Inflation of small true vacuum bubble by quantization of
  Einstein-Hilbert action
  We study the quantization of the Einstein-Hilbert action for a small true
vacuum bubble without matter or scalar field. The quantization of action
induces an extra term of potential called quantum potential in Hamilton-Jacobi
equation, which gives expanding solutions including the exponential expansion
solutions of the scalar factor $a$ for the bubble. We show that exponential
expansion of the bubble continues with a short period (about a Planck time
$t_p$), no matter whether the bubble is closed, flat or open. The exponential
expansion ends spontaneously when the bubble becomes large, i.e., the scalar
factor $a$ of the bubble approaches a Planck length $l_p$. We show that it is
quantum potential of the small true vacuum bubble that plays the role of the
scalar field potential suggested in the slow-roll inflation model. With the
picture of quantum tunneling, we calculate particle creation rate during
inflation, which shows that particles created by inflation have the capability
of reheating the universe.
