1. Effects of sterile neutrino and modified gravity on primordial nucleosynthesis
Motohiko Kusakabe1,2
collaborators
K. S. Kim1, Myung-Ki Cheoun2, Seoktae Koh3,
A. B. Balantekin4, Toshitaka Kajino5,6,Y. Pehlivan7,
Hiroyuki Ishida8,Hiroshi Okada9
1Korea Aerospace Univ., 2Soongsil Univ.,
3Jeju National Univ., 4Univ. Wisconsin, Madison,
5National Astronomical Observatory of Japan,
6Univ. Tokyo, 7Mimar Sinan Fine Arts Univ.,
8Tohoku Univ., 9KIAS
Workshop on Neutrino Physics and Astrophysics
2015/3/20

2. Introduction 1. Solar abundance Ryan (2000) H, He
(big bang nucleosynthesis; BBN)
Ryan (2000)
Ne, Si, S, Ca (C, O, Si burning in massive star)
Nucl. SE (supernova Ia)
Li, Be, B
(cosmic ray spallation+…)

3. 1. Solar abundance Production after BBN Galactic chemical evolution
Interstellar matter
massive star
Cosmic ray from
supernova
spallation
Prediction in standard BBN model (Coc et al., 2012)
Ryan (2000)
Production after BBN

4. 1. Solar abundance Light elements: good probe of the early universe
Prediction in standard BBN model (Coc et al., 2012)
Ryan (2000)
Li, Be, B
(cosmic ray spallation+…)
Light elements: good probe of the early universe

5. 2. Primordial light element abundances
Standard BBN
parameter: baryon-to-photon ratio h
CMB constraint on h
Observation of metal-poor stars (MPSs)
7Li abundance is smaller than theory
by a factor of ~3
Primordial abundances of Be, B, …
are not detected yet.
Izotov et al. (2014)
Cooke et al. (2014)
Bania et al. (2002)
ESA and the Planck Collaboration
Sbordone et al. (2010)
Lind et al. (2013)

6. 3. Li problem 7LiBBN Li problem 7Li/H in MPSs < 7Li/H in SBBN
7Li/H=( )× fit of LiI 6708 A line
(Spite & Spite 1982, Ryan et al. 2000, Melendez & Ramirez 2004, Asplund et al , Bonifacio et al. 2007, Shi et al. 2007, Aoki et al. 2009, Sbordone 2010)
log(Li/H)+12
Sbordone et al. (2010)
7LiBBN
Aoki et al. (2009)
Asplund06
Li problem
Aoki09
Sbordone10
Gonzalez Hernandez08
Old stars ~ primordial

7. 4. Standard BBN (1) The Space expands Gravitational Interaction Weak
Electromagnetic e±
Coulomb
Scattering p A
Strong Interaction

8. 4. Standard BBN (2) n↔p equilibrium (n/p)EQ=exp(-Q/T) Q≡mn-mp=1.293MeV
t~1sec,T=TF~1MeV(week interaction freeze-out)
nn e+e gg
n↔p
e± gg (T~me/3)
(n/p)freeze-out=exp(-Q/TF)~1/6
(1MeV=1.16×1010 K)
Kawano code (1992)
Rates:
Smith et al. (1993)
+Descouvemont et al. (2004)
+JINA REACLIB (Dec., 2014)
tn=880.3s
(Olive et al. [PDG] 2014)
7Li(p,a)4He
7Be7Li
e--capture after recombination
3H(a,g)7Li
h=nb/ng=6.037×10-10
Planck (Ade et al. 2014)
3He(a,g)7Be
T9≡T/(109K)

9. 5. Possibilities of exotic particles & modified gravity
Astronomical observations dark Matter, dark energy
Need for beyond the standard model
(e.g. sterile n, SUSY, or modified gravity)
exotic particles, or exotic equations of motion of Universe
Goal
checking effects on BBN, and deriving constraints on models
checking possible signatures on light element abundances
Li problem? X g
Nuclear reactions triggered by decay products
Nuclear reactions of exotic atoms and exotic nuclei X-
nuclide A
X-nucleus X0
nuclide A
X-nucleus
(Cahn & Glashow 1981)
(Dover et al. 1979)

10. Effects of modified gravity
Small baryon number in the universe, i.e., h〜6×10-10
solution by the modified gravity
(Davoudiasl et al. 2004)
# of intrinsic degrees of
freedom of baryons
Cutoff scale
Baryon current
Interaction that violate the baryon number
f(R)∝Rn with n〜0.97 gives
the observed baryon number density
(Lambiase & Scarpetta, 2006)
constraint from 4He abundance 
(Kang & Panotopoulos, 2009)
(Kang & Panotopoulos, 2009)

11. Model: f(R) gravity (1) Action Variation with respect to gmn
Friedmann-LemaÎtre-Robertson-Walker metric
Energy-momentum tensor
equations of motion

12. Model: f(R) gravity (2) f(R) terms Solution: a(t) ∝ta/2, a=n/2
(for n>1)
(for n<1)
(Kang & Panotopoulos, 2009)
Solution:
a(t) ∝ta/2, a=n/2
Cosmic expansion rate

13. Result: f(R) gravity
Small difference in the index n (or a) changes nuclear abundances.
4He and D abundances 

14. Model: f(G) gravity (1) Action Gauss-Bonnet term Field equation:
Energy-momentum tensor

15. Model: f(G) gravity (2) model 3 parameters
(in the range of 102 ≥ T9 ≥ 10-2)
Equations of motion

16. Results: f(G) gravity (1)
Requirements for
(1) a smooth evolution of cosmic expansion
(2) successful BBN
ex. 1: real positive solution disappears
ex. 2: elemental abundances changes

17. Results: f(G) gravity (2)
Negative L<0 effect
f(G) is smaller
When the deviation of expansion rate from the standard case is small

18. Effects of sterile neutrino decay
Energetic g is generated  photodisintegration of nuclei
(Lindley 1979, Ellis et al , Reno & Seckel 1988, Dimopoulos et al ,
Kawasaki et al , Khlopov et al , Jedamzik 2000-, MK et al )
Decay of X generation of very energetic g
7Be can be destroyed But other nuclei are simultaneously destroyed
7Li problem cannot be solved (Ellis et al. 2005)
MK, Kajino, Mathews,
PRD 74, (2006)
decay life

19. Model: nonthermal nucleosynthesis
Assumption: exotic particle (X) decays
→g with energy Eg0
life time
abundance parameter
Interactions with background g and e± X AX g
AX’
1st
2nd
1. Primary (1st) process
g disintegrates background nuclei
(Cyburt et al. 2003)
2H(g,n)p, H(g,n)2H, H(g,np)n, 3He(g,p)d, 3He(g,np)p,
4He(g,p)t, He(g,n)3He, He(g,d)d, He(g,np)d,
6Li(g,np)4He, Li(g,X)3A, Li(g,t)4He, Li(g,n)6Li,
7Li(g,2np)4He, Be(g,3He)4He, Be(g,p)6Li, Be(g,2pn)4He
Interactions with background g and e±
2. Secondary (2nd) process
Reactions of primary product with background nuclei
6Li production (Cyburt et al. 2003)
Destruction of d,t,3He,6Li produced in 1st processes
3H(p,dp)n
3H(p,2np)p
3He(p,dp)p
3He(p,2pn)p
2H(p,pn)p
6Li(p,3He)4He
MK, Kajino, Mathews,
PRD 74, (2006)

20. Results: radiative decay (1)
Solution: MeV < Eg0 < 2.22 MeV
fine tuned photon energy
[assumption] thermal freezeout abundance
of weakly interacting massive particles
Nuclei
threshold
(MeV)
Reaction
7Be
1.587
7Be(g, a)3He D
2.225
2H(g, n)1H
7Li
2.467
7Li(g, t)4He
3He
5.494
3He(g, p)2H 3H
6.527
3H(g, n)2H
4He
19.814
4He(g, p)3H
7Be(g, a)3He
7Li reduction
without other
effects
MK, Balantekin, Kajino, Pehlivan,
PRD 87, (2013)

21. Results: radiative decay (2)
Constraint on the mass, life time, & magnetic moment of sterile n
ns  nl + g
best region
MK, Balantekin, Kajino, Pehlivan,
PRD 87, (2013)

22. Model: sterile n with mixing to active n (1)
Dirac sterile neutrino, mass MnH=O(10) MeV, active-sterile mixing Q<<1
Lagrangian Z nH ne e- e+ W nH e- ne e+ Z nH ne na -

23. Model: sterile n with mixing to active n (2)
nH decay  injection of energetic e± and n
n free-streaming after BBN
nonthermal n production n energy density is increased
energies of e± are transferred to background g
via g*+e±g*+e±* and g*+ge-*+e+*
background g is heated
baryons and thermal background n’s are diluted small h & Neff
(Shvartsman 1969, Steigman et al. 1977, Scherrer & Turner 1988)
g injection spectrum
Diff. decay rate
Energy spectrum of primary g
produced via inverse Compton
scatterings of e± (Ee)
Energy spectrum of g produced
in the electromagnetic cascade
showers of primary g (Eg0)

24. Results: decay into e± and n (1)
Time evolution of quantities
MnH=14 MeV
tnH=4×104 s
znHe=3×10-7 GeV
Neff value is increased
(Ishida, MK, Okada, PRD 90, , 2014)

25. Results: decay into e± and n (2)
(Ishida, MK, Okada, PRD 90, , 2014)
Constraints
7Be(g, a)3He
weak 7Li reduction
in the allowed region
The nH decay alone cannot be a solution to the Li abundance of MPSs
It could be a solution if the stellar Li abundances are depleted by a factor 〜2
This model can be tested with future measurements of Neff

26. Summary We study effects of the modified gravity on BBN
constraints are derived
f(R) ∝Rn (n -1) =(-0.81±1.19)×10-4
f’(G) ∝tp amplitude is constrained in parameter planes
Note: Li problem is not solved
modified expansion affects abundances of all nuclei
We study effects of decaying sterile n on primordial abundances
radiative decay:
efficient destruction of 7Be, for ms 〜( ) MeV
possible solution to 7Li problem
decay into e±n:
nonthermal photon spectrum is softer
7Be cannot be destroyed significantly without D destruction
ms 〜14 MeV is the best case for 7Li reduction
The maximum destruction fraction is 〜0.1 26