Fluctuations of the Gravitational Constant Induced by Primordial Bubbles

We consider the classical fluctuations of the gravitational constant generated by bubbles in the inflationary universe. For extended inflation, we demonstrate numerically how and how large fluctuations are produced during bubble expansion. The amplitude of the fluctuations depends on the Brans-Dicke parameter $\omega$: if $\omega$ is of the order of unity, the amplitude becomes of the order of unity within one Hubble expansion time; if $\omega$ is large (say, $\omega =1000$), the growth rate of the fluctuations is small, but it keeps growing without freezing during inflation. We also discuss some astrophysical implications of our results.