Page 1

arXiv:1202.5603v1 [astro-ph.CO] 25 Feb 2012

Solution to Big-Bang Nucleosynthesis in Hybrid Axion Dark Matter Model

Motohiko Kusakabe1,∗A.B. Balantekin2,3,†Toshitaka Kajino3,4,‡and Y. Pehlivan3,5§

1Institute for Cosmic Ray Research, University of Tokyo, Kashiwa, Chiba 277-8582, Japan

2Department of Physics, University of Wisconsin, Madison, WI 53706, USA

3National Astronomical Observatory of Japan 2-21-1 Osawa, Mitaka, Tokyo, 181-8588, Japan

4Department of Astronomy, Graduate School of Science,

University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo, 113-0033, Japan and

5Mimar Sinan Fine Arts University, Besiktas, Istanbul 34349, Turkey

(Dated: February 28, 2012)

Following a recent suggestion of axion cooling of photons between the nucleosynthesis and recom-

bination epochs in the Early Universe, we investigate a hybrid model with both axions and relic

supersymmetric particles. In this model we demonstrate that the7Li abundance can be consistent

with observations without destroying the important concordance of deuterium abundance.

PACS numbers: 26.35.+c, 98.80.Cq, 98.80.Es, 98.80.Ft

Introduction – Low-metallicity halo stars exhibit a

plateau of7Li abundance, indicating the primordial ori-

gin of7Li [1]. However, the amount of7Li needed to be

consistent with the cosmic microwave background obser-

vations [2] is significantly more than7Li observed in old

halo stars [3]. (Even though7Li can be both produced

and destroyed in stars, old halo dwarf stars are expected

to have gone through little nuclear processing). Recent

improvements in the observational and experimental data

seem to make the discrepancy worse [4, 5]. One possible

solution is to invoke either nuclear physics hitherto ex-

cluded from the Big-Bang Nucleosynthesis (BBN) [6, 7]

or new physics such as variations of fundamental cou-

plings [8, 9], and particles not included in the Standard

Model [10–42]. Effects of massive neutral relic particles

on BBN were extensively studied [10–28].

More recently an alternative solution to the lithium

puzzle was proposed. Since the last photon scattering oc-

curs after the end of the nucleosynthesis, one can search

for a mechanism for the cooling of photons before they

decouple. It was suggested that dark matter axions could

form a Bose-Einstein condensate (BEC) [43, 44]. Such

a condensate would cool the photons between the end

of BBN and epoch of photon decoupling, reducing the

baryon-to-photon ratio WMAP infers, as compared to

its BBN value [45]. An alternative mechanism for such a

cooling is resonant oscillations between photons and light

abelian gauge bosons in the hidden sector [46]. There are

two prima facie problems with the axion BEC-photon

cooling hypothesis: it overpredicts primordial deuterium

(D) abundance as well as the effective number of neu-

trinos. Even though D is easy to destroy, one does not

expect the sum of abundances of D and3He to change

significantly in the course of cosmic evolution [47]. Hence

it is important to find a parameter region in which pre-

dicted abundances of D and7Li are consistent with ob-

servations. In this letter we demonstrate the existence of

such a parameter region using a model with axions and

massive relic particles.

The Hybrid Model – We carried out BBN net-

work calculations using Kawano’s code [50, 51] by in-

cluding Sarkar’s correction for

JINA REACLIB Database V1.0 [53] is used for light nu-

clear (A ≤ 10) reaction rates including uncertainties to-

gether with data [54–56]. Adopted neutron lifetime is

878.5 ± 0.7stat± 0.3sys s [57] based on improved mea-

surements [48]. Taking into account the uncertainties in

the rates of twelve important reactions in BBN [51], we

employ regions of 95% C. L. in our calculations.

We compare our results with the abundance con-

straints from observations. For the primordial D abun-

dance, the mean value estimated from Lyman-α absorp-

tion systems in the foreground of high redshift quasi-

stellar objects is log(D/H) = −4.55 ± 0.03 [58].

adopt this value together with a 2σ uncertainty, i.e.,

2.45 × 10−5

< D/H < 3.24 × 10−5.

dance measurements in Galactic HII regions through the

8.665 GHz hyperfine transition of3He+yield a value of

3He/H=(1.9 ± 0.6) × 10−5[59]. Although the constraint

should be rather weak considering its uncertainty, we

take a 2σ upper limit and adopt3He/H < 3.1 × 10−5.

We also utilize a limit on the sum of primordial abun-

dances of D and3He taken from an abundance for the

protosolar cloud determined from observations of solar

wind, i.e., (D+3He)/H=(3.6 ± 0.5) × 10−5[60].

abundance can be regarded as constant at least within

the standard cosmology since it is not affected by stellar

activities significantly despite an effect of D burning into

3He via2H(p,γ)3He would exist [47].

For the primordial4He abundance, we adopt two dif-

ferent constraints from recent reports: Yp = 0.2565 ±

0.0051 [61] and Yp= 0.2561 ± 0.0108 [62] both of which

are derived from observations of metal-poor extragalactic

HII regions. Adding 2σ uncertainties leads to 0.2463 <

Yp< 0.2667 [61] and 0.2345 < Yp< 0.2777 [62].

6Li plateau of metal-poor halo stars (MPHSs), yields

the upper limit of6Li/H= (7.1±0.7)×10−12[3]. Adding

a 2σ uncertainty, we adopt6Li/H < 8.5 × 10−12.

4He abundances [52].

We

3He abun-

This

Page 2

2

FIG. 1. Abundances of4He (mass fraction), D,3He,7Li and

6Li (number ratio relative to H) as a function of the baryon-to-

photon ratio η or the baryon energy density parameter ΩBh2

of the universe. The thick dashed curves are for SBBN. The

thin dashed curves around them show the regions of 95% C.

L. in accordance with the nuclear reaction rate uncertainties.

The boxes correspond to the adopted abundance constraints

on the SBBN model. The vertical stripes represent the 2σ

limits on ΩBh2or η for the SBBN model (taken from the

constraint by WMAP [49] and labeled as WMAP7) and for

the axion BEC model (labeled as axion). The solid curves

are the results obtained with the long-lived decaying particle

model with parameters fixed to (τX, ζX)=(106s, 2 × 10−10

GeV) (see text).

Forthe

7Li abundance,weadoptthelimits

log(7Li/H)= −12+(2.199±0.086) (with 95% C. L.) de-

rived from recent observations of MPHSs in the 3D non-

local thermal equilibrium model [63], i.e. 1.06×10−10<

7Li/H < 2.35 × 10−10.

Figure 1 shows the abundances of4He (Yp; mass frac-

tion), D,3He,7Li and6Li (number ratio relative to H) as

a function of the baryon-to-photon ratio η or the baryon

energy density parameter ΩBh2of the universe, where h

is the Hubble constant in units of 100 km/s/Mpc. The

thick dashed curves are the results of the standard BBN

(SBBN) with a neutron lifetime of 878.5 ± 0.8 s. Thin

dashed curves around them show regions of 95% C. L.

from uncertainties in the nuclear reaction rates.

boxes represent adopted abundance constraints as sum-

marized above. The vertical stripes correspond to the 2σ

limits on ΩBh2or η. The values provided by WMAP [49]

(labeled WMAP7) are

The

ΩBh2= 0.02258+0.00114

−0.00112

η = (6.225+0.314

−0.309)×10−10. (1)

Values predicted by the BEC model (labeled axion) are

smaller by a factor of (2/3)3/4at the BBN epoch [45]:

ΩBh2= 0.01666+0.00084

−0.00083

η = (4.593+0.232

−0.228)×10−10. (2)

It can be seen that the adoption of the η value from

WMAP leads to a7Li abundance calculated in the ax-

ion BEC model, which is in reasonable agreement with

the observations. However, we lose the important consis-

tency in D abundance. Ref. [45] noted that astronom-

ical measurements of primordial D abundance can have

a significant uncertainty as well as a possibility that D

is burned by nonstandard stellar processes. Even if their

assumption were true, stellar processes are not expected

to change the sum of D and3He abundances [47]. As

seen in Fig. 1, the constraint on (D+3He)/H abundance

seems to exclude the original axion BEC model. Ulti-

mately, this model is viable only when the abundance of

(D+3He)/H is reduced through some exotic processes.

It is known that nonthermal photons can be generated

through electromagnetic energy injections by the radia-

tive decay of long-lived particles after the BBN epoch [11,

16].These nonthermal photons can photodisintegrate

background light elements [10, 11, 19, 20, 24, 25]. We

adopt the method of Ref. [25] to calculate the nonther-

mal nucleosynthesis, where we incorporated new thermal

reaction rates as described above. In addition, we adopt

updated reaction rates of4He photodisintegration [26]

derived from the cross section data using precise mea-

surements with laser-Compton photons [64, 65]. Effects

of electromagnetic energy injection depend on two pa-

rameters. One is ζX = (n0

the number ratio of the decaying particle X and the back-

ground radiation before the decay of X, and Eγ0is the

energy of photon emitted at the radiative decay. The

other is τX, the lifetime of the X particle.

Figure 2 shows the parameter space in our hybrid

model. For4He, we adopt the conservative constraint

with larger uncertainty [62]. We also show the contour

for6Li production at the observed level, i.e.,

7.1 × 10−12. This figure shows the result of nonthermal

nucleosynthesis induced by the radiative decay of long-

lived particles with the η value of the axion BEC model

[Eq. (2)]. Except for D and7Li, contours are similar to

those represented in Ref [25] where BBN epoch η value

is assumed to be the same as WMAP η value [Eq. (1)].

X/n0

γ)Eγ0 where (n0

X/n0

γ) is

6Li/H=

Page 3

3

FIG. 2. Parameter space of the hybrid model (τX,ζX) for the

value of η = 4.6 × 10−10provided by the axion BEC model.

The contours identify the regions where the nuclei are over-

produced or underproduced (“over” and “low”, respectively)

with respect to the adopted abundance constraints.

fraction (red line) and3He/H (black lines), D/H (green solid

and dashed lines for upper and lower limits, respectively),

and7Li/H (blue line) number ratios are shown. The orange

line is the contour of6Li/H=7.1 ×10−12. In the gray-colored

region all abundances are within the limits of observational

constraints.

4He mass

In the very small colored region, calculated primordial

abundances of all nuclides including D and7Li are simul-

taneously in ranges of adopted observational constraints.

We conclude that the present model eliminates the main

drawback of the original axion BEC model by reducing

primordial D abundance via2H(γ,n)1H reaction, where

γ’s are nonthermal photons. We note that the decaying

particle model with the WMAP η value cannot resolve

the7Li problem by itself [23, 25].

The effect of the radiative decay on other elemental

abundances is not significant except for7Li. Since ener-

getic photons produced quickly collide with background

photons and create e+e−pairs, nonthermal photon spec-

tra developed by the decay has a cutoff energy EC =

m2

e/22T where meis the electron mass [16]. The decay

at earlier (hotter) universe then triggers nonthermal pho-

tons with lower cutoff energies. The threshold energies

of7Be and D photodisintegration,7Be+γ →3He+4He

and D+γ → n + p are 1.5866 MeV and 2.2246 MeV,

respectively. These two nuclei are very fragile against

photodisintegration. When the decay occurs early at rel-

atively high T9≡ T/(109K)>

to τX<

∼106s, nonthermal photon spectra contain pho-

tons to dissociate7Be and D, while keeping other nuclides

intact. The gray region indicates parameters which re-

sult in moderate destruction of D which is overproduced

in the original BEC model because of low η. Above that

region, D is destroyed too much by photodisintegration,

∼10−2which corresponds

FIG. 3.

tively) and number ratios of other nuclides relative to H as

a function of T9. Solid lines show the abundances calculated

in the hybrid model with the parameters (τX, ζX)=(106s,

2×10−10GeV) which correspond to the point indicated with

a star in Fig. 2. The dashed lines show the SBBN prediction.

Mass fractions of H and4He (Xp and Yp, respec-

while below it D abundance is too high.

We next present the results of a BBN calculation in our

hybrid model with a fixed set of parameters given by (τX,

ζX)=(106s, 2×10−10GeV) and the η value given in Eq.

(2). This corresponds to the point indicated with a star in

Fig. (2) and yields the required D and7Li abundances as

seen in Figure 3. This figure shows H and4He mass frac-

tions (denoted by Xpand Yp), and n, D, T,3He,6Li,7Li

and7Be number ratios relative to H as a function of the

temperature. The abundances calculated using the axion

BEC + long-lived decaying particle model with the pa-

rameters (τX, ζX)=(106s, 2×10−10GeV) and the η value

provided by BEC model [Eq. (2)] are shown in solid lines

whereas the SBBN prediction is plotted by dashed lines.

The small difference at T9>

∼0.06 observed between solid

and dashed lines is caused by difference between initial

η values. At 0.06>

∼T9>

∼7×10−3(corresponding to the

cosmic time of t ∼ 5×104–4×106s), effects of2H(γ,n)1H

are seen in the decrease of D and the increase of n abun-

dances.We find a slight decrease in

This is caused through reactions7Be(γ,3He)4He (thresh-

old energy: 1.5866MeV),7Be(γ,p)6Li (5.6858 MeV), and

7Be(γ,2pn)4He (9.3047 MeV). The second reaction in-

creases the6Li abundance. Finally, at T9<

where the abundance of long-lived X particle is already

less than 3 % of the initial abundance, effect of4He pho-

todisintegration is to increase3H and n abundances.

In Fig. 1, solid lines show the results for the SBBN

+ long-lived decaying particle model with the same pa-

rameter values, i.e., (τX, ζX)=(106s, 2 × 10−10GeV).

Obviously the abundances of D and7Li (produced partly

as7Be) are reduced, while that of6Li is increased from

those of SBBN.

7Be abundance.

∼7 × 10−3,

Page 4

4

Conclusions – We used a hybrid axion and massive

relic particle model in which axions cool the photons and

relic particles produce non-thermal photons to eliminate

the high D abundance in the original axion BEC model.

Our hybrid model also produces6Li keeping7Li abun-

dance at the level of Population II Spite plateau. Our

work thus demonstrates that the7Li abundance can be

consistent with observations without destroying the im-

portant concordance of deuterium abundance.

This work was supported in part by Grants-in-Aid

for Scientific Research of the JSPS (200244035) and

for Scientific Research on Innovative Area of MEXT

(20105004), in part by JSPS Grant No.21.6817, in part by

the U.S. National Science Foundation Grant No. PHY-

0855082, in part by the Council of Higher Education of

Turkey, and in part by the University of Wisconsin Re-

search Committee with funds granted by the Wisconsin

Alumni Research Foundation.

∗kusakabe@icrr.u-tokyo.ac.jp

†baha@physics.wisc.edu

‡kajino@nao.ac.jp

§ypehlivan@me.com

[1] F. Spite and M. Spite, Astron. Astrophys. 115, 357–366

(1982).

[2] E. Komatsu et al. [WMAP Collaboration], Astrophys. J.

Suppl. 192, 18 (2011).

[3] M. Asplund et al., Astrophys. J. 644, 229 (2006).

[4] R. H. Cyburt, B. D. Fields and K. A. Olive, JCAP 0811,

012 (2008).

[5] A. Coc et al., Astrophys. J. 744, 158 (2012).

[6] N. Chakraborty, B. D. Fields and K. A. Olive, Phys. Rev.

D 83, 063006 (2011).

[7] R. H. Cyburt and M. Pospelov, Int. J. Mod. Phys. E 21,

1250004 (2012).

[8] A. Coc et al., Phys. Rev. D 76, 023511 (2007).

[9] M. K. Cheoun, T. Kajino, M. Kusakabe and G. J. Math-

ews, Phys. Rev. D 84, 043001 (2011).

[10] D. Lindley, Mon. Not. R. Astron. Soc. 188, 15P (1979).

[11] J. R. Ellis, D. V. Nanopoulos and S. Sarkar, Nucl. Phys.

B 259, 175 (1985).

[12] S. Dimopoulos,R.Esmailzadeh,

G. D. Starkman, Astrophys. J. 330, 545 (1988).

[13] M. H. Reno and D. Seckel, Phys. Rev. D 37, 3441 (1988).

[14] N. Terasawa, M. Kawasaki and K. Sato, Nucl. Phys. B

302, 697 (1988).

[15] M. Kawasaki and T. Moroi, Prog. Theor. Phys. 93, 879

(1995).

[16] M. Kawasaki and T. Moroi, Astrophys. J. 452, 506

(1995).

[17] K. Jedamzik, Phys. Rev. Lett. 84, 3248 (2000).

[18] M. Kawasaki, K. Kohri and T. Moroi, Phys. Rev. D 63,

103502 (2001).

[19] R. H. Cyburt, J. R. Ellis, B. D. Fields and K. A. Olive,

Phys. Rev. D 67, 103521 (2003).

[20] M. Kawasaki, K. Kohri and T. Moroi, Phys. Rev. D 71,

083502 (2005).

[21] K. Jedamzik, Phys. Rev. D 70, 063524 (2004).

L.J.Halland

[22] K. Jedamzik, Phys. Rev. D 70, 083510 (2004).

[23] J. R. Ellis, K. A. Olive and E. Vangioni, Phys. Lett. B

619, 30 (2005).

[24] K. Jedamzik, Phys. Rev. D 74, 103509 (2006).

[25] M. Kusakabe, T. Kajino and G. J. Mathews, Phys. Rev.

D 74, 023526 (2006).

[26] M. Kusakabe et al., Phys. Rev. D 79, 123513 (2009).

[27] R. H. Cyburt et al., JCAP 1010, 032 (2010).

[28] M. Pospelov and J. Pradler, Phys. Rev. D 82, 103514

(2010).

[29] M. Pospelov, Phys. Rev. Lett. 98, 231301 (2007).

[30] K. Kohri and F. Takayama, Phys. Rev. D 76, 063507

(2007).

[31] R. H. Cyburt et al., JCAP 0611, 014 (2006).

[32] K. Jedamzik, Phys. Rev. D 77, 063524 (2008).

[33] M. Pospelov, arXiv:0712.0647 [hep-ph].

[34] T. Jittoh et al., Phys. Rev. D 76, 125023 (2007).

[35] K. Hamaguchi et al., Phys. Lett. B 650, 268 (2007).

[36] M. Kusakabe et al., Phys. Rev. D 76, 121302 (2007).

[37] M. Kamimura, Y. Kino and E. Hiyama, Prog. Theor.

Phys. 121, 1059 (2009).

[38] M. Kusakabe, T. Kajino, T. Yoshida and G. J. Mathews,

Phys. Rev. D 81, 083521 (2010).

[39] T. Jittoh et al., Phys. Rev. D 82, 115030 (2010).

[40] C. Bird, K. Koopmans and M. Pospelov, Phys. Rev. D

78, 083010 (2008).

[41] K. Jedamzik and M. Pospelov, New J. Phys. 11, 105028

(2009).

[42] M. Pospelov and J. Pradler, Ann. Rev. Nucl. Part. Sci.

60, 539 (2010).

[43] P. Sikivie and Q. Yang, Phys. Rev. Lett. 103, 111301

(2009).

[44] O.Erken,P.Sikivie,

arXiv:1111.1157 [astro-ph.CO].

[45] O. Erken, P. Sikivie, H. Tam and Q. Yang, Phys. Rev.

Lett. 108, 061304 (2012).

[46] J. Jaeckel, J. Redondo and A. Ringwald, Phys. Rev. Lett.

101, 131801 (2008).

[47] G. Steigman and M. Tosi, Astrophys. J. 453, 173 (1995);

F. Iocco et al., Phys. Rept. 472, 1 (2009).

[48] A. Serebrov et al., Phys. Lett. B 605, 72 (2005).

[49] D. Larson et al., Astrophys. J. Suppl. 192, 16 (2011).

[50] L. Kawano, NASA STI/Recon Technical Report N 92,

25163 (1992).

[51] M. S. Smith, L. H. Kawano and R. A. Malaney, Astro-

phys. J. Suppl. 85, 219 (1993).

[52] S. Sarkar, Rept. Prog. Phys. 59, 1493 (1996).

[53] R. H. Cyburt et al., Astrophys. J. Suppl. Ser. 189, 240

(2010).

[54] P. Descouvemont et al., At. Data Nucl. Data Tables 88,

203 (2004).

[55] S. Ando, R. H. Cyburt, S. W. Hong and C. H. Hyun,

Phys. Rev. C 74, 025809 (2006).

[56] R. H. Cyburt and B. Davids, Phys. Rev. C 78, 064614

(2008).

[57] A. P. Serebrov and A. K. Fomin, Phys. Rev. C 82, 035501

(2010).

[58] M. Pettini et al., Mon. Not. R. Astron. Soc. 391, 1499

(2008).

[59] T. M. Bania, R. T. Rood and D. S. Balser, Nature 415,

54 (2002).

[60] J. Geiss and G. Gloeckler, Space Sci. Rev. 84, 239 (1998).

[61] Y. I. Izotov and T. X. Thuan, Astrophys. J. 710, L67

(2010).

H.Tamand Q.Yang,

Page 5

5

[62] E. Aver, K. A. Olive and E. D. Skillman, JCAP 1005,

003 (2010).

[63] L. Sbordone et al., Astron. Astrophys. 522, A26 (2010).

[64] T. Shima et al., Phys. Rev. C 72, 044004 (2005).

[65] T. Kii, T. Shima, Y. Nagai and T. Baba, Nucl. Instrum.

Meth. A 552, 329 (2005).