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

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n↔p equilibrium (n/p) EQ =exp(-Q/T) Q≡m 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=1.16×10 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 =6.037×10 -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., 〜 6×10 -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-LemaÎtre-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<1)

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

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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 Equations of motion (in the range of 10 2 ≥ T 9 ≥ 10 -2 )

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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 disappearsex. 2: elemental abundances changes

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Results: f(G) gravity (2) When the deviation of expansion rate from the standard case is small Negative <0 effect f(G) is smaller >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 AX’AX’ 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 <<1 Z H e e-e- e+e+ W H ee e e+e+ Z H e Model: sterile with mixing to active (1)

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H decay injection of energetic e ± and free-streaming after BBN nonthermal production energy density is increased energies of e ± are transferred to background via +e ± +e ±* and + e -* +e +* background is heated baryons and thermal background ’s are diluted small & N eff injection spectrum Diff. decay rate Energy spectrum of primary produced via inverse Compton scatterings of e ± (E e ) Energy spectrum of produced in the electromagnetic cascade showers of primary (E 0 ) (Shvartsman 1969, Steigman et al. 1977, Scherrer & Turner 1988) Model: sterile with mixing to active (2)

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N eff value is increased Time evolution of quantities M H =14 MeV H =4×10 4 s H e =3×10 -7 GeV Results: decay into e ± and (1) (Ishida, MK, Okada, PRD 90, 083519, 2014)

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weak 7 Li reduction in the allowed region 7 Be( , ) 3 He The H 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 N eff (Ishida, MK, Okada, PRD 90, 083519, 2014) Constraints Results: decay into e ± and (2)

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We study effects of the modified gravity on BBN constraints are derived f(R) ∝ R n (n -1) =(-0.81±1.19)×10 -4 f’(G) ∝ t p 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 on primordial abundances radiative decay: efficient destruction of 7 Be, for m s 〜 (3.2-4.4) MeV possible solution to 7 Li problem decay into e ± : nonthermal photon spectrum is softer 7 Be cannot be destroyed significantly without D destruction m s 〜 14 MeV is the best case for 7 Li reduction The maximum destruction fraction is 〜 0.1 Summary

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