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Motohiko Kusakabe 1,2 collaborators K. S. Kim 1, Myung-Ki Cheoun 2, Seoktae Koh 3, A. B. Balantekin 4, Toshitaka Kajino 5,6,Y. Pehlivan 7, Hiroyuki Ishida 8,Hiroshi Okada 9 1 Korea Aerospace Univ., 2 Soongsil Univ., 3 Jeju National Univ., 4 Univ. Wisconsin, Madison, 5 National Astronomical Observatory of Japan, 6 Univ. Tokyo, 7 Mimar Sinan Fine Arts Univ., 8 Tohoku Univ., 9 KIAS 2015/3/20 Effects of sterile neutrino and modified gravity on primordial nucleosynthesis Workshop on Neutrino Physics and Astrophysics

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

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

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

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

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7 Li/H in MPSs < 7 Li/H in SBBN 7 Li/H=(1.1-1.5)10 -10 fit of LiI 6708 A line (Spite & Spite 1982, Ryan et al. 2000, Melendez & Ramirez 2004, Asplund et al. 2006, Bonifacio et al. 2007, Shi et al. 2007, Aoki et al. 2009, Sbordone 2010) 7 Li BBN 3. Li problem Asplund06 Sbordone10 Aoki09 Gonzalez Hernandez08 Li problem Old stars ~ primordial Sbordone et al. (2010) Aoki et al. (2009) log(Li/H)+12

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Weak Interaction Electromagnetic Interaction ee Coulomb Scattering p n A Strong Interaction The Space expands Gravitational Interaction 4. Standard BBN (1)

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np equilibrium (n/p) EQ =exp(-Q/T) Qm n -m p =1.293MeV t ~ 1sec,T=T F ~1MeV(week interaction freeze-out) e + e - n p e (T~m e /3) (n/p) freeze-out =exp(-Q/T F )~1/6 (1MeV=1.1610 10 K) Kawano code (1992) Rates: Smith et al. (1993) +Descouvemont et al. (2004) +JINA REACLIB (Dec., 2014) n =880.3s (Olive et al. [PDG] 2014) n b /n =6.03710 -10 Planck (Ade et al. 2014) 7 Be 7 Li e - -capture after recombination T 9 T/(10 9 K) 3 He( , ) 7 Be 3 H( , ) 7 Li 7 Li(p, ) 4 He 4. Standard BBN (2)

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Astronomical observations dark Matter, dark energy Need for beyond the standard model (e.g. sterile, SUSY, or modified gravity) exotic particles, or exotic equations of motion of Universe Li problem? 5. Possibilities of exotic particles & modified gravity Nuclear reactions of exotic atoms and exotic nuclei (Cahn & Glashow 1981)(Dover et al. 1979) Goal checking effects on BBN, and deriving constraints on models checking possible signatures on light element abundances X-X- nuclide A X-nucleus X0X0 nuclide A X-nucleus X Nuclear reactions triggered by decay products

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I.Effects of modified gravity (Kang & Panotopoulos, 2009) Small baryon number in the universe, i.e., 610 -10 solution by the modified gravity Cutoff scaleBaryon current Interaction that violate the baryon number # of intrinsic degrees of freedom of baryons (Davoudiasl et al. 2004) f(R) R n with n 0.97 gives the observed baryon number density (Lambiase & Scarpetta, 2006) constraint from 4 He abundance (Kang & Panotopoulos, 2009)

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Model: f(R) gravity (1) Action Variation with respect to g Friedmann-Lematre-Robertson-Walker metric Energy-momentum tensor equations of motion

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

Results: f(G) gravity (2) When the deviation of expansion rate from the standard case is small Negative 0

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decay life MK, Kajino, Mathews, PRD 74, 023526 (2006) Energetic is generated photodisintegration of nuclei (Lindley 1979, Ellis et al. 1985-, Reno & Seckel 1988, Dimopoulos et al. 1988-, Kawasaki et al. 1988-, Khlopov et al. 1994-, Jedamzik 2000-, MK et al. 2006-) Decay of X generation of very energetic 7 Be can be destroyed But other nuclei are simultaneously destroyed 7 Li problem cannot be solved (Ellis et al. 2005) II.Effects of sterile neutrino decay

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Assumption: exotic particle (X) decays with energy E 0 1. Primary (1 st ) process disintegrates background nuclei Interactions with background and e (Cyburt et al. 2003) Interactions with background and e 2. Secondary (2 nd ) process Reactions of primary product with background nuclei 6 Li production (Cyburt et al. 2003) Destruction of d,t, 3 He, 6 Li produced in 1 st processes abundance parameterlife time X AXAX AXAX 1 st 2 nd 3 H(p,dp)n 3 H(p,2np)p 3 He(p,dp)p 3 He(p,2pn)p 2 H(p,pn)p 6 Li(p, 3 He) 4 He MK, Kajino, Mathews, PRD 74, 023526 (2006) 2 H( ,n)p, 3 H( ,n) 2 H, 3 H( ,np)n, 3 He( ,p)d, 3 He( ,np)p, 4 He( ,p)t, 4 He( ,n) 3 He, 4 He( ,d)d, 4 He( ,np)d, 6 Li( ,np) 4 He, 6 Li( ,X) 3 A, 7 Li( ,t) 4 He, 7 Li( ,n) 6 Li, 7 Li( ,2np) 4 He, 7 Be( , 3 He) 4 He, 7 Be( ,p) 6 Li, 7 Be( ,2pn) 4 He Model: nonthermal nucleosynthesis

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7 Li reduction without other effects Solution: 1.59 MeV < E 0 < 2.22 MeV fine tuned photon energy 7 Be( , ) 3 He MK, Balantekin, Kajino, Pehlivan, PRD 87, 085045 (2013) Nucleithreshold (MeV) Reaction 7 Be1.587 7 Be( , ) 3 He D2.225 2 H( , n) 1 H 7 Li2.467 7 Li( , t) 4 He 3 He5.494 3 He( , p) 2 H 3H3H6.527 3 H( , n) 2 H 4 He19.814 4 He( , p) 3 H [assumption] thermal freezeout abundance of weakly interacting massive particles Results: radiative decay (1)

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best region MK, Balantekin, Kajino, Pehlivan, PRD 87, 085045 (2013) Constraint on the mass, life time, & magnetic moment of sterile s l + Results: radiative decay (2)

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Lagrangian Dirac sterile neutrino, mass M H =O(10) MeV, active-sterile mixing