112 The hot universe
see later thatη 10 can be determined with high precision from data on deuterium
abundance and CMB fluctuations.
It follows from (3.141) that nucleosynthesis begins earlier in a more dense uni-
verse and hence more neutrons are available. Therefore, the final helium-4 abun-
dance depends logarithmically on the baryon density and, according to (3.143),
increases by 1% or so if the baryon density is 10 times larger.
3.5.4 Deuterium
To calculate the time evolution and freeze-out abundance of deuterium, we make
a series of assumptions which drastically simplify our task. The validity of these
assumptions can be checkeda posteriori.
First, we ignore^7 Be and^7 Li because their abundances turn out to be small
compared to the abundances of^3 He and T. Second, we assume that the^3 He and
T abundances take on theirquasi-equilibrium values, that is, they are completely
determined by the condition that “the total flux coming into each corresponding
reservoir must be equal to the outgoing flux” (see Figure 3.6). Concretely, in the
case of^3 He,the amount of^3 He produced within a given time interval via DD and
Dpreactions should be equal to the amount of^3 He destroyed within the same time
in^3 HeD and^3 Henreactions.
Let us describe the primordial nucleosynthesis process once more, but this time
in greater detail. When the deuterium concentration reachesXD 10 −^2 the DD
reactions become efficient and the deuterium produced in thepnreaction is quickly
converted into^3 He and T. Thus, further deuterium accumulation stops and, in fact,
its concentration begins to decrease. As a result, neutrons are taken from thenp
reservoir and sent, without delay in the D reservoir, directly to the^3 He and T
reservoirs along the DD and Dppipes. From there they proceed through^3 HeD and
TD pipes to their final destination−the^4 He reservoir.
Not all the neutrons reach the^4 He reservoir on their first attempt; some of them
“leak out” on the way there. Concretely, neutrons are released in the reactions
DD→^3 Henand TD→^4 Henand they return to thenpreservoir. From there, they
again try to reach the^4 He reservoir. Thus, after the beginning of nucleosynthesis,
there is a steady flux of neutrons from thenpreservoir to the^4 He reservoir through
the intermediate D,^3 He and T reservoirs. The system of pipes is self-regulating and
maintains the^3 He and T concentrations in accordance with the demands of quasi-
equilibrium. To be precise, the rate of destruction of^3 He and T is proportional to
their concentrations and if, for example, the abundance of^3 He becomes larger or
smaller than the quasi-equilibrium concentration, then the size of the^3 Hen pipe
grows or shrinks respectively, and the concentration quickly returns to its quasi-
equilibrium value.