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For three decades, the big bang theory has dominated cosmology. According
to this theory, the Universe began expanding in a titanic explosion between
10 and 15 billion years ago. We observe this expansion in the recession
of most other galaxies from ours, and we see the afterglow of the explosion
itself in the microwave background radiation that permeates the Universe.

The standard theory of the big bang says that in the minutes following
the explosion the Universe was fairly smooth and homogeneous. Recently,
however, a new big bang theory has emerged, postulating that matter was
spread very unevenly in the early Universe, with regions of high density
and low density. These inhomogeneities of matter would not have imprinted
themselves on the microwave background, which is smooth, because particles
of matter were then only a trace component in a Universe that was filled
with photons. But such inhomogeneities may have altered the abundance of
the lightest elements in ways that astronomers can detect today.

According to the standard theory, the big bang created significant quantities
of only five nuclei, all lightweight. These nuclei formed from nuclear reactions
through a process astronomers call nucleosynthesis. The principal products
of this primordial process were hydrogen-1 (which consists of just one proton)
and helium-4 (which consists of two protons and two neutrons), and today
most of the Universe is still hydrogen-1 and helium-4. The big bang also
produced a little deuterium (an isotope of hydrogen, which has one proton
and one neutron), another helium isotope, helium-3 (two protons and one
neutron), and lithium-7 (three protons and four neutrons).

The big bang theory predicts how much of each of these elements were
created . Hydrogen-1 made up roughly 76 per cent of the mass of the early
Universe and helium-4, about 24 per cent, whereas the numbers of deuterium
and helium-3 nuclei were thousands of times less and the number of lithium-7
nuclei billions of times less than the number of hydrogen-1 nuclei. Astronomers
measure these abundances in objects that reveal the composition of the early
Universe, such as the oldest stars in our Milky Way.

This agreement vindicates the standard big bang theory. Yet scientists
have reason to consider alternatives. In 1984, Ed Witten, a physicist at
Princeton University, speculated that before the Universe was one second
old, it might have broken into regions of matter with high density and low
density. In 1985, James Applegate of Columbia University and Craig Hogan
of the University of Arizona explored how such inhomogeneities would affect
primordial nucleosynthesis. Since then, scientists have studied the consequences
in more detail.

The differences can be drastic. In the standard big bang, protons outnumber
neutrons everywhere. In an inhomogeneous big bang, the same is also true
– at first. Protons, neutrons, and electrons are concentrated in the high-density
regions, and all try to diffuse into the low-density regions. But only the
neutrons succeed. The protons cannot, because they have positive charge
and get trapped in the high-density regions by electrons, which have negative
charge. The neutrons, however, lack charge, escape the high-density regions,
and fill the low-density regions. Thus, two different regimes emerge: proton-rich
high-density regions and neutron-rich low-density regions.

Nuclear reactions in the high-density regions mimic those predicted
by the standard big bang because protons drive the nucleosynthesis. In the
low-density regions, however, neutrons dominate. Under the right conditions,
these low-density regions produce elements heavier than hydrogen, helium
and lithium, which have atomic numbers of 1, 2 and 3. Small amounts of beryllium
and boron, with atomic numbers of 4 and 5, may arise, as may even heavier
elements .

In 1989, Richard Boyd of Ohio State University and Toshitaka Kajino
of Tokyo Metropolitan University reported that an inhomogeneous Universe
could produce measurable amounts of beryllium and boron. Boyd and Kajino
included a nuclear reaction that other scientists had neglected. In this
reaction, two neutron-rich isotopes meet to form beryllium. Both neutron-rich
isotopes should be common in the neutron-rich low-density regions. Hydrogen-3
(one proton and two neutrons) hits lithium-7 (three protons and four neutrons)
to create beryllium-9 (four protons and five neutrons) and a neutron. Beryllium-9
is the only stable, non-radioactive isotope of beryllium. If it formed during
the big bang, it could survive until the present. By including this beryllium-producing
reaction, Boyd and Kajino also found that even a homogeneous early Universe
would produce a small quantity of beryllium, yielding a beryllium to hydrogen
ratio of 1.5 x 10^-16 to 1. This is too tiny to measure, but
it is 10 million times greater than previous estimates. Finally, Boyd and
Kajino discovered that an inhomogeneous early Universe might also produce
boron, which is even heavier than beryllium.

Beryllium and boron are rare. The Sun, for example, has a beryllium
to hydrogen ratio of only 1.4 x 10^-11 to 1 and a boron to hydrogen
ratio of about 4 x 10^-10 to 1. Beryllium and boron are rare
because stars do not normally produce them. In contrast, an element such
as iron is common because some stars create it and eject it into the Galaxy
when they die. ¿ìè¶ÌÊÓƵs believe that the little beryllium and boron that
is present in the Sun formed before the Sun was born, from cosmic rays that
hit heavier atoms in the interstellar medium and broke them into smaller
nuclei, such as beryllium and boron. This break-up process is called spallation.
Through spallation, the dust and gas in the Galaxy has acquired a trace
of beryllium and boron. When the Sun formed from this dust and gas, it inherited
the beryllium and boron.

Because a homogeneous big bang cannot produce detectable amounts of
beryllium and boron, and an inhomogeneous big bang may, the presence of
beryllium and boron could distinguish between the two theories. But the
beryllium and boron in the Sun tell us nothing useful, because the Sun was
born billions of years after the big bang and does not contain pure material
from the early Universe. To investigate the composition of the early Universe,
we must turn instead to the oldest stars in the Galaxy. These stars harbour
material that emerged from the big bang, so beryllium and boron in old stars
could signify an inhomogeneous big bang.

Astronomers recognise old stars in our Galaxy because the stars have
much less iron than the Sun. According to the standard theory, the big bang
produced no iron, which has atomic number 26. Instead, stars create iron
when they explode. Over time, as more and more stars have exploded, the
Galaxy has grown more and more iron-rich. Old stars, born when the Galaxy
had little iron, have little iron themselves.

In 1988, astronomers reported detecting beryllium in three old stars
with between one-tenth to one-twentieth the Sun’s abundance of iron. The
beryllium to hydrogen ratio in these stars is between 1 x 10^-12
and 2.5 x 10^-12 to 1 – smaller than in the Sun, but some 10
000 times more than the standard big bang model predicts.

Old though these stars are, they may not be old enough to probe the
early Universe. In 1991, astronomers announced they had discovered beryllium
in an even older and more iron-poor star. Gerard Gilmore of Cambridge University,
Bengt Edvardsson of the Astronomical Observatory in Uppsala, Sweden, and
Poul Nissen of Aarhus University in Denmark observed HD 140283, a star with
only one-four-hundredth the iron abundance of the Sun. They measured the
beryllium to hydrogen ratio of HD 140283 to be 1.6 x 10¹³ to
1 – about 1000 times more than the standard big bang model calls for (New
¿ìè¶ÌÊÓƵ, Science, 2 November).

These results are tantalising but not definitive, because even in such
an old star the beryllium may have come not from the big bang but from spallation.
To distinguish between the two possibilities, astronomers must find boron.
Inhomogeneous big bang models usually produce more beryllium than boron,
whereas spallation produces more boron than beryllium. (The Sun, for example,
has more boron than beryllium.) So, if iron-poor stars have more beryllium
than boron, these elements probably formed in an inhomogeneous big bang.
But no one has yet discovered boron in an iron-poor star. Boron is difficult
to detect by the standard methods of spectroscopy because its characteristic
lines of absorption lie in the ultraviolet part of the spectrum, which the
Earth’s atmosphere blocks. To detect the +element requires a satellite,
such as the Hubble Space Telescope.

Inhomogeneous big bang models can yield more than just beryllium and
boron, however. They can also produce even heavier elements, such as carbon,
nitrogen, oxygen and iron. And that may solve a mystery that has long puzzled
astronomers. If the Universe began with only hydrogen, helium and lithium,
then the first stars that arose in the Galaxy should consist only of these
three elements. For decades, astronomers have searched for such stars but
have never found any. If the early Universe was inhomogeneous, then the
big bang may have created heavy elements, explaining why all stars in the
Galaxy have been found to contain heavy elements.

An inhomogeneous Universe has another major effect: it could change
astronomers’ estimates of how much mass the Universe has. If the Universe
has a low density of mass, the Universe will expand forever. If the Universe
has a high density of mass, the gravitational pull of the mass will someday
halt the expansion of the Universe and cause the Universe to collapse. The
dividing line between these two outcomes is called the critical density.
To denote the density of the Universe, which controls the destiny of the
Universe, astronomers employ the last letter of the Greek alphabet, &Ogr;
(&Ogr;). The critical density is &Ogr; = 1.00. Less mass means a smaller
&Ogr;. If &Ogr; is less than 1.00, the Universe will expand forever; if
&Ogr; exceeds 1.00, the Universe will someday collapse.

Using the standard theory of the big bang, we can estimate &Ogr; from
the primordial abundances of the light elements – hydrogen-1, helium-4,
deuterium, helium-3 and lithium-7 – because the abundance of these elements
depends on how fast the nuclear reactions happened in the first few minutes
after the big bang. The denser the Universe and the greater &Ogr;, the faster
the reactions proceeded. It turns out that the higher &Ogr;, the more helium-4
and the less deuterium and helium-3 there should be .

Unfortunately, another factor also affects the predictions – the Hubble
constant, which is unknown. The Hubble constant takes its name from American
astronomer Edwin Hubble, who in the 1920s discovered that the Universe was
expanding. It quantifies the fact that distant galaxies recede from Earth
faster than nearby galaxies. Most astronomers believe that the Hubble constant
lies between 50 and 100 kilometres per second per megaparsec. (One megaparsec
is 3.26 million light years.) For example, if the Hubble constant is 75,
a galaxy that is 1 megaparsec farther than another recedes from us at 75
kilometres per second faster than the other. The bigger the Hubble constant,
the faster the Universe expands and the greater the density of the Universe
must be to halt the expansion. So, the density given by the abundance of
light element will imply a lower value of &Ogr; if the Hubble constant is
bigger.

Despite the huge uncertainty in the Hubble constant,the abundances of
the light elements tightly constrain the density of the Universe. In 1991,
a team led by Terry Walker of the Harvard-Smithsonian Center for Astrophysics
published the latest analysis. The scientists find that if the Hubble constant
is 100, &Ogr; lies between 0.01 and 0.015; if the Hubble constant is 50,
&Ogr; lies between 0.04 and 0.06. Thus, if the big bang was homogeneous
and the Hubble constant lies between 50 and 100, &Ogr; is 0.01 to 0.06,
and the Universe will expand forever.

Most astronomers, however, believe that &Ogr; is greater than this.
Visible matter implies that &Ogr; is around only 0.01, but the outer parts
of many galaxies, including our own, rotate quickly and suggest that large
haloes of dark matter surround galaxies. Moreover, clusters of galaxies
would fly apart if the gravitational pull of dark matter did not restrain
the galaxies. Studies of galaxy clusters imply that &Ogr; is around 0.10
or 0.20 or 0.30.

And some cosmologists think it is even higher. In particular, inflationary
cosmology, which postulates that the Universe expanded rapidly when it was
a fraction of a second old, predicts that &Ogr; = 1.00. To explain the discrepancy
between the prediction (&Ogr; = 1.00) and the measurement (&Ogr; = 0.01
to 0.06), inflationary cosmologists invent another form of dark matter.
They call this matter ‘non-baryonic’ to distinguish it from normal matter,
composed of baryons such as protons and neutrons. Conveniently for the theory,
this non-baryonic matter did not participate in the primordial nucleosynthesis
and therefore does not affect the abundance of light elements. Because the
light element abundances imply that the density of (baryonic) matter is
only 0.01 to 0.06, most of the Universe’s mass must be non-baryonic if &Ogr;
equals 1.00. No one has ever found this non-baryonic matter, but inflationary
cosmologists consider that a minor point (see ‘What’s wrong with the new
physics?’, ¿ìè¶ÌÊÓƵ, 22/29 December 1990).

However, even astronomers who hate inflation may need non-baryonic matter,
because &Ogr; derived from measuring the density of galaxy clusters (around
0.20) exceeds that derived from the abundances of light elements produced
in a homogeneous big bang (0.01 to 0.06). There is an alternative: an inhomogeneous
big bang. An inhomogeneous big bang produces different abundances of the
light elements. If the early Universe was inhomogeneous, it can have a higher
density of baryonic matter, consistent with that inferred from motions of
galaxies in clusters, and still produce the observed abundances of light
elements. Some scientists had even hoped that an inhomogeneous big bang
might allow &Ogr; to equal 1.00, but that no longer seems likely. Any big
bang, whether homogeneous or inhomogeneous, with a baryonic mass density
of 1.00 would create more helium-4 than is observed.

Despite its appeal, the inhomogeneous big bang has problems. In the
standard homogeneous model, the light element abundances depend on just
one parameter other than the Hubble constant: &Ogr;. In contrast, inhomogeneous
big bang models employ at least three additional parameters – one to describe
how much denser the high-density regions were than the low-density regions,
another to express what fraction of the early Universe the high-density
regions occupied, and a third to measure how far the high-density regions
were from one another. Choose different parameters and you predict different
abundances. For example, though an inhomogeneous big bang can produce far
more beryllium than the standard model, it can also produce far less, depending
on the parameters.

Most astronomers, therefore, will need more evidence before they junk
the standard big bang. Beryllium and boron will be crucial elements, but
so will others, such as carbon. Nowadays, most carbon is carbon-12 (six
protons and six neutrons), because stars create carbon-12 by fusing three
helium-4 nuclei together. But the neutron-rich low-density regions of an
inhomogeneous big bang could have created a lot of carbon-13, which has
one more neutron than carbon-12. So the material that emerged from an inhomogeneous
big bang might have a higher carbon-13 to carbon-12 ratio than Earth does.

To see whether such nuclei formed in the big bang, we need not look
to the edge of the Universe. Instead, the best objects to study are right
here in the Milky Way Galaxy, where the composition of the oldest stars
may reveal how the entire Universe began.

Ken Croswell is an astronomer in Berkeley, California.

Further reading Workshop on Primordial Nucleosynthesis, edited by William
J. Thompson, Bruce W. Carney and Hugon J. Karwowski, World Scientific, 1990.

* * *

1: PRIMORDIAL ALCHEMY AND THE DENSITY OF THE UNIVERSE

The standard big bang theory explains the radically different abundances
of five light nuclei observed in old stars and galaxies lacking in iron:
hydrogen-1, helium-4, deuterium, helium-3, and lithium-7. Forged in the
fiery aftermath of the big bang, these elements reveal the density of the
entire Universe, &Ogr;.

Pretend the early Universe is an epic play, in which the various nuclei
are actors. Two of the five actors – hydrogen-1 and helium-4 – will emerge
from the play as the victors, splitting between them more than 99.9 per
cent of the mass of the Universe. Hydrogen-1 is the simplest nucleus, with
one proton and no neutrons. Helium-4 is the most tightly bound light nucleus.
It has two protons and two neutrons.

Playing secondary, but nonetheless vital, roles will be deuterium, helium-3
and lithium-7. Deuterium, or hydrogen-2, contains one proton and one neutron.
Helium-3 is the lighter of the two stable isotopes of helium. It has two
protons but only one neutron. Lithium-7 will be the heaviest stable actor,
with three protons and four neutrons. Finally, two species will make fleeting
appearances, tritium (hydrogen-3) and beryllium-7. Both are radioactive,
so any that are formed during the big bang will not last.

Let the play begin. The scene: the expanding Universe, one second after
the big bang. The temperature is 10 billion degrees. Photons are everywhere,
vastly outnumbering protons and neutrons. Protons themselves outnumber neutrons,
by about a factor of five. It turns out that the denser the Universe, the
higher the neutron to proton ratio. Because nearly all neutrons will get
incorporated into helium-4 (recall that hydrogen-1 has no neutrons), the
greater the neutron-to-proton ratio, the more helium-4 will emerge. Thus,
the denser the Universe and the higher &Ogr;, the more helium-4 there will be.

The Universe expands, the clock reads 10 seconds, and the temperature
falls to 3 billion degrees. But not much happens. Protons and neutrons smash
into each other, trying to form nuclei of deuterium (hydrogen-2),

p + n → H²

but because the Universe is so hot, high-energy photons tear the deuterium
apart. Without deuterium, nucleosynthesis cannot proceed.

Finally, about 100 seconds after the big bang, the temperature falls
to 1 billion degrees and high-energy photons diminish, allowing deuterium
to survive. Protons and neutrons and even other deuterons quickly convert
deuterium into hydrogen-3 and helium-3:

H² + n → H³

H² + H² → H³H + p

H² + p → H³e

H² + H² → H³e + n

Hydrogen-3 and helium-3 do not last long. They get turned into ultrastable
helium-4:

H³ + p → H⁴e

H³ + H² → H⁴e + n

H³e + n → H⁴e

H³e + H² → H⁴e + p

H³e + H³e → H⁴e + p + p

The denser the Universe, the more collisions there are and the faster
these reactions convert deuterium and helium-3 into helium-4. So, the denser
the Universe and the higher &Ogr;, the less deuterium and helium-3 will emerge
from the big bang.

Nuclei with masses of 5 or 8 are not stable, so species heavier than
helium-4 do not form easily. Nevertheless, a little lithium-7 arises when
helium-4 meets tritium,

H⁴e + H³ → L⁷i

but it is destroyed by protons,

L⁷i + p → H⁴e + H⁴e

The denser the Universe, the more protons destroy lithium-7, and the
less lithium-7 will emerge. However, at still higher densities, a new actor
– beryllium-7 – debuts:

H⁴e + H³e → B⁷e

Beryllium-7 is unstable. It captures an electron and decays into lithium-7:

B⁷e + e^– → L⁷i

All nucleosynthesis ceases about 1000 seconds after the big bang, when
the Universe becomes too cool for nuclear reactions. But the half-life of
beryllium-7 is 53 days, so beryllium-7 decays long after nucleosynthesis
stops. Therefore, the lithium-7 created from beryllium-7 survives, because
protons no longer have enough energy to tear the lithium-7 apart. The denser
the Universe, the more beryllium-7 forms, so the more lithium-7 forms. As
a result, lithium-7 is more complicated than the other species: the abundance
of lithium-7 first decreases with increasing &Ogr; but then increases with
increasing &Ogr;.

The abundances of deuterium, helium-3, helium-4 and lithium-7 relative
to hydrogen-1 therefore all depend in different ways on &Ogr;. By analysing
the data, scientists find that, if the big bang was homogeneous, &Ogr; lies
between 0.01 and 0.06.

* * *

2: BREWING HEAVY ELEMENTS IN A BUMPY BIG BANG

An inhomogeneous big bang excites astronomers in part because it may
explain why the Galaxy has no stars made purely of hydrogen, helium and
lithium. A homogeneous big bang produces only these three light elements,
so the first stars born should contain no heavy elements. Yet astronomers
have never found a star without heavy elements.

In a homogeneous big bang, protons outnumber neutrons, and the heaviest
element created is lithium-7. If a proton hits lithium-7,

L⁷i + p → H⁴e + H⁴e

the lithium-7 disintegrates into two helium-4 nuclei, and the party is over: no heavy
elements form. In contrast, in an inhomogeneous big bang, the low-density
regions may build elements heavier than lithium, because the low-density
regions abound with neutrons rather than protons. As a result, lithium-7
can get hit by a neutron, creating lithium-8:

L⁷i + n → L⁸i

Like all nuclei with mass 8, lithium-8 is radioactive. It has a half-life
of just 0.8 second. If, before it decays, lithium-8 meets helium-4,

L⁸i + H⁴e → B¹¹ + n

then boron-11 is created, and boron-11 is stable. Boron-11 can also form from beryllium-9,
which itself arises when lithium-7 meets the neutron-heavy isotope hydrogen-3:

L⁷i + H³ → B⁹e + n

B⁹e + H³ → B¹¹ + n

Even if a homogeneous big bang created boron-11, it would not do any
good, because a proton would split the boron-11 into three helium-4 nuclei,

B¹¹ + p → H⁴e + H⁴e + H⁴e

and again the party is over. In contrast, in the low-density regions of
an inhomo-geneous big bang, the boron-11 is more likely to meet a neutron,
which creates a heavier isotope of boron:

B¹¹ + n → B¹²

Boron-12 is radioactive. It emits an electron and decays into carbon:

B¹² → C¹² + e^–

Additional hits by neutrons create heavier isotopes of carbon:

C¹² + n –> C¹³

C¹³ + n –> C¹⁴

C¹⁴ + n –> C¹⁵

the last of which decays into nitrogen-15:

C¹⁵ → N¹⁵ + e^–

Further nuclear reactions create still heavier elements. If the material
emerging from the big bang harboured a trace of these heavy elements as
well as hydrogen, helium and lithium, then the first stars that formed should
contain a small amount of heavy elements, in perfect agreement with observations.