Proc. Natl. Acad. Sci. USAVol. 90, pp. 4782-4788, June 1993Colloquium Paper

This paper was presented at a colloquium entitled "Physical Cosmology," organized by a committee chaired by DavidN. Schramm, held March 27 and 28, 1992, at the National Academy of Sciences, Irvine, CA.

Cosmological implications of light element abundances: TheoryDAVID N. SCHRAMMAstronomy and Astrophysics Centers 140, The University of Chicago, 5640 South Ellis Avenue, Chicago, IL 60637; and National Aeronautic and SpaceAdministration/Fermilab Astrophysics Center, Fermi National Accelerator Laboratory, Box 500, Batavia, IL 60510-0500

ABSTRACT Primordial nucleosynthesis provides (withthe microwave background radiation) one of the two quanti-tative experimental tests of the hot Big Bang cosmologicalmodel (versus alternative explanations for the observed Hubbleexpansion). The standard homogeneous-isotropic calculationfits the light element abundances ranging from 'H at 76% and4He at 24% by mass through 2H and 3He at parts in 105 downto 7Li at parts in 1010. It is also noted how the recent LargeElectron Positron Collider (and Stanford Linear Collider)results on the number of neutrinos (N,,) are a positive labora-tory test of this standard Big Bang scenario. The possiblealternate scenario ofquark-hadron-induced inhomogeneities isalso discussed. It is shown that when this alternative scenariois made to fit the observed abundances accurately, the resultingconclusions on the baryonic density relative to the criticaldensity (fQb) remain approximately the same as in the standardhomogeneous case, thus adding to the robustness of the stan-dard model and the conclusion that fQb 0.06. This latter pointis the driving force behind the need for nonbaryonic darkmatter (assuming total density fitt = 1) and the need for darkbaryonic matter, since the density of visible matter 1iksib1e <fQb. The recent Population II B and Be observations are alsodiscussed and shown to be a consequence of cosmic rayspallation processes rather than primordial nucleosynthesis.The light elements and N,, successfully probe the cosmologicalmodel at times as early as 1 sec and a temperature (1) of -1010K (-1 MeV). Thus, they provided the first quantitativearguments that led to the connections of cosmology to nuclearand particle physics.

Yacov Zeldovich (1) noted in material written just before hedied in 1987 that "the greatest success of the Big Bang theoryis the fact that the quantitative observation of the lightelement abundances agrees with the prediction of the theoryof nucleosynthesis." Such praise from Zeldovich is indeedpleasing, for the field and, hopefully, the recent develop-ments that will be described in this paper would not havedetracted from Zeldovich's views.

This paper will review the present status of primordialnucleosynthesis. After briefly reviewing the history, thispaper will make special emphasis of the remarkable agree-ment of the observed light element abundances with thecalculations upon which Zeldovich based his comments. Itshould be remembered that this agreement is one of the twoprime tests of the Big Bang itself (the other being themicrowave background) as the successful framework inwhich to place the observed Hubble expansion. The agree-ment of abundances and predictions works only if the baryondensity is well below the cosmological critical value. Thereview will also mention the nucleosynthesis prediction ofthe

The publication costs of this article were defrayed in part by page chargepayment. This article must therefore be hereby marked "advertisement"in accordance with 18 U.S.C. §1734 solely to indicate this fact.

number of neutrino families and its subsequent verificationby the Large Electron Positron Collider (LEP) and theStanford Linear Collider (SLC).Also discussed is the possibility that a first-order quark-

hadron phase transition could have produced variations fromthe standard homogeneous model. It will be shown thatcontrary to initial indications, first-order quark-hadron-inspired results are consistent with the homogeneous modelresults.

Finally, a discussion of the recent B and Be observationsin Population (Pop) II stars will be made. It will be shown thatall the Be and B observations, to date, are best explained bygalactic cosmic ray spallation (2) in Pop II environments andnot by any cosmological process.

This report will draw on two recent reviews (3 and 4) andin some ways is an update (20 years later) ofthe light elementsummary of ref. 5.

History of Big Bang Nucleosynthesis (BBN)

It should be noted that there is a symbiotic connectionbetween primordial nucleosynthesis (hereafter referred to asBBN) and the 3 K background dating back to Gamow and hisassociates Alpher and Herman. The initial BBN calculationsof Gamow's group (6) assumed pure neutrons as an initialcondition and thus were not particularly accurate, but theirinaccuracies had little effect on the group's predictions for abackground radiation.Once Hayashi (7) recognized the role of neutron-proton

equilibration, the framework for BBN calculations them-selves has not varied significantly. The work of Alpher et al.(8) and Hoyle and Taylor (9), preceding the discovery of the3 K background, and Peebles (10) and Wagoner et al. (11),immediately following the discovery, and the more recentwork of our group of collaborators (12-18) all do essentiallythe same basic calculation, the results of which are shown inFig. 1. As far as the calculation itself goes, solving thereaction network is relatively simple by using the numericalprocedures developed slightly earlier for explosive nucleo-synthesis calculations in supernovae (and nuclear weaponstests), with the calculational changes over the last 25 yearsbeing mainly in terms of more recent nuclear reaction ratesas input, not as any great calculational insight [although thecurrent Kawano code (18) is somewhat streamlined relativeto the earlier Wagoner code (11)]. With the possible excep-tion of 7Li yields (and possibly Be and B to be discussedlater), the reaction rate changes over the past 25 years havenot had any major affect. The one key improved input is abetter neutron lifetime determination (19).With the exception of the effects of elementary particle

assumptions to which we will return, the real excitement for

Abbreviations: BBN, Big Bang nucleosynthesis; HDM, hot darkmatter; CDM, cold dark matter; LEP, Large Electron PositronCollider; SLC, Stanford Linear Collider; Pop, population.

4782

Dow

nloa

ded

by g

uest

on

Janu

ary

11, 2

021

Proc. Natl. Acad. Sci. USA 90 (1993) 4783

-v 0.01 0.1 1.01.0

o i- j 4He(mass' 10

2| fraction)

Z 0.1 1. I 0 0

F 1. BH+rHe

3He

1-8 CONCORDANCE-"1

_j 160-

density (,q) for a homogeneous universe.

BBN over the last 25 years has not really been in redoing thebasic calculation. Instead, the true action is focused onunderstanding the evolution of the light element abundancesand using that information to make powerful conclusions. Inthe 1960s, the main focus was on 4He, which is very insen-sitive to the baryon density. The agreement between BBNpredictions and observations helped support the basic BigBang model but gave no significant information, at that time,with regard to density. In fact, in the mid-1960s, the otherlight isotopes (which are, in principle, capable of givingdensity information) were generally assumed to have beenmade by spallation processes during the T-Tauri phase ofstellar evolution (20) and so were not then taken to havecosmological significance. It was during the 1970s that BBNfully developed as a tool for probing the universe. Thispossibility was in part stimulated by Ryter et al. (21) whoshowed that the T-Tauri mechanism for light element syn-thesis failed. Furthermore, 2H abundance determinationsimproved significantly with solar wind measurements and theinterstellar work from the Copernicus satellite (22-24).Reeves et al. (5) argued for a purely cosmological origin for2H and were able to place a constraint on the baryon densityexcluding a universe closed with baryons. Subsequently, the2H arguments were cemented when Epstein et al. (25) provedthat because of the remarkably low nuclear binding energyper nucleon of 2H, no realistic astrophysical process otherthan the Big Bang could produce significant 2H. It was alsointeresting that the baryon density thus implied by BBN wasin good agreement with the density implied by the darkgalactic halos (26).By the late 1970s, a complimentary argument to 2H had also

developed using 3He. In particular, it was argued (27) that,unlike 2H, 3He was made in stars; thus, its abundance wouldincrease with time. Since 3He like 2H monotonically de-creased with cosmological baryon density, this argumentcould be used to place a lower limit on the baryon density (28)by using 3He measurements from solar wind (21) or inter-stellar determinations (29). Since the bulk of the 2H wasconverted in stars to 3He, the constraint was shown to bequite restrictive (15). Not only has this basic picture remainedintact now for almost 20 years, but as we shall see, theconfidence level in the argument has increased dramaticallywith time.For example, it was interesting that the lower boundary

from 3He and the upper boundary from 2H yielded therequirement that 7Li be near its minimum of 7Li/H ---10-10,wichL1 was, veife +bythe Pop II L m e of Spiteand Spite (ref. 30; see also refs. 31 and 32), hence yielding the

situation emphasized by Yang et al. (15) that the light elementabundances are consistent over 9 orders of magnitude withBBN, but only if the cosmological baryon density is con-strained to be around 5% of the critical value.The other development of the 1970s for BBN was the

explicit calculation of Steigman (33) showing that the numberof neutrino generations, NV, had to be small to avoid over-production of 4He. [Earlier independent work (9, 34, 35) hadcommented about a dependence on the energy density ofexotic particles but had not done explicit calculations probingNv] This will subsequently be referred to as the Steigman,Schramm, and Gunn (SSG) limit. To put this in perspective,one should remember that the mid-1970s also saw the dis-covery of charm, bottom, and tau, so that it almost seemedas if each new detector produced new particle discoveries,and yet, cosmology was arguing against this "conventional"wisdom. Over the years, the SSG limit on NV improved with4He abundance measurements, neutron lifetime measure-ments, and limits on the lower bound to the baryon density,hovering at NV, : 4 for most of the 1980s and dropping tobelow 4 (but not excluding 3) just before LEP and SLC turnedon (16, 17, 36, 37). The recent verification of this cosmolog-ical prediction by the LEP and SLC results (79), where N,, =2.99 ± 0.05, is the first verification of a cosmological pre-diction by a high-energy collider. Thus, in some sense LEP(and SLC) have checked the Big Bang model at temperaturesof -101" K and times of -1 sec.The power of homogeneous BBN comes from the fact that

essentially all of the physics input is well determined in theterrestrial laboratory. The appropriate temperature regimes,0.1-1 MeV, are well explored in nuclear physics laboratories.Thus, what nuclei do under such conditions is not a matter ofguesswork but is precisely known. In fact, it is known forthese temperatures far better than it is for the centers of starslike our sun. The center of the sun is only a little over 1 keV,thus, below the energy where nuclear reaction rates yieldsignificant results in laboratory experiments, and only thelong times and higher densities available in stars enableanything to take place.To calculate what happens in the Big Bang, all one has to

do is follow what a gas of baryons with density Pb does as theuniverse expands and cools. As far as nuclear reactions areconcerned, the only relevant region is from a little above 1MeV (-1010 K) down to a little below 100 keV (=109 K). Athigher temperatures, no complex nuclei other than free singleneutron and protons can exist, and the ratio of neutrons toprotons (nip) is just determined by n/p = eQ/T, where Q =(m" - mp)c2 1.3 MeV, where m. is the mass of the neutron,mp is the mass of the proton, and c is the speed of light.Equilibrium applies because the weak interaction rates aremuch faster than the expansion of the universe at tempera-tures much above 1010 K. At temperatures much below 109 K,the electrostatic repulsion of nuclei prevents nuclear reac-tions from proceeding as fast as the cosmological expansionseparates the particles.

After the weak interaction drops out of equilibrium, a little>1010 K, the ratio of neutrons to protons changes moreslowly due to free neutrons decaying to protons, and similartransformations of neutrons to protons via interactions withthe ambient leptons. By the time the universe reaches 109 K(0.1 MeV), the ratio is slightly <1/7. For temperatures >109K, no significant abundance of complex nuclei can exist dueto the continued existence of y-rays with energies >1 MeV.Note that the high photon to baryon ratio in the universe(=101") enables significant population of the mega electronvolt high-energy Boltzman tail until T S 0.1 MeV.Once the temperature drops to 109 K, sufficient abun-

dances of nuclei can exist in statistical equilibrium throughreactions such as n + p + 2H + 'y, where y is a y-ray and 2H+ p ++ 3He + -y and 2H + n <-+ 3H + y, which in turn react

Colloquium Paper: Schramm

Dow

nloa

ded

by g

uest

on

Janu

ary

11, 2

021

4784 Colloquium Paper: Schramm

to yield 4He. Since 4He is the most tightly bound nucleus inthe region, the flow of reactions converts almost all theneutrons that exist at 109 K into 4He. The flow essentiallystops there because there are no stable nuclei at either mass-5or mass-8. Since the baryon density at BBN is relatively low(-10% the density of terrestrial air) and the time scale is short(t 5 102 sec), only reactions involving two-particle collisionsoccur. It can be seen that combining the most abundantnuclei, protons and 4He, via two-body interactions alwaysleads to unstable mass-5. Even when one combines 4He withrarer nuclei like 3H or 3He, we still get only to mass-7, whichwhen hit by a proton, the most abundant nucleus around,yields mass-8. (As we will discuss, a loophole around themass-8 gap can sometimes be found if nlp > 1, so that excessneutrons exist; but for the standard case, n/p < 1.) Eventu-ally, 3H decays radioactively to 3He, and any mass-7 maderadioactively decays to 7Li. Thus, BBN makes 4He withtraces of 2H, 3He, and 7Li. (Also, all the protons left over thatdid not capture neutrons remain as hydrogen.) For standardhomogeneous BBN, all other chemical elements are madelater in stars and in related processes. (Starsjump the mass-5and -8 instability by having gravity compress the matter tosufficient densities and have much longer times available sothat three-body collisions can occur, 3 4He -+ 12C + y.)

Inhomogeneous BBN

As noted above, BBN yields all agree with observations usingonly one freely adjustable parameter, 71, or equivalently, p,.Thus, BBN can make strong statements regarding Pb if theobserved light element abundances cannot be fit with anyalternative theory. The most significant alternative that hasbeen discussed involves quark-hadron-transition-inspired in-homogeneities (38-40). While inhomogeneity models hadbeen looked at previously (see ref. 15) and were found tomake little difference, the quark-hadron-inspired models hadthe added ingredient of variations in n/p ratios. Cosmologistsare well aware that current trends in lattice gauge calculationsimply that the transition is probably second order or not aphase transition at all. Nevertheless, it has been important toexplore the maximal cosmological impact that can occur.This maximal impact requires a first-order phase transition.The initial claim by Applegate and coworkers (38), fol-

lowed by a similar argument from Alcock et al. (39), that Qb1 might be possible, created tremendous interest. Their

argument was that if the quark-hadron transition was afirst-order phase transition, then it was possible that largeinhomogeneities could develop at T - 100 MeV. The pref-erential diffusion of neutrons versus protons out of thehigh-density regions could lead to BBN occurring underconditions with both density inhomogeneities and variablen/p ratios. In the first round of calculations, it was claimedthat such conditions might allowQb 1, while fitting theobserved primordial abundances of 4He, 2H, and 3He with anoverproduction of 7Li. Since 7Li is the most recent of thecosmological abundance constraints and has a different ob-served abundance in Pop I stars versus the traditionally moreprimitive Pop II stars (30-32), some argued (39) that perhapssome special depletion process might be going on to reducethe excess 7Li.At first it appeared that if the Li constraint could be

surmounted, then the constraints of standard BBN mightdisintegrate. To further stimulate the flow through the loop-hole, Fowler and Malaney (40) showed that, in addition tolooking at the diffusion of neutrons out of high-densityregions, one must also look at the subsequent effect of excessneutrons diffusing back into the high-density regions as thenucleosynthesis goes to completion in the low-density re-gions. (The initial calculations treated the two regions sepa-rately.) Fowler and Malaney (40) argued that for certain

phase-transition parameter values (e.g., nucleation site sep-arations are -10 m at the time of the transition), this backdiffusion could destroy much of the excess Li.However, Kurki-Suonio et al. (41), the Tokyo group (43),

and the Livermore group (44) have eventually argued that, intheir detailed diffusion models, the back diffusion affects notonly 7Li but also the other light nuclei. They find that for Q1b

1, 4He is also significantly overproduced (although it doesgo to a minimum for similar parameter values as does the Li).One can understand why these models might tend to over-produce 4He and 7Li by remembering that in standard ho-mogeneous BBN, high baryon densities lead to excesses inthese nuclei. As back diffusion evens out the effects of theinitial fluctuation, the averaged result should approach thehomogeneous value. Furthermore, it can be argued that anynarrow range of parameters, such as those that yield rela-tively low Li and He, are unrealistic since in most realisticphase transitions there are distributions of parameter values(distribution of nucleation sites, separations, density fluctu-ations, etc.). Therefore, narrow minima are washed out thatwould bring the 7Li and 4He values back up to their excessivelevels for all parameter values with fQ 1. Furthermore,Freese and Adams (45) and G. Baym (personal communica-tion) have argued that the boundary between the two phasesmay be fractal-like rather than smooth. The large surface areaof a fractal-like boundary would allow more interactionbetween the regions and minimize exotic effects.

Fig. 2 shows the updated results of Kurki-Suonio et al. (41)for nucleation spacing 1 with the constraints from the differentlight element abundances. Notice that the Li, 2H, and eventhe 4He constraint do not allow Qb 1. Note also that, withthe Pop II 7Li constraint, the results for flb are quite similarto the standard model with a slight excess in fQb possible if 1is tuned to -10. Thus, even an optimally tuned first-orderquark-hadron transition is not able to alter the basic conclu-sions of homogeneous BBN regarding Qb. (It also cannotsignificantly change the N, argument.) Furthermore, it ap-pears that optimally tuned quark-hadron-inspired models arenot even able (46) to significantly lower the minimal 4He massfraction compatible with 3He, 2H, and N, = 3; such models,even relaxing the 7Li bound, never have concordance with Ybelow 0.23. In fact, the main role that a quark-hadron optionhas played forBBN is to show how robust the standard modelresults are.

Boron, Beryllium, and the Spallation Process

While quark-hadron-inspired variations have not been ableto alter the basic conclusions of BBN, an important question

1000

2H+3He "He Li H"He

100 2

E

7Li,,:10

2H 7Li,1 10 100

Xx 1010

FIG. 2. Updated results of Kurki-Suonio et al. (41) showing thateven allowing for a first-order quark-hadron transition with nucle-ation site spacing I optimized for maximal effect, the light elementabundances constrain the baryon-to-photon ratio (il) and thus Qb toessentially the same values as those obtained in the homogeneouscase with only slightly large QIb values possible with 1 10.

Proc. Natl. Acad. Sci. USA 90 (1993)

Dow

nloa

ded

by g

uest

on

Janu

ary

11, 2

021

Proc. Natl. Acad. Sci. USA 90 (1993) 4785

remains; namely, is there an observable signature that coulddifferentiate quark-hadron-inspired variations from the ho-mogeneous model? On the theoretical side, this point hasbeen debatable. Several authors have argued (41, 47, 48) thatbecause of the high n/p region in the inhomogeneous models,leakage beyond the mass-5 and -8 instability gaps can occur,and traces of 9Be, '0B, 11B, and maybe even r-processelements can be produced. Thus, detection of nuclei beyond7Li in primitive objects may be a signature. However, Satoand Tarasawa (43) have argued that such leakage is negligi-ble. Because of this debate as well as the recent experimentalresults (49-52), we have started theoretically examining thisquestion ourselves. However, before discussing our results,let me first comment on some recent observations of Be andB in primitive Pop II stars.

In particular, there has been much recent attention given toreports (49-51) of Be lines being observed in extreme Pop IIstars. For one very metal poor Pop II star, HD140283, B wasalso observed (52). The observations yielded

Be/H -10-130.3, [1]

which represents a combination of the two Be/H measure-ments with Gilmore et al. (49) obtaining a factor of -3 higherBe/H than Ryan et al. (50). The B was measured using theHubble Space Telescope where a value was obtained (52) of

B/H lo-12±0.1 [2]

The resulting B/Be ratio is

B/Be 10 + 5. [3]

This particular star has its Fe abundance depleted relative tothe standard Pop I (present galactic disk) Fe abundance by afactor of _10-2.6, and its 0 is depleted relative to Pop I by-10-2-1. The high O/Fe ratio in extreme Pop II stars is wellunderstood (53) as due to heavy-element production in mas-sive Type II supernova producing a high O/Fe ratio, whereaslater Pop I abundances also get a significant admixture oflow-mass slow-to-explode Type I supernova ejecta where Feis dominant over 0. Because 0 is chiefly made in Type IIsupernova, whereas Fe has at least two significant sources,we feel it is mandatory to use 0 as a measure of the Type IIsupernova contribution to such stars. In this regard, it isimportant to note that the Be/O ratio for these stars is, withinexperimental errors, the same as Be/O ratio for those highsurface temperature Pop I stars whose convective zones arenot deep enough to destroy their original Be. Thus, contraryto some initial claims, the Be/H observation does not requirecosmological origin, only a scaling with 0 of the same processthat produced Be in the Pop I stars.The presumed process that produced Be and B in Pop I

stars (as well as the 6Li) is thought to be cosmic ray spallation(2, 5). For Be and B, such spallation comes from the breakupof heavy nuclei such as C, N, 0, Ne, Mg, Si, S, Ca, and Feby protons and a-particles. As noted by Epstein et al. (54, 55)for Li one must also include a-a fusion processes as well.This latter point was well noted by Steigman and Walker (56)who emphasized that Be and B spallation production on PopII abundances would imply a significant enhancement of Lifrom a-a relative to the reduced production ofBe and B fromdepleted heavy nuclei. While the 6Li so produced would bedestroyed at the base of the convective zones in the starsobserved (57, 58), the 7Li would survive and might result inobservable effects in the Spite (30, 31) Pop II lithium plateau(59). However, Olive and Schramm (59) have shown thatcorrecting for the Li produced along with the Be and B doesnot in any way detract from the Spite plateau but reduces the

x2 value of the 7Li cosmological solution and makes stellardepletion models even less likely.

Perhaps most critical to any spallation origin is the result-ant B/Be ratio. It is also known, from actual measurements,that the cosmic rays themselves (60) show B/Be 14 (and Band Be are pure spallation products in the cosmic rays) witha C/O ratio exceeding unity (Pop I has C/O G 0.5). Sincespallation offC favors B relative to Be (mass-11 requires onlya single nucleon ejected from mass-12), whereas 0 beingfarther from either shows less favoritism, the cosmic rayobservations are actually an upper limit on what B/Be ratioone might expect in Pop I cosmic rays. However, of moreconcern here is the lower limit on B/Be achievable by aspallation process (61). Note that cosmic ray spectra that areflatter than E-2-6 (where E is energy) will be less favorabletoward B production. This is because the "B productionthreshold is below that for 9Be. Thus, steeper spectra favorB relative to Be, whereas flatter spectra remove the role ofthe threshold effects and yield relatively higher Be. Further-more, Pop II composition has a lower C/O ratio than doesPop I. Like Fe, C is not a pure Type II supernova product.Spallation on pure Type II ejecta would have targets of 0,Ne, Mg, Si, etc., but less C and N than Pop I. Recent y-RayObservatory (GRO/EGRET) -ray results show extragalac-tic high-energy spectra with -E-20. Thus, flat spectra maybe quite reasonable.

Spallation calculations for flat spectra on Pop II materialhave been carried out (4, 61). The cross sections we used forthe spallation calculations are a combination of all measuredcross-section data (62) and our semiempirical estimates (4,61, 64, 65). The resultant ratio is

B/Be ; 7.6. [4]

The initially reported B/Be ratio for HD140283 was belowthis limit, which at first looked awkward for the spallationmodel, but revised data analysis by the observers (52) nowyields a ratio quite consistant with the model. (Of course, thecorrelation of Be and B with metalicity showed that Be andB in Pop II stars were not of cosmological origin, but noalternative to spallation has yet been developed.)

It is important to note that if spallation processes do indeedproduce the observed Be and B in Pop II stars, then thecosmic ray flux is probably stronger than it is in the presentGalaxy. Remember that the present Pop I abundance of Beand B and 6Li can be explained by the present cosmic ray fluxhitting the Pop I C, N, and 0 abundances (2, 5) integratedover the lifetime of the Galactic disk prior to the formation ofthe observed stars. However, for these Pop II stars, the C, N,0, and heavier element abundances are down and the starspresumably formed relatively early, before the disk formed.While some Galactic evolution models (66, 67) expect thispredisk formation epoch to be several gigayears long, it isnonetheless shorter than the age of the disk. If the predisktime is merely the massive star stellar evolution time scale,then it can be very short. The shorter time scale thus requiresa consummately higher flux if the ratios to 0 observed in PopI are to be retained in the Pop II objects. Of course, manygalactic evolution models (66, 67) predict higher early super-nova rates that produce just such a higher cosmic ray flux, soconsistent models do exist.From the above, at present, there is no cause to invoke

anything other than spallation; however, if objects are ob-served with decreasing O/H ratios, but Be/O and B/O ratiosare found not to keep falling, then one would have toconclude that there is primordial cosmological production ofBe and B.

Fig. 3 shows the trace element yields in a standard homo-geneous BBN calculation, with Fig. 3A showing 2H, 3He, 6Li,and 7Li yields and Fig. 3B showing the 9Be, '0B, and "1B

Colloquium Paper: Schramm

Dow

nloa

ded

by g

uest

on

Janu

ary

11, 2

021

4786 Colloquium Paper: Schramm

A

X0c0

B

0)~~~~00

°-20

-25 .,,,,.... ,,,.. l10.01 0.1 1 10 100 1000

1110FIG. 3. (A) Standard homogeneous BBN yields showing 2H, 3He,

6Li, and 7Li for six orders of magnitude in nb/71y. Note that 6Li isalways negligible relative to 7Li. X, abundance. (B) Standard homo-geneous BBN yields for 9Be, '0B, and "B. The various curves for 9Beand '0B represent different cross-section assumptions. The "B yieldis double-humped due to production both directly as "B and also as"1C, which p-decays to "B.

yields. This work is part of an extensive study ofA . 6 BBNby Thomas et al. (68) (where A is the atomic mass number),using a more extensive reaction network than previouslyused. Note, in particular, that 9Be/H yields are always<10-14 regardless of Tq = nb/nly. Also note that, for thestandard model that is concordant with the other light ele-ments, i- 3 x 10-10, Be/H and B/H ratios are -10-18. Inother words, homogeneous BBN cannot yield a Be/H ratioconsistent with the Pop II stellar observations. To explorepreliminarily the alternative of inhomogeneous models, wehave taken our extensive network and looked at high n/pratios. For regions with n/p> 3, we can obtain Be/H 10-14but no more for parameter values that still fit the A < 7abundances. However, any realistic model will have a sig-nificant dilution of this material with low n/p regions. Thus,we tentatively view the achievement of such values assomewhat problematic, as do Sato and Tarasawa (44). Wewill continue to explore a full inhomogeneous model, whichincludes regions ofextremely high n/p, to see how robust anyleakage to A > 7 truly is. Such an exploration is justbeginning.

Ifsome Be and B can be shown to be cosmological, it wouldhave great implications for BBN. If simple inhomogeneitiesare unable to produce it, then more exotic ones will be

required. The source of such inhomogeneities would have tobe either the quark-hadron transition or some other activityaround that same cosmological epoch (no earlier than theelectroweak transition) so that density variations are re-tained. Of course, whatever these variations might be, theymust not alter the spectacular agreement for A c 7 abun-dances and for N,.

Limits on ib and Dark Matter Requirements

The success and robustness ofBBN in the face of the Be andB results as well as the quark-hadron variations give renewedconfidence to the limits on the baryon density constraints.Let us convert this density regime into units of the criticalcosmological density for the allowed range of Hubble expan-sion rates. For the BBN constraints (16, 42), the dimension-less baryon density flb, that fraction of the critical densitythat is in baryons, is <0.11 and >0.02 for 0.4 s ho 5 0.7,where ho is the Hubble constant in units of 100 km per sec perMpc [1 parsec (pc) = 30.9 x 1016 m]. The lower bound on hocomes from direct observational limits and the upper boundfrom age of the universe constraints (69). The constraint onflb still means that the universe cannot be closed withbaryonic matter. [This point was made 20 years ago (5) andhas proven to be remarkably strong.] If the universe is trulyat its critical density, then nonbaryonic matter is required.This argument has led to one of the major areas of researchat the particle-cosmology interface, namely, the search fornonbaryonic dark matter.Another important conclusion regarding the allowed range

in baryon density is that it is in very good agreement with thedensity implied from the dynamics ofgalaxies, including theirdark halos. An early version of this argument, using only 2H,was described >15 years ago (26). As time has gone on, theargument has strengthened, and the fact remains that galaxydynamics and nucleosynthesis agree at =5% of the criticaldensity. Thus, if the universe is indeed at its critical density,as many of us believe, it requires most matter not to beassociated with galaxies and their halos and to be nonbary-onic. Let us put the nucleosynthetic arguments in context.The arguments requiring some sort of dark matter fall into

separate and quite distinct areas. These arguments are sum-marized in Fig. 4. First are the arguments using Newtonianmechanics (and stellar observations) applied to various as-tronomical systems that show that there is more matterpresent than the amount that is shining. It should be notedthat these arguments reliably demonstrate that galactic halosseem to have a mass =10 times the visible mass.Note however that BBN requires that the bulk of the

baryons in the universe be dark since the density of visible

IRAS/GA1.0F

10-1

10-21

ICLUSTER

_fa -e

SIBEHALO

VISIBLE

10-31 0.0.001 0.01 0.1 1 10 100

rh5O, Mpc

FIG. 4. Implied densities versus the scale of the measurements.IRAS/GA, infrared astronomical satellite/Great Attractor; Mpc,megaparsec r, distance scale; h50, Hubble constant in units of 50 kmper sec per Mpc.

Proc. NatL Acad. Sci. USA 90 (1993)

.L

Dow

nloa

ded

by g

uest

on

Janu

ary

11, 2

021

Proc. Natl. Acad. Sci. USA 90 (1993) 4787

matter (fij) << fQb. Thus, the dark halos could in principlebe baryonic (26). Recently arguments on very large scales(70) (bigger than clusters of galaxies) from the velocity flowsobserved in the infrared astronomical satellite catalogue andin the Great Attractor hint that fl on those scales is indeedgreater than flb, thus forcing us to need nonbaryonic matter.An fl of unity is, of course, preferred on theoretical

grounds since, as noted by cosmologists in the 1930s, that isthe only long-lived natural value for what we now call Q andmost of us feel that inflation (71, 72) or something like itprovided the early universe with the mechanism to achievethat value and thereby solve the flatness and smoothnessproblems. (Note that our need for exotica is not dependent onthe existence of dark galactic halos. This point is frequentlyforgotten, not only by some members of the popular press butoccasionally by active workers in the field.)Some baryonic dark matter must exist since we know that

the lower bound from BBN is greater than the upper limits onthe amount of visible matter in the universe. However, we donot know the form of this baryonic dark matter. It could beeither in condensed objects in the halo, such as brown dwarfsand jupiters [objects with ;0.08 the mass of the Sun (M D) sothey are not bright shining stars] or in black holes (which atthe time of nucleosynthesis would have been baryons). Or, ifthe baryonic dark matter is not in the halo, it could be in hotintergalactic gas, hot enough not to show absorption lines inthe Gunn-Peterson test, but not so hot as to be seen in thex-rays. Evidence for some hot gas is found in clusters ofgalaxies. However, the amount of gas in clusters would notbe enough to make up the entire missing baryonic matter.Another possible hiding place for the dark baryons would befailed galaxies, large clumps of baryons that condense grav-itationally but did not produce stars. Such clumps are pre-dicted in galaxy formation scenarios that include largeamounts of biasing where only some fraction of the clumpsshine.Hegyi and Olive (73) have argued that dark baryonic halos

are unlikely. However, they do allow for the loopholesmentioned above of low-mass objects or of massive blackholes. It is worth noting that these loopholes are not thatunlikely. If we look at the initial mass function for starsforming with Pop I composition, we know that the massfunction falls off roughly like the Salpeter power law forstandard size stars. Or, even if we apply the Miller-Scalomass function, the falloff is only a little steeper. In both casesthere seems to be some sort of lower cut-off near 0.1 Mo.However, we do not know the origin of this mass function andits shape. No true star formation model based on fundamentalphysics predicts it.We do believe that whatever is the origin of this mass

function, it is probably related to the metalicity ofthe material,since metalicity affects cooling rates, etc. It is not unreason-able to expect the initial mass function that was present in theprimordial material that had no heavy elements (only theproducts of BBN) would be peaked either much higher thanthe present mass function or much lower-higher if the lowercooling from low metals resulted in larger clumps or lower ifsome sort of rapid cooling processes ("cooling flows") wereset up during the initial star formation epoch, as seems to bethe case in some primative galaxies. In either case, movingeither higher or lower produces the bulk of the stellar popu-lation in brown dwarfs and jupiters or in massive black holes.Thus, the most likely scenarios are that a first generation ofcondensed objects would be in a form of dark baryonic matterthat could make up the halos and could explain why there isan interesting coincidence between the implied mass in halosand the implied amount of baryonic material. However, itshould also be remembered that a consequence ofthis scenariois to have the condensation of the objects occur prior to theformation of the disk. If the first large objects to form are less

than galactic mass, as many scenarios imply, then mergers arenecessary for eventual galaxy size objects. Mergers stimulatestarformation while putting early objects into halos rather thandisks. Mathews and Schramm (66, 67) have recently devel-oped a galactic evolution model that does just that and givesa reasonable scenario for chemical evolution. Thus, whilemaking halos out of exotic material may be more exciting, itis certainly not impossible for the halos to be in the form ofdark baryons. The new microlensing projects by groups inFrance, the United States, Australia, and Poland shouldeventually test this possibility.Nonbaryonic matter can be divided following Bond and

Szalay (74) into two major categories for cosmological pur-poses: hot dark matter (HDM) and cold dark matter (CDM).HDM is matter that is relativistic until just before the epochof galaxy formation, the best example being low-mass neu-trinos with a mass mi,- 25 eV. [Remember ,, -- m,(eV)/100hQ.] CDM is matter that is moving slowly at theepoch ofgalaxy formation. Because it is moving slowly, it canclump on very small scales, whereas HDM tends to havemore difficulty in being confined on small scales. ExamplesofCDM could be the lightest supersymmetric particle, whichis presumed to be stable and might have a mass ofseveral tensofgigaelectron volts or even a teraelectron volt. According toMichael Turner (personal communication), any such weaklyinteracting massive particle is called a "WIMP." Axions,while very light, would also be moving very slowly (75) and,thus, would clump on small scales. Or, one could also go tononelementary particle candidates, such as planetary massblackholes or quark nuggets of strange quark matter, possiblyproduced at the quark-hadron transition (76, 77). Anotherpossibility would be any sort of massive topological remnantleft over from some early phase transition. Note that CDMwould clump in halos, thus requiring the dark baryonic matterto be out between galaxies, whereas HDM would allowbaryonic halos.While the recent (and very impressive) Cosmic Back-

ground Explorer (COBE) large-scale anisotropy results (78)are consistent with a Harrison-Zeldovich gaussian fluctua-tion spectrum, the small scale (:3O) results that correspondto observed galaxy structures have not been measured yet.The actual galaxy observations seem to require more power(and/or nongaussian behavior), on the scale of 2 to 3°, thana flat Harrison-Zeldovich spectrum can deliver. Since HDMdoes not work well with a Harrison-Zeldovich gaussianspectrum butCDM does, it is still too early to ascertain whichis correct (or maybe a mixture of both is needed). In partic-ular, remember that a nongaussian model or a mixed modelcan work with HDM, which becomes particularly attractiveif recent hints from the gallium experiments require thesolution to the solar neutrino problem to have neutrinomixing with ve - v,, mass scales of '10-3 eV, making electronvolt mass scales for vT quite plausible in those see-saw typemodels where m,,: mM(mt0/mtop/Mchm) (2).

Conclusion

Primordial nucleosynthesis has indeed become one of thecornerstones ofmodern cosmology. Ifanything, the situationis even more compelling since Yacov Zeldovich's marvelousquote (1). As with any good physical theory, the model is bothpredictive and falsifiable. For example, if the 4He massfraction were found to be <23% (without altering the 3He and2H bound) or if Be or B were truly shown to be primordial,there would be difficulties. At present, no such difficulties areestablished.

I thank my recent collaborators, Brian Fields, George Fuller,Rocky Kolb, Grant Mathews, Keith Olive, Gary Steigman, DavidThomas, Jim Truran, Michael Turner, and Terry Walker for many

Colloquium Paper: Schramm

Dow

nloa

ded

by g

uest

on

Janu

ary

11, 2

021

4788 Colloquium Paper: Schramm

useful discussions. I further thank Doug Duncan, Lew Hobbs, andDon York, for valuable discussion regarding the Be and B observa-tions. This work was supported in part by National Science Foun-dation Grant AST 90-22629, by National Aeronautics and SpaceAdministration (NASA) Grant NAGW-1321, and by Department ofEnergy (DOE) Grant DE-FG02-91-ER40606 at the University ofChicago, and by the DOE and NASA Grant NAGW-2381 at theNASA/Fermilab Astrophysics Center.

1. Zeldovich, Y. B. (1992) My Universe (Harwood, Reading,U.K.).

2. Reeves, H., Fowler, W. & Hoyle, F. (1970) Nature (London)226, 727-729.

3. Schramm, D. N. (1991) Phys. Scr. T36, 22-29.4. Schramm, D. N., Fields, B. & Thomas, D. (1992) Nucl. Phys.

A 544, 267c-278c.5. Reeves, H., Audouze, J., Fowler, W. A. & Schramm, D. N.

(1973) Astrophys. J. 179, 909-930.6. Alpher, R. A., Bethe, H. & Gamow, G. (1948) Phys. Rev. 73,

803-813.7. Hayashi, C. (1950) Prog. Theor. Phys. 5, 224-235.8. Alpher, R. A., Follin, J. W.& Herman, R. C. (1953) Phys. Rev.

92, 1347-1361.9. Hoyle, F. & Taylor, R. (1964) Nature (London) 203,1108-1110.

10. Peebles, P. J. E. (1966) Phys. Rev. Lett. 16, 410-413.11. Wagoner, R., Fowler, W. A. & Hoyle, F. (1967) Astrophys. J.

148, 3-36.12. Schramm, D. N. & Wagoner, R. V. (1977) Annu. Rev. Nucl.

Sci. 27, 37-74.13. Olive, K., Schramm, D. N., Steigman, G., Turner, M. & Yang,

J. (1981) Astrophys. J. 246, 557-568.14. Boesgaard, A. & Steigman, G. (1985) Annu. Rev. Astron.

Astrophys. 23, 319-378.15. Yang, J., Turner, M., Steigman, G., Schramm, D. N. & Olive,

K. (1984) Astrophys. J. 281, 493-511.16. Olive, K., Schramm, D. N., Steigman, G. & Walker, T. (1990)

Phys. Lett. B 236, 454-460.17. Walker, T., Steigman, G., Schramm, D. N., Olive, K. & Kang,

H.-S. (1991) Astrophys. J. 376, 51-69.18. Kawano, L., Schramm, D. N. & Steigman, G. (1988) Astro-

phys. J. 327, 750-754.19. Mampe, W., Ageron, P., Bates, C., Pendlebury, J. M. &

Steyerl, A. (1989) Phys. Rev. Lett. 63, 593-596.20. Fowler, W., Greenstein, J. & Hoyle, F. (1962) Geophys. J. R.

Astron. Soc. 6, 148-220.21. Ryter, C., Reeves, H., Gradstajn, E. & Audouze, J. (1970)

Astron. Astrophys. 8, 389-397.22. Geiss, J. & Reeves, H. (1972) Astron. Astrophys. 18, 126-132.23. Black, D. (1971) Nature (London) 234, 148-149.24. Rogerson, J. & York, D. (1973) Astrophys. J. Lett. 186,

L95-L98.25. Epstein, R., Lattimer, J. & Schramm, D. N. (1976) Nature

(London) 263, 198-202.26. Gott, J. R., III, Gunn, J., Schramm, D. N. & Tinsley, B. M.

(1974) Astrophys. J. 194, 543-553.27. Rood, R. T., Steigman, G. & Tinsley, B. M. (1976) Astrophys.

J. Lett. 207, L57-L60.28. Yang, J., Schramm, D. N., Steigman, G. & Rood, R. T. (1979)

Astrophys. J. 227, 697-704.29. Wilson, T., Rood, R. T. & Bania, T. M. (1983) in Proceedings

of the ESO Workshop on Primordial Healing, eds. Shaver, P.,Kunth, D. & Kjar, K. (Eur. Southern Observatory, Garching,F.R.G.), pp. 379-384.

30. Spite, F. & Spite, M. (1982) Astron. Astrophys. 115, 357-366.31. Rebolo, R., Molaro, P. & Beckman, J. (1988) Astron. Astro-

phys. 192, 192-205.32. Hobbs, L. & Pilachowski, C. (1988) Astrophys. J. Lett. 326,

L23-L26.33. Steigman, G., Schramm, D. N. & Gunn, J. (1977) Phys. Lett.

B 66, 202-204.34. Schvartzman, V. F. (1969) JETP Lett. 9, 184-186.35. Peebles, P. J. E. (1971) Physical Cosmology (Princeton Univ.

Press, Princeton, NJ).36. Schramm, D. N. & Kawano, L. (1989) Nucl. Instrum. Methods

Phys. Res. A 284, 84-88.37. Pagel, B. (1987) in Starburst and Galaxy Evolutions, eds.

Thuan, T. X., Montmerle, T. & Van, J. T. T. (Editions Fron-tieres, Paris), 227-232.

38.

39.

40.41.

42.

43.

44.

45.46.

47.

48.49.

50.

51.

52.

53.

54.

55.

56.

57.

58.

59.

60.61.

62.63.

64.

65.66.

67.

68.

69.

70.71.72.

73.74.75.

76.

77.

78.79.

Scherrer, R., Applegate, J. & Hogan, C. (1987) Phys. Rev. D 35,1151-1160.Alcock, C., Fuller, G. & Mathews, G. (1987) Astrophys. J. 320,439-447.Fowler, W. A. & Malaney, R. (1988) Astrophys. J. 333, 14-20.Kurki-Suonio, H., Matzner, R., Olive, K. & Schramm, D. N.(1990) Astrophys. J. 353, 406-410.Applegate, J., Hogan, C. & Scherrer, R. (1988) Astrophys. J.329, 572-579.Sato, K. & Tarasawa, N. (1991) in The Birth and EarlyEvolution of Our Universe: Proceedings ofNobel Symposium79, eds. Nilsson, J. S., Gustafson, B. & Skagerstam, B. S.(World Scientific, Singapore), p. 60.Mathews, G., Meyer, B., Alcock, C. & Fuller, G. (1991)Astrophys. J. 358, 36-46.Freese, K. & Adams, F. (1990) Phys. Rev. D. 41, 2449-2461.Mathews, G., Schramm, D. N. & Meyer, B. (1993) Astrophys.J., in press.Kawano, L., Fowler, W. & Malaney, R. (1991) Astrophys. J.372, 1-7.Boyd, R. & Kajino, T. (1990) Astrophys. J. 359, 267-276.Gilmore, G., Edvardson, B. & Nissen, P. (1991) Astrophys. J.378, 17-21.Ryan, S., Bessel, M., Sutherland, R. & Norris, J. (1990)Astrophys. J. Lett. 348, L57-L60.Ryan, S. G., Norris, J. E., Bessell, M. S. & Deliyannis, C. P.(1992) Astrophys. J. 388, 184-189.Duncan, D., Lambert, D. & Lemke, D. (1992) Astrophys. J.,401, 584-595.Wheeler, J. C., Sneden, C. & Truran, J. (1989) Annu. Rev.Astron. Astrophys. 27, 279-349.Epstein, R., Arnett, W. D. & Schramm, D. N. (1974) Astro-phys. J. Lett. 190, L13-L16.Epstein, R., Arnett, W. D. & Schramm, D. N. (1976) Astro-phys. J. Suppl. 31, 111-141.Steigman, G. & Walker, T. (1992) Astrophys. J. Lett. 385,L13-L16.Brown, L. & Schramm, D. N. (1988) Astrophys. J. Lett. 329,L103-L106.Pinsonnealt, M., Deliyannis, C. & Demarque, P. (1992) Astro-phys. J. Suppl. 78, 179-203.Olive, K. & Schramm, D. N. (1993) Nature (London) 360,439-442.Simpson, J. (1983) Annu. Rev. Nucl. Part. Sci. 33, 323-381.Walker, T., Steigman, G., Schramm, D. N., Olive, K. & Fields,B. (1993) Astrophys. J., in press.Reed, S. & Viola, V. (1984) At. Data Nucl. Data Tables 31, 359.Gupta, M. & Webber, W. R. (1989) Astrophys. J. 340, 1124-1134.Silberberg, R. & Tsao, C. H. (1973) Astrophys. J. Suppl. 25,315-333.Rudstam, G. (1966) Z. Naturforsch. A 21, 1027 (abstr.).Mathews, G. & Schramm, D. N. (1993) Astrophys. J., 404,468-475.Burkert, A., Truran, J. & Hensler, G. (1992) Astrophys. J. 391,651-658.Thomas, D., Schramm, D. N., Olive, K. & Fields, B. (1993)Astrophys. J. 405, 569-579.Freese, K. & Schramm, D. N. (1984) Nucl. Phys. B 233,161-188.Fisher, C. (1992) Ph.D. thesis (Univ. of California, Berkeley).Guth, A. (1981) Phys. Rev. D 23, 347-356.Linde, A. (1990) Particle Physics and Inflationary Cosmology(Harwood, New York).Hegyi, D. & Olive, K. (1986) Astrophys. J. 303, 56-65.Bond, R. & Szalay, A. (1983) Ann. N. Y. Acad. Sci. 422, 82-92.Turner, M., Wilczek, F. & Zee, A. (1983) Phys. Lett. B 125,35-40, 519.Crawford, M. & Schramm, D. N. (1982) Nature (London) 298,538-540.Alcock, C. & Olinto, A. (1988) Annu. Rev. Nucl. Part. Phys. 38,161-184.Smoot, G. (1992) Astrophys. J. 396, L1-L5.ALEP, L3, OPAL & DELPHI Groups (1992) in Proceedings ofthe Joint International Lepton-Photon Symposium and Euro-physics Conference on High Energy Physics, eds. Hegarty, S.,Potter, K. & Querigh, E. (World Scientific, Singapore).

Proc. Natl. Acad Sci. USA 90 (1993)

Dow

nloa

ded

by g

uest

on

Janu

ary

11, 2

021