  The O(4)-symmetric regular instanton solutions are studied within the
framework of the Eddington-inspired-Born-Infeld gravity (EiBI). We find that
the behavior of the solution would deviate from that in Einstein gravity when
the kinetic energy of the scalar field is sufficiently large. The tunneling
probability is calculated numerically in different parameter space. We find
that the tunneling probability would increase with the Born-Infeld coupling
constant, which is assumed to be positive in this paper. Furthermore, we
discover a neck feature in the physical instanton solutions when the kinetic
energy of the scalar field is sufficiently large. This feature can be
interpreted as a Lorentzian time-like wormhole geometry formed during the
bubble materialization.
