An inflationary universe in Brans-Dicke theory: a hopeful sign of theoretical estimation of the gravitational constant

A revised model of the inflationary universe under the framework of Brans-Dicke theory is proposed. It is shown that the scale factor of the universe during the inflation varies as R approximately t^w+1/2 and not exponentially, but still it gives rise to enough inflation to solve the cosmological puzzles. It is found that the quantum gravity effects come into play in the same scale as that of grand unified theories (i.e. at T approximately 10¹⁴ GeV) rather than at T approximately 10¹⁹ GeV, hence providing a natural solution to the 'milder version' of the flatness problem inherent in the conventional inflationary scenarios. This scenario also provides a simple way to estimate theoretically the present value of the gravitational constant. The estimated value agrees well with the actual value despite many approximations and the ignorance of quantum gravity; the difference is only by a factor of the order of 10^-2.