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**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

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**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+…)

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**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

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**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

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**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)

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**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

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**4. Standard BBN (1) The Space expands Gravitational Interaction Weak**

Electromagnetic e± Coulomb Scattering p A Strong Interaction

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**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 7Be7Li 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)

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**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)

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**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)

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**Model: f(R) gravity (1) Action Variation with respect to gmn**

Friedmann-LemaÎtre-Robertson-Walker metric Energy-momentum tensor equations of motion

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**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

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

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**Model: f(G) gravity (1) Action Gauss-Bonnet term Field equation:**

Energy-momentum tensor

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**Model: f(G) gravity (2) model 3 parameters**

(in the range of 102 ≥ T9 ≥ 10-2) Equations of motion

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**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

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**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

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**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

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**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)

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**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)

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**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)

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**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 -

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**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*+ge-*+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)

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**Results: decay into e± and n (1)**

Time evolution of quantities MnH=14 MeV tnH=4×104 s znHe=3×10-7 GeV Neff value is increased (Ishida, MK, Okada, PRD 90, , 2014)

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**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

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**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

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