Physics
Scientific paper
Aug 1982
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1982ijtp...21..665g&link_type=abstract
International Journal of Theoretical Physics, Volume 21, Issue 8-9, pp. 665-672
Physics
Scientific paper
Dirac’s large number hypothesis (LNH), in the form G/ G 0= HH {0/-1}, is applied to the matter-dominated cosmological era, using the framework of the scale covariant theory (Canuto et al., 1977). We obtain explicit expressions for R and β a as functions of R E , where R and R E are the scale factors of the cosmological Robertson-Walker metric, expressed in atomic and gravitational units, respectively, and β a is the ratio between the rates of gravitational and atomic clocks. The parameters in these expressions arebar q_0 , the deceleration parameter in gravitational units, anddot β _a ( t 0) H {0/-1} wheredot β _a ( t 0) is the present epoch value of the derivative of β a with respect to atomic time. We find that a necessary condition for the LNH to be compatible with a Robertson-Walker model is thatdot β _a ( t 0) H {0/-1}≥{2/1}. The only experimental values fordot β _a ( t 0) available at present are those based on the lengthening of the Moon’s period of revolution around the Earth, suggesting 0.86≥dot β _a ( t 0) H {0/-1}≥0.21; the more promising technique of radar ranging to the inner planets has not yet produced a value fordot β _a ( t 0). Using the lunar data, it follows that 0≤bar q_0 ≲0.42 corresponding to an open universe ( k=-1). Closed models ( k=1,bar q_0 >1/2) are not compatible with the LNH since the required values ofdot β _a ( t 0) H {0/-1} are more than an order of magnitude above the observational upper limit.
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