Mathematics – Logic
Scientific paper
Aug 1971
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1971phrvd...4..946m&link_type=abstract
Physical Review D, vol. 4, Issue 4, pp. 946-954
Mathematics
Logic
9
Scientific paper
The Brans-Dicke (BD) cosmological equations for flat Friedmann-type expanding universes with p=ɛρ are solved parametrically for time t(z), density ρ(z), expansion parameter a(z), and scalar field λ(z). These results reduce to a previously obtained exact solution to the radiation cosmology when ɛ=13. Furthermore, asymptotically they reduce to the simple power-law solutions discussed in another paper. Moreover, it is found that in the limit as a-->0 these solutions have characteristics similar to the radiation solutions in the same limit. In particular, the result that the scalar-field energy density dominates the radiation energy density as one approaches the initial singularity may be extended to all Friedmann models in the BD theory. Finally, as t-->∞ it is found that the fractional change in the gravitational constant at the present epoch is Λ˙0<~10-11yr for a Hubble age tH=4×1017 sec and that this limit decreases with increasing pressure, becoming extremely small for a radiation cosmology. Hence, although the scalar field may be undetectable at the present epoch, if it exists it must play an important role as one approaches the initial singularity of the cosmology.
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