437.
S
haposhnikov, M., 2007, arXiv:0706.1894.
S
haposhnikov, M., and Tkachev, I., 2006, Ph
y
s. Lett. B
6
3
9
,4
1
4.
S
hi, X. D., and Fuller, G. M., 1999, Phys. Rev. Lett. 8
2
,
2832
.
S
hrock, R. E., 1982, Nucl. Phys.
B
206
, 359.
S
ilk, J., 1968,
A
stroph
y
s. J
.
1
51
,4
59.
S
moot, G. F.,
e
ta
l
.
,
1992, Astrophys. J
.
3
9
6
,
L1.
S
trumia, A., and Vissani, F., 2006, arXiv:hep-ph
/
0606054
.
374 10 Neutrinos and
C
osmolo
g
ical
S
tructure
s
T
homas, S.
A
.,
A
bdalla, F. B., and Lahav, O., 2010, Ph
y
s. Rev. Lett
.
105
,
0
31301.
T
rinczek, M.,
et al.
,
2003, Phys. Rev. Lett
.
90
,
012501
.
W
hite, M., Scott, D., and Silk, J., 1994,
A
nn. Rev.
A
stron.
A
stroph
y
s
.
32
, 319.
Z
wicky, F., 1933, Helv. Phys. Act
a
6
, 110.
Z
wicky, F., 1937, Astrophys. J.
86
,
21
7.
11
Cosmological Matter-antimatter
A
symmetry
The observed matter-antimatter asymmetry of the Universe is a bi
g
puzzle i
n
particle physics and cosmology. Although the hot Big Bang model of cosmol
-
ogy is very successful in predicting the cosmic microwave background
(
CMB
)
radiation and the primordial abundances of li
g
ht elements, it does not explain
w
h
yt
h
e cosmic
b
aryon-to-p
h
oton rati
o
η
≡
n
B
/n
γ
i
sa
b
out
6
×
10
−
10
a
n
d
wh
y
the primordial number densit
y
o
f
antibar
y
ons
n
B
is vanis
h
in
g
.Int
h
i
s
c
hapter we shall first present some experimental evidence for such a bar
y
o
n
n
umber asymmetry, and then outline a few interesting dynamic scenarios t
o
a
ccount for it.
A
mon
g
the presently-proposed baryo
g
enesis mechanisms, th
e
l
eptogenesis mechanism is most promising because it is intrinsically relate
d
to the popular seesaw mechanisms of neutrino mass generation. So we shall
pay particular attention to the details o
f
this mechanism and
g
ive a broad
overview of its recent develo
p
ments
.
11.1 Baryon Asymmetry of the Universe
S
hortl
y
a
f
ter the discover
y
o
f
the positron, the antiparticle o
f
the electron,
P
aul Dirac made an intriguing conjecture in his Nobel lecture
(
Dirac, 1933
)
:
“If we accept the view of complete symmetry between positive and negativ
e
electric char
g
eso
f
ar as concerns the
f
undamental laws o
f
Nature, we mus
t
regard it rather as an accident that the Earth
(
and presumably the whole solar
s
ystem
)
, contains a preponderance of negative electrons and positive protons
.
It is quite possible that
f
or some o
f
the stars it is the other wa
y
about, thes
e
tars being built up mainly of positrons and negative protons. In fact, there
m
ay be half the stars of each kind. The two kinds of stars would both show
exactly the same spectra, and there would be no way o
f
distin
g
uishin
g
the
m
by present astronomical methods.” Unfortunately, current observational dat
a
ndicate that there are no stars or
alaxies made o
antimatter at all in th
visible Universe. I
f
there existed a lar
g
ere
g
ion o
f
antimatter, the matte
r
a
nd antimatter would have unavoidably annihilated with each other at thei
r
Z.-Z. Xing et al., Neutrinos in Particle Physics, Astronomy and Cosmology
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