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

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

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

ABSTRACT Primordial provides (with number of families and its subsequent verification the background ) one of the two quanti- by the Large Electron Positron Collider (LEP) and the tative experimental tests of the hot cosmological Stanford Linear Collider (SLC). model (versus alternative explanations for the observed Hubble Also discussed is the possibility that a first-order quark- expansion). The standard homogeneous-isotropic calculation hadron could have produced variations from fits the light element abundances ranging from 'H at 76% and the standard homogeneous model. It will be shown that 4He at 24% by mass through 2H and 3He at parts in 105 down contrary to initial indications, first-order quark-hadron- to 7Li at parts in 1010. It is also noted how the recent Large inspired results are consistent with the homogeneous model Electron Positron Collider (and Stanford Linear Collider) results. results on the number of (N,,) are a positive labora- Finally, a discussion of the recent B and Be observations tory test of this standard Big Bang scenario. The possible in Population (Pop) II will be made. It will be shown that alternate scenario ofquark-hadron-induced inhomogeneities is all the Be and B observations, to date, are best explained by also discussed. It is shown that when this alternative scenario galactic spallation (2) in Pop II environments and is made to fit the observed abundances accurately, the resulting not by any cosmological process. conclusions on the baryonic density relative to the critical This report will draw on two recent reviews (3 and 4) and density (fQb) remain approximately the same as in the standard in some ways is an update (20 later) ofthe light element homogeneous case, thus adding to the robustness of the stan- summary of ref. 5. dard model and the conclusion that fQb 0.06. This latter point is the driving force behind the need for nonbaryonic dark History of (BBN) matter (assuming total density fitt = 1) and the need for dark baryonic matter, since the density of visible matter 1iksib1e < It should be noted that there is a symbiotic connection fQb. The recent Population II B and Be observations are also between primordial nucleosynthesis (hereafter referred to as discussed and shown to be a consequence of cosmic ray BBN) and the 3 K background dating back to Gamow and his spallation processes rather than primordial nucleosynthesis. associates Alpher and Herman. The initial BBN calculations The light elements and N,, successfully probe the cosmological of Gamow's group (6) assumed pure neutrons as an initial model at as early as 1 sec and a (1) of -1010 condition and thus were not particularly accurate, but their K (-1 MeV). Thus, they provided the first quantitative inaccuracies had little effect on the group's predictions for a arguments that led to the connections of cosmology to nuclear background radiation. and particle . Once Hayashi (7) recognized the role of neutron- equilibration, the framework for BBN calculations them- selves has not varied significantly. The work of Alpher et al. Yacov Zeldovich (1) noted in material written just before he (8) and Hoyle and Taylor (9), preceding the discovery of the died in 1987 that "the greatest success ofthe Big Bang theory 3 K background, and Peebles (10) and Wagoner et al. (11), is the fact that the quantitative observation of the light immediately following the discovery, and the more recent element abundances agrees with the prediction of the theory work of our group of collaborators (12-18) all do essentially of nucleosynthesis." Such praise from Zeldovich is indeed the same basic calculation, the results of which are shown in pleasing, for the field and, hopefully, the recent develop- Fig. 1. As far as the calculation itself goes, solving the ments that will be described in this paper would not have reaction network is relatively simple by using the numerical detracted from Zeldovich's views. procedures developed slightly earlier for explosive nucleo- This paper will review the status of primordial synthesis calculations in supernovae (and nuclear weapons nucleosynthesis. After briefly reviewing the history, this tests), with the calculational changes over the last 25 years paper will make special emphasis of the remarkable agree- being mainly in terms of more recent nuclear reaction rates ment of the observed light element abundances with the as input, not as any great calculational insight [although the calculations upon which Zeldovich based his comments. It current Kawano code (18) is somewhat streamlined relative should be remembered that this agreement is one of the two to the earlier Wagoner code (11)]. With the possible excep- prime tests of the Big Bang itself (the other being the tion of 7Li yields (and possibly Be and B to be discussed microwave background) as the successful framework in later), the reaction rate changes over the past 25 years have which to place the observed Hubble expansion. The agree- not had any major affect. The one key improved input is a ment of abundances and predictions works only if the better neutron lifetime determination (19). density is well below the cosmological critical value. The With the exception of the effects of review will also mention the nucleosynthesis prediction ofthe assumptions to which we will return, the real excitement for

The publication costs of this article were defrayed in part by page charge Abbreviations: BBN, Big Bang nucleosynthesis; HDM, hot dark payment. This article must therefore be hereby marked "advertisement" matter; CDM, cold ; LEP, Large Electron Positron in accordance with 18 U.S.C. §1734 solely to indicate this fact. Collider; SLC, Stanford Linear Collider; Pop, population. 4782 Downloaded by guest on September 29, 2021 Colloquium Paper: Schramm Proc. Natl. Acad. Sci. USA 90 (1993) 4783 situation emphasized by Yang et al. (15) that the light element of with 0.01 0.1 1.0 abundances are consistent over 9 orders magnitude -v 1.0 BBN, but only if the cosmological baryon density is con- strained to be around 5% of the critical value. o i- j 4He(mass ' 10 | BBN was the 2 fraction) The other development of the 1970s for explicit calculation of Steigman (33) showing that the number of neutrino generations, NV, had to be small to avoid over- production of 4He. [Earlier independent work (9, 34, 35) had F 1. BH+rHe commented about a dependence on the density of exotic particles but had not done explicit calculations probing 3He Nv] This will subsequently be referred to as the Steigman, Schramm, and Gunn (SSG) limit. To put this in perspective, Z 0.1 1. I 0 0 one should remember that the mid-1970s also saw the dis- 1-8 CONCO RDANCE-"1 covery of charm, bottom, and tau, so that it almost seemed as if each new detector produced new particle discoveries, _j 160- and yet, cosmology was arguing against this "conventional" wisdom. Over the years, the SSG limit on NV improved with 4He 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 to density (,q) for a homogeneous . below 4 (but not excluding 3) just before LEP and SLC turned on (16, 17, 36, 37). The recent verification of this cosmolog- BBN over the last 25 years has not really been in redoing the ical prediction by the LEP and SLC results (79), where N,, = basic calculation. Instead, the true action is focused on 2.99 ± 0.05, is the first verification of a cosmological pre- understanding the of the light element abundances diction by a high-energy collider. Thus, in some sense LEP and using that information to make powerful conclusions. In (and SLC) have checked the Big Bang model at the 1960s, the main focus was on 4He, which is very insen- of -101" K and times of -1 sec. sitive to the baryon density. The agreement between BBN The power of homogeneous BBN comes from the fact that predictions and observations helped support the basic Big essentially all of the physics input is well determined in the Bang model but gave no significant information, at that , terrestrial laboratory. The appropriate temperature regimes, with regard to density. In fact, in the mid-1960s, the other 0.1-1 MeV, are well explored in nuclear physics laboratories. light (which are, in principle, capable of giving Thus, what nuclei do under such conditions is not a matter of density information) were generally assumed to have been guesswork but is precisely known. In fact, it is known for made by spallation processes during the T-Tauri phase of these temperatures far better than it is for the centers of stars (20) and so were not then taken to have like our . The center of the sun is only a little over 1 keV, cosmological significance. It was during the 1970s that BBN thus, below the energy where nuclear reaction rates yield fully developed as a tool for probing the universe. This significant results in laboratory experiments, and only the possibility was in part stimulated by Ryter et al. (21) who long times and higher densities available in stars enable showed that the T-Tauri mechanism for light element syn- anything to take place. thesis failed. Furthermore, 2H abundance determinations To calculate what happens in the Big Bang, all one has to improved significantly with solar wind measurements and the do is follow what a gas of with density Pb does as the interstellar work from the Copernicus satellite (22-24). universe expands and cools. As far as nuclear reactions are Reeves et al. (5) argued for a purely cosmological origin for concerned, the only relevant region is from a little above 1 2H and were able to place a constraint on the baryon density MeV (-1010 K) down to a little below 100 keV (=109 K). At excluding a universe closed with baryons. Subsequently, the higher temperatures, no complex nuclei other than free single 2H arguments were cemented when Epstein et al. (25) proved neutron and can exist, and the ratio of neutrons to that because of the remarkably low nuclear protons (nip) is just determined by n/p = eQ/T, where Q = per nucleon of 2H, no realistic astrophysical process other (m" - mp)c2 1.3 MeV, where m. is the mass of the neutron, than the Big Bang could produce significant 2H. It was also mp is the mass of the proton, and c is the speed of light. interesting that the baryon density thus implied by BBN was Equilibrium applies because the weak interaction rates are in good agreement with the density implied by the dark much faster than the expansion of the universe at tempera- galactic halos (26). tures much above 1010 K. At temperatures much below 109 K, By the late 1970s, a complimentary argument to 2H had also the electrostatic repulsion of nuclei prevents nuclear reac- developed using 3He. In particular, it was argued (27) that, tions from proceeding as fast as the cosmological expansion unlike 2H, 3He was made in stars; thus, its abundance would separates the particles. increase with time. Since 3He like 2H monotonically de- After the weak interaction drops out of equilibrium, a little creased with cosmological baryon density, this argument >1010 K, the ratio of neutrons to protons changes more could be used to place a lower limit on the baryon density (28) slowly due to free neutrons decaying to protons, and similar by using 3He measurements from solar wind (21) or inter- transformations of neutrons to protons via interactions with stellar determinations (29). Since the bulk of the 2H was the ambient leptons. By the time the universe reaches 109 K converted in stars to 3He, the constraint was shown to be (0.1 MeV), the ratio is slightly <1/7. For temperatures >109 quite restrictive (15). Not only has this basic picture remained K, no significant abundance of complex nuclei can exist due intact now for almost 20 years, but as we shall see, the to the continued existence of y-rays with >1 MeV. confidence level in the argument has increased dramatically Note that the high to baryon ratio in the universe with time. (=101") enables significant population of the mega electron For example, it was interesting that the lower boundary volt high-energy Boltzman tail until T S 0.1 MeV. from 3He and the upper boundary from 2H yielded the Once the temperature drops to 109 K, sufficient abun- requirement that 7Li be near its minimum of 7Li/H ---10-10, dances of nuclei can exist in statistical equilibrium through wichL1 was, veife +bythe Pop II L m e of Spite reactions such as n + p + 2H + 'y, where y is a y-ray and 2H and Spite (ref. 30; see also refs. 31 and 32), hence yielding the + p ++ 3He + -y and 2H + n <-+ 3H + y, which in turn react Downloaded by guest on September 29, 2021 4784 Colloquium Paper: Schramm Proc. Natl. Acad. Sci. USA 90 (1993) to yield 4He. Since 4He is the most tightly bound nucleus in phase-transition parameter values (e.g., nucleation site sep- the region, the flow of reactions converts almost all the arations are -10 m at the time of the transition), this back neutrons that exist at 109 K into 4He. The flow essentially diffusion could destroy much of the excess Li. stops there because there are no stable nuclei at either mass-5 However, Kurki-Suonio et al. (41), the Tokyo group (43), or mass-8. Since the baryon density at BBN is relatively low and the Livermore group (44) have eventually argued that, in (-10% the density ofterrestrial air) and the time scale is short their detailed diffusion models, the back diffusion affects not (t 5 102 sec), only reactions involving two-particle collisions only 7Li but also the other light nuclei. They find that for Q1b occur. It can be seen that combining the most abundant 1, 4He is also significantly overproduced (although it does nuclei, protons and 4He, via two-body interactions always go to a minimum for similar parameter values as does the Li). leads to unstable mass-5. Even when one combines 4He with One can understand why these models might tend to over- rarer nuclei like 3H or 3He, we still get only to mass-7, which produce 4He and 7Li by remembering that in standard ho- when hit by a proton, the most abundant nucleus around, mogeneous BBN, high baryon densities lead to excesses in yields mass-8. (As we will discuss, a loophole around the these nuclei. As back diffusion evens out the effects of the mass-8 gap can sometimes be found if nlp > 1, so that excess initial fluctuation, the averaged result should approach the neutrons exist; but for the standard case, n/p < 1.) Eventu- homogeneous value. Furthermore, it can be argued that any ally, 3H decays radioactively to 3He, and any mass-7 made narrow range of parameters, such as those that yield rela- radioactively decays to 7Li. Thus, BBN makes 4He with tively low Li and He, are unrealistic since in most realistic traces of2H, 3He, and 7Li. (Also, all the protons left over that phase transitions there are distributions of parameter values did not capture neutrons remain as .) For standard (distribution of nucleation sites, separations, density fluctu- homogeneous BBN, all other chemical elements are made ations, etc.). Therefore, narrow minima are washed out that later in stars and in related processes. (Starsjump the mass-5 would bring the 7Li and 4He values back up to their excessive and -8 instability by having compress the matter to levels for all parameter values with fQ 1. Furthermore, sufficient densities and have much longer times available so Freese and Adams (45) and G. Baym (personal communica- that three-body collisions can occur, 3 4He -+ 12C + y.) tion) have argued that the boundary between the two phases may be fractal-like rather than smooth. The large surface area Inhomogeneous BBN of a fractal-like boundary would allow more interaction between the regions and minimize exotic effects. As noted above, BBN yields all agree with observations using Fig. 2 shows the updated results of Kurki-Suonio et al. (41) only one freely adjustable parameter, 71, or equivalently, p,. for nucleation spacing 1 with the constraints from the different Thus, BBN can make strong statements regarding Pb if the light element abundances. Notice that the Li, 2H, and even observed light element abundances cannot be fit with any the 4He constraint do not allow Qb 1. Note also that, with alternative theory. The most significant alternative that has the Pop II 7Li constraint, the results for flb are quite similar been discussed involves quark-hadron-transition-inspired in- to the with a slight excess in fQb possible if 1 homogeneities (38-40). While inhomogeneity models had is tuned to -10. Thus, even an optimally tuned first-order been looked at previously (see ref. 15) and were found to quark-hadron transition is not able to alter the basic conclu- make little difference, the quark-hadron-inspired models had sions of homogeneous BBN regarding Qb. (It also cannot the added ingredient ofvariations in n/p ratios. Cosmologists significantly change the N, argument.) Furthermore, it ap- are well aware that current trends in lattice gauge calculations pears that optimally tuned quark-hadron-inspired models are imply that the transition is probably second order or not a not even able (46) to significantly lower the minimal 4He mass phase transition at all. Nevertheless, it has been important to fraction compatible with 3He, 2H, and N, = 3; such models, explore the maximal cosmological impact that can occur. even relaxing the 7Li bound, never have concordance with Y This maximal impact requires a first-order phase transition. below 0.23. In fact, the main role that a quark-hadron option The initial claim by Applegate and coworkers (38), fol- has played for BBN is to show how robust the standard model lowed by a similar argument from Alcock et al. (39), that Qb results are. 1 might be possible, created tremendous interest. Their argument was that if the quark-hadron transition was a Boron, Beryllium, and the Spallation Process first-order phase transition, then it was possible that large inhomogeneities could develop at T - 100 MeV. The pref- While quark-hadron-inspired variations have not been able erential diffusion of neutrons versus protons out of the to alter the basic conclusions of BBN, an important question high-density regions could lead to BBN occurring under conditions with both density inhomogeneities and variable 1000 n/p ratios. In the first round of calculations, it was claimed H that such conditions might allowQb 1, while fitting the 2H+3He "He Li observed primordial abundances of4He, 2H, and 3He with an "He overproduction of 7Li. Since 7Li is the most recent of the 100 2 cosmological abundance constraints and has a different ob- E served abundance in I stars versus Pop the traditionally more 7Li,,: primitive Pop II stars (30-32), some argued (39) that perhaps 10 some special depletion process might be going on to reduce the excess 7Li. At first it appeared that if the Li constraint could be 2H 7Li, surmounted, then the constraints of standard BBN might disintegrate. To further stimulate the flow through the loop- 1 10 100 hole, Fowler and Malaney (40) showed that, in addition to Xx 1010 looking at the diffusion of neutrons out of high-density one must FIG. 2. Updated results of Kurki-Suonio et al. (41) showing that regions, also look at the subsequent effect ofexcess even allowing for a first-order quark-hadron transition with nucle- neutrons diffusing back into the high-density regions as the ation site spacing I optimized for maximal effect, the light element nucleosynthesis goes to completion in the low-density re- abundances constrain the baryon-to-photon ratio (il) and thus Qb to gions. (The initial calculations treated the two regions sepa- essentially the same values as those obtained in the homogeneous rately.) Fowler and Malaney (40) argued that for certain case with only slightly large QIb values possible with 1 10. Downloaded by guest on September 29, 2021 Colloquium Paper: Schramm Proc. Natl. Acad. Sci. USA 90 (1993) 4785 remains; namely, is there an observable signature that could x2 value of the 7Li cosmological solution and makes stellar differentiate quark-hadron-inspired variations from the ho- depletion models even less likely. mogeneous model? On the theoretical side, this point has Perhaps most critical to any spallation origin is the result- been debatable. Several authors have argued (41, 47, 48) that ant B/Be ratio. It is also known, from actual measurements, because ofthe high n/p region in the inhomogeneous models, that the cosmic rays themselves (60) show B/Be 14 (and B leakage beyond the mass-5 and -8 instability gaps can occur, and Be are pure spallation products in the cosmic rays) with and traces of 9Be, '0B, 11B, and maybe even r-process a C/O ratio exceeding unity (Pop I has C/O G 0.5). Since elements can be produced. Thus, detection of nuclei beyond spallation offC favors B relative to Be (mass-11 requires only 7Li in primitive objects may be a signature. However, Sato a single nucleon ejected from mass-12), whereas 0 being and Tarasawa (43) have argued that such leakage is negligi- farther from either shows less favoritism, the cosmic ray ble. Because ofthis debate as well as the recent experimental observations are actually an upper limit on what B/Be ratio results (49-52), we have started theoretically examining this one might expect in Pop I cosmic rays. However, of more question ourselves. However, before discussing our results, concern here is the lower limit on B/Be achievable by a let me first comment on some recent observations of Be and spallation process (61). Note that cosmic ray spectra that are B in primitive Pop II stars. flatter than E-2-6 (where E is energy) will be less favorable In particular, there has been much recent attention given to toward B production. This is because the "B production reports (49-51) of Be lines being observed in extreme Pop II threshold is below that for 9Be. Thus, steeper spectra favor stars. For one very metal poor Pop II , HD140283, B was B relative to Be, whereas flatter spectra remove the role of also observed (52). The observations yielded the threshold effects and yield relatively higher Be. Further- more, Pop II composition has a lower C/O ratio than does Be/H -10-130.3, [1] Pop I. Like Fe, C is not a pure Type II product. Spallation on pure Type II ejecta would have targets of 0, which represents a combination of the two Be/H measure- Ne, Mg, Si, etc., but less C and N than Pop I. Recent y-Ray ments with Gilmore et al. (49) obtaining a factor of -3 higher Observatory (GRO/EGRET) -ray results show extragalac- Be/H than Ryan et al. (50). The B was measured using the tic high-energy spectra with -E-20. Thus, flat spectra may where a value was obtained (52) of be quite reasonable. Spallation calculations for flat spectra on Pop II material B/H lo-12±0.1 [2] have been carried out (4, 61). The cross sections we used for the spallation calculations are a combination of all measured The resulting B/Be ratio is cross-section data (62) and our semiempirical estimates (4, 61, 64, 65). The resultant ratio is B/Be 10 + 5. [3] B/Be ; 7.6. [4] This particular star has its Fe abundance depleted relative to the standard Pop I (present galactic disk) Fe abundance by a The initially reported B/Be ratio for HD140283 was below factor of _10-2.6, and its 0 is depleted relative to Pop I by this limit, which at first looked awkward for the spallation -10-2-1. The high O/Fe ratio in extreme Pop II stars is well model, but revised data analysis by the observers (52) now understood (53) as due to heavy-element production in mas- yields a ratio quite consistant with the model. (Of course, the sive Type II supernova producing a high O/Fe ratio, whereas correlation of Be and B with metalicity showed that Be and later Pop I abundances also get a significant admixture of B in Pop II stars were not of cosmological origin, but no low-mass slow-to-explode Type I supernova ejecta where Fe alternative to spallation has yet been developed.) is dominant over 0. Because 0 is chiefly made in Type II It is important to note that ifspallation processes do indeed supernova, whereas Fe has at least two significant sources, produce the observed Be and B in Pop II stars, then the we feel it is mandatory to use 0 as a measure of the Type II cosmic ray flux is probably stronger than it is in the present supernova contribution to such stars. In this regard, it is . Remember that the present Pop I abundance of Be important to note that the Be/O ratio for these stars is, within and B and 6Li can be explained by the present cosmic ray flux experimental errors, the same as Be/O ratio for those high hitting the Pop I C, N, and 0 abundances (2, 5) integrated surface temperature Pop I stars whose convective zones are over the lifetime ofthe Galactic disk prior to the formation of not deep enough to destroy their original Be. Thus, contrary the observed stars. However, for these Pop II stars, the C, N, to some initial claims, the Be/H observation does not require 0, and heavier element abundances are down and the stars cosmological origin, only a scaling with 0 ofthe same process presumably formed relatively early, before the disk formed. that While some Galactic evolution models (66, 67) expect this produced Be in the Pop I stars. predisk formation epoch to be several gigayears long, it is The presumed process that produced Be and B in Pop I nonetheless shorter than the age of the disk. If the predisk stars (as well as the 6Li) is thought to be cosmic ray spallation time is merely the massive star stellar evolution time scale, (2, 5). For Be and B, such spallation comes from the breakup then it can be very short. The shorter time scale thus requires of heavy nuclei such as C, N, 0, Ne, Mg, Si, S, Ca, and Fe a consummately higher flux ifthe ratios to 0 observed in Pop by protons and a-particles. As noted by Epstein et al. (54, 55) I are to be retained in the Pop II objects. Of course, many for Li one must also include a-a fusion processes as well. galactic evolution models (66, 67) predict higher early super- This latter point was well noted by Steigman and Walker (56) rates that producejust such a higher cosmic ray flux, so who emphasized that Be and B spallation production on Pop consistent models do exist. II abundances would imply a significant enhancement of Li From the above, at present, there is no cause to invoke from a-a relative to the reduced production ofBe and B from anything other than spallation; however, if objects are ob- depleted heavy nuclei. While the 6Li so produced would be served with decreasing O/H ratios, but Be/O and B/O ratios destroyed at the base of the convective zones in the stars are found not to keep falling, then one would have to observed (57, 58), the 7Li would survive and might result in conclude that there is primordial cosmological production of observable effects in the Spite (30, 31) Pop II plateau Be and B. (59). However, Olive and Schramm (59) have shown that Fig. 3 shows the trace element yields in a standard homo- correcting for the Li produced along with the Be and B does geneous BBN calculation, with Fig. 3A showing 2H, 3He, 6Li, not in any way detract from the Spite plateau but reduces the and 7Li yields and Fig. 3B showing the 9Be, '0B, and "1B Downloaded by guest on September 29, 2021 4786 Colloquium Paper: Schramm Proc. NatL Acad. Sci. USA 90 (1993) A required. The source of such inhomogeneities would have to be either the quark-hadron transition or some other activity around that same cosmological epoch (no earlier than the electroweak transition) so that density variations are re- tained. Of course, whatever these variations might be, they must not alter the spectacular agreement for A c 7 abun- dances and for N,. X Limits on ib and Dark Matter Requirements 0c0 The success and robustness of BBN in the face ofthe Be and B results as well as the quark-hadron variations give renewed confidence to the limits on the baryon density constraints. Let us convert this density regime into units of the critical cosmological 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 density that 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 per B Mpc [1 (pc) = 30.9 x 1016 m]. The lower bound on ho comes from direct observational limits and the upper bound from constraints (69). The constraint on flb still means that the universe cannot be closed with baryonic matter. [This point was made 20 years ago (5) and has proven to be remarkably strong.] If the universe is truly at its critical density, then nonbaryonic matter is required. 0)~~~~0 This argument has led to one of the major areas of research 0 at the particle-cosmology interface, namely, the search for nonbaryonic dark matter. °-20 Another important conclusion regarding the allowed range in baryon density is that it is in very good agreement with the density implied from the dynamics ofgalaxies, including their dark halos. An early version of this argument, using only 2H, was described >15 years ago (26). As time has gone on, the argument has strengthened, and the fact remains that galaxy -25 .,,,,.... ,,,.. l1 0.01 0.1 1 10 100 1000 dynamics and nucleosynthesis agree at =5% of the critical 1110 density. Thus, if the universe is indeed at its critical density, as many of us believe, it requires most matter not to be FIG. 3. (A) Standard homogeneous BBN yields showing 2H, 3He, associated with and their halos and to be nonbary- 6Li, and 7Li for six orders of magnitude in nb/71y. Note that 6Li is onic. Let us put the nucleosynthetic arguments in context. always negligible relative to 7Li. X, abundance. (B) Standard homo- The arguments requiring some sort of dark matter fall into geneous BBN yields for 9Be, '0B, and "B. The various curves for 9Be separate and quite distinct areas. These arguments are sum- and '0B represent different cross-section assumptions. The "B yield is double-humped due to production both directly as "B and also as marized in Fig. 4. First are the arguments using Newtonian "1C, which p-decays to "B. mechanics (and stellar observations) applied to various as- tronomical systems that show that there is more matter yields. This work is part of an extensive study ofA . 6 BBN present than the amount that is shining. It should be noted by Thomas et al. (68) (where A is the atomic mass number), that these arguments reliably demonstrate that galactic halos using a more extensive reaction network than previously seem to have a mass =10 times the visible mass. used. Note, in particular, that 9Be/H yields are always Note however that BBN requires that the bulk of the <10-14 regardless of Tq = nb/nly. Also note that, for the baryons in the universe be dark since the density of visible standard model that is concordant with the other light ele- IRAS/GA ments, i- 3 x 10-10, Be/H and B/H ratios are -10-18. In 1.0F other words, homogeneous BBN cannot yield a Be/H ratio consistent with the Pop II stellar observations. To explore ICLUSTER .L preliminarily the alternative of inhomogeneous models, we 10-1 a e have taken our extensive network and looked at high n/p _f - ratios. For regions with n/p > 3, we can obtain Be/H 10-14 SIBEHALO but no more for parameter values that still fit the A < 7 abundances. However, any realistic model will have a sig- 10-21 nificant dilution of this material with low n/p regions. Thus, we tentatively view the achievement of such values as VISIBLE somewhat problematic, as do Sato and Tarasawa (44). We will continue to explore a full inhomogeneous model, which 10-31 0. includes regions ofextremely high n/p, to see how robust any 0.001 0.01 0.1 1 10 100 leakage to A > 7 truly is. Such an exploration is just rh5O, Mpc beginning. FIG. 4. Implied densities versus the scale of the measurements. Ifsome Be and B can be shown to be cosmological, it would IRAS/GA, infrared astronomical satellite/Great Attractor; Mpc, have great implications for BBN. If simple inhomogeneities megaparsec r, distance scale; h50, Hubble constant in units of 50 km are unable to produce it, then more exotic ones will be per sec per Mpc. Downloaded by guest on September 29, 2021 Colloquium Paper: Schramm Proc. Natl. Acad. Sci. USA 90 (1993) 4787 matter (fij) << fQb. Thus, the dark halos could in principle than galactic mass, as many scenarios imply, then mergers are be baryonic (26). Recently arguments on very large scales necessary for eventual galaxy size objects. Mergers stimulate (70) (bigger than clusters of galaxies) from the velocity flows starformation while putting early objects into halos ratherthan observed in the infrared astronomical satellite catalogue and disks. Mathews and Schramm (66, 67) have recently devel- in the Great Attractor hint that fl on those scales is indeed oped a galactic evolution model that does just that and gives greater than flb, thus forcing us to need nonbaryonic matter. a reasonable scenario for chemical evolution. Thus, while An fl of unity is, of course, preferred on theoretical making halos out of exotic material may be more exciting, it grounds since, as noted by cosmologists in the 1930s, that is is certainly not impossible for the halos to be in the form of the only long-lived natural value for what we now call Q and dark baryons. The new microlensing projects by groups in most of us feel that (71, 72) or something like it France, the United States, Australia, and Poland should provided the early universe with the mechanism to achieve eventually test this possibility. that value and thereby solve the flatness and smoothness Nonbaryonic matter can be divided following Bond and problems. (Note that our need for exotica is not dependent on Szalay (74) into two major categories for cosmological pur- the existence of dark galactic halos. This point is frequently poses: hot dark matter (HDM) and (CDM). forgotten, not only by some members ofthe popular press but HDM is matter that is relativistic until just before the epoch occasionally by active workers in the field.) of galaxy formation, the best example being low-mass neu- Some must exist since we know that trinos with a mass mi,- 25 eV. [Remember ,, -- m, the lower bound from BBN is greater than the upper limits on (eV)/100hQ.] CDM is matter that is moving slowly at the the amount ofvisible matter in the universe. However, we do of formation. Because it is not know the form of this baryonic dark matter. It could be epoch galaxy moving slowly, it can either in condensed in as clump on very small scales, whereas HDM tends to have objects the halo, such brown dwarfs more difficulty in on and jupiters [objects with ;0.08 the mass of the Sun (M D) so being confined small scales. Examples they are not bright shining stars] or in black holes (which at ofCDM could be the lightest supersymmetric particle, which the time of nucleosynthesis would have been baryons). Or, if is presumed to be stable and might have a mass ofseveral tens the baryonic dark matter is not in the halo, it could be in hot ofgigaelectron volts or even a teraelectron volt. According to intergalactic gas, hot enough not to show absorption lines in Michael Turner (personal communication), any such weakly the Gunn-Peterson test, but not so hot as to be seen in the interacting massive particle is called a "WIMP." , x-rays. Evidence for some hot gas is found in clusters of while very light, would also be moving very slowly (75) and, galaxies. However, the amount of gas in clusters would not thus, would clump on small scales. Or, one could also go to be enough to make up the entire missing baryonic matter. nonelementary particle candidates, such as planetary mass Another possible hiding place for the dark baryons would be blackholes or quark nuggets ofstrange quark matter, possibly failed galaxies, large clumps of baryons that condense grav- produced at the quark-hadron transition (76, 77). Another itationally but did not produce stars. Such clumps are pre- possibility would be any sort of massive topological remnant dicted in galaxy formation scenarios that include large left over from some early phase transition. Note that CDM amounts of biasing where only some fraction of the clumps would clump in halos, thus requiring the dark baryonic matter shine. to be out between galaxies, whereas HDM would allow Hegyi and Olive (73) have argued that dark baryonic halos baryonic halos. are unlikely. However, they do allow for the loopholes While the recent (and very impressive) Cosmic Back- mentioned above of low-mass objects or of massive black ground Explorer (COBE) large-scale results (78) holes. It is worth noting that these loopholes are not that are consistent with a Harrison-Zeldovich gaussian fluctua- unlikely. If we look at the initial mass function for stars tion spectrum, the small scale (:3O) results that correspond forming with Pop I composition, we know that the mass to observed galaxy structures have not been measured yet. function falls off roughly like the Salpeter power law for The actual galaxy observations seem to require more power standard size stars. Or, even if we apply the Miller-Scalo (and/or nongaussian behavior), on the scale of 2 to 3°, than mass function, the falloffis only a little steeper. In both cases a flat Harrison-Zeldovich spectrum can deliver. Since HDM there seems to be some sort of lower cut-off near 0.1 Mo. does not work well with a Harrison-Zeldovich gaussian However, we do not know the origin ofthis mass function and spectrum but CDM does, it is still too early to ascertain which its shape. No true star formation model based on fundamental is correct (or maybe a mixture of both is needed). In partic- physics predicts it. ular, remember that a nongaussian model or a mixed model We do believe that whatever is the origin of this mass can work with HDM, which becomes particularly attractive function, it is probably related to the metalicity ofthe material, if recent hints from the gallium experiments require the since metalicity affects cooling rates, etc. It is not unreason- solution to the solar neutrino problem to have neutrino able to expect the initial mass function that was present in the mixing with ve - v,, mass scales of '10-3 eV, making electron primordial material that had no heavy elements (only the volt mass scales for vT quite plausible in those see-saw type products of BBN) would be peaked either much higher than models where m,,: mM(mt0/mtop/Mchm) (2). the present mass function or much lower-higher if the lower cooling from low metals resulted in larger clumps or lower if Conclusion some sort of rapid cooling processes ("cooling flows") were set up during the initial star formation epoch, as seems to be Primordial nucleosynthesis has indeed become one of the the case in some primative galaxies. In either case, moving cornerstones ofmodern cosmology. Ifanything, the situation either higher or lower produces the bulk of the stellar popu- is even more compelling since Yacov Zeldovich's marvelous lation in brown dwarfs andjupiters or in massive black holes. quote (1). As with any good physical theory, the model is both Thus, the most likely scenarios are that a first generation of predictive and falsifiable. For example, if the 4He mass condensed objects would be in a form of dark baryonic matter fraction were found to be <23% (without altering the 3He and that could make up the halos and could explain why there is 2H bound) or if Be or B were truly shown to be primordial, an interesting coincidence between the implied mass in halos there would be difficulties. At present, no such difficulties are and the implied amount of baryonic material. 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