Stars as Laboratories for Fundamental Physics - MPP Theory Group

548 Chapter 15
argument to constrain ρ from the yield of 4 He and other light elements,
and thus to constrain the effective number of neutrino degrees of freedom
at nucleosynthesis (Yang et al. 1979, 1984; Olive et al. 1990; Walker
et al. 1991). Because the number of low-mass sequential neutrino families
is now known to be 3, such constraints can be translated into
constraints on the value of G N pertaining to the nucleosynthesis epoch.
An extra neutrino species would add around 15% to ρ. It appears
reasonably conservative to assume that big-bang nucleosynthesis does
not allow for a deviation of the standard number of effective neutrino
degrees of freedom by more than 1 so that G N at that time must
have been within about ±15% of its present-day value. It is possible,
however, that G N was considerably smaller if this reduction was compensated
by additional exotic degrees of freedom such as right-handed
neutrinos which increase ρ. Moreover, it was assumed that Fermi’s
constant had its present-day value at nucleosynthesis, contrary to the
speculations discussed in Sect. 15.1. Still, barring fortuitous compensating
effects, nucleosynthesis excludes an O(1) deviation of G N from
its standard value at nucleosynthesis.
This sort of result can be compared with the present-day bounds
of Sect. 15.2.1 only by assuming a specific functional form for G N (t)
which is often taken to be
G N (t) = G N (t 0 ) (t 0 /t) β , (15.1)
where t 0 refers to the present epoch. Assuming that G N at nucleosynthesis
was within ±50% of its standard value one finds |β| ∼ < 0.01 which
would imply |ĠN/G N | today ∼ < 10 −12 yr −1 , at least a factor of ten below
the present-day limits. One should keep in mind, however, that a powerlaw
variation of G N is a relatively arbitrary assumption. For example,
in scalar-tensor extensions of general relativity such as the Brans-Dicke
theory G N varies as a power law during the matter-dominated epoch
while it remains constant when radiation dominates. Either way, while
the nucleosynthesis bounds are probably somewhat more restrictive
than the celestial-mechanics ones it is interesting that the resulting
bounds |ĠN/G N | today ∼ < 1−10×10 −12 yr −1 are of the same general order
of magnitude. They leave room for a considerable variation of G N over
cosmic time scales.