  A detailed study of quantum and semiclassical Euclidean wormholes for
Einstein's theory with a minimally coupled scalar field has been performed for
a class of potentials. Massless, constant, massive (quadratic in the scalar
field) and inverse (linear) potentials admit Hawking and Page wormhole boundary
condition both in the classically forbidden and allowed regions. Inverse
quartic potential has been found to exhibit semiclassical wormhole
configuration. Classical wormholes under suitable back-reaction leading to a
finite radius of the throat, where strong energy condition is satisfied, have
been found for the zero, constant, quadratic and exponential potentials.
Treating such classical Euclidean wormholes as initial condition, late stage of
cosmological evolution has been found to remain unaltered from standard
Friedmann cosmology, except for the constant potential which under
back-reaction produces a term like negative cosmological constant.
