Stars as Laboratories for Fundamental Physics - MPP Theory Group

Miscellaneous Exotica 547
Table 15.1. Bounds on the present-day ĠN/G N . (Adapted from Will 1993.)
Method Ġ N /G N References
[10 −12 yr −1 ]
Laser ranging (Moon) 0 ± 10 Müller et al. (1991)
Radar ranging (Mars) −2 ± 10 Shapiro (1990)
Binary pulsar 1913+16 11 ± 11 Damour and Taylor (1991)
Spin-down PSR 0655+64 < 55 Goldman (1990)
recent discussions have also addressed the possibility of an oscillating
G N (Hill, Steinhardt, and Turner 1990; Accetta and Steinhardt 1991)
with a rate of change much faster than H. The following discussion
does not generically address such extreme model assumptions.
The G N rate of change can be tested by a detailed study of the
orbits of celestial bodies. Particularly precise data exist in the solar
system from laser ranging of the moon and radar ranging of planets,
notably by the Viking landers on Mars. Very precise orbital data
also exist beginning 1974 for the binary pulsar PSR 1913+16; among
other things its orbital decay reveals the emission of gravitational radiation.
A weaker but also less model-dependent bound can be derived
from the spin-down rate of the pulsar PSR 0655+64. These
present-day limits on ĠN/G N are summarized in Tab. 15.1; altogether
|ĠN/G N | < ∼ 20×10 −12 yr −1 is probably a safe limit. The Hubble expansion
parameter today is H 0 = h 100 km s −1 Mpc −1 = h 1.02×10 −10 yr −1
(observationally 0.4 < ∼ h < ∼ 1). Thus today |σ| < ∼ 0.2 h −1 .
15.2.2 Big-Bang Nucleosynthesis
An interesting constraint on the value of G N in the early universe arises
from the observed primordial light element abundances as first discussed
by Barrow (1978). 94 In a Friedman-Robertson-Walker model of
the universe the expansion rate is given by H 2 = (Ṙ/R)2 = 8π 3 G N ρ
in terms of the energy density ρ which, during the epoch of nucleosynthesis,
is dominated by radiation (photons, neutrinos). It is a standard
94 Apparently there is an earlier discussion of this limit by G. Steigman in an
unpublished essay for the 1976 Gravity Research Foundation Awards. Subsequent
refinements include Rothman and Matzner (1982), Accetta, Krauss, and
Romanelli (1990), Damour and Gundlach (1991), and Casas, García-Bellido, and
Quirós (1992).