  We consider here a spherically symmetric but inhomogeneous universe filled
with a massless scalar field. The model obeys two constraints. The first one is
that the gradient of the scalar field is timelike everywhere. The second
constraint is that the radial coordinate basis vector is a unit vector field in
the comoving coordinate system. We find that the resultant dynamical solutions
compose a one-parameter family of self-similar models which is known as the
Roberts solution. The solutions are divided into three classes. The first class
consists of solutions with only one spacelike singularity in the
synchronous-comoving chart. The second class consists of solutions with two
singularities which are null and spacelike, respectively. The third class
consists of solutions with two spacelike singularities which correspond to the
big bang and big crunch, respectively. We see that, in the first case, a
comoving volume exponentially expands as in an inflationary period; the fluid
elements are accelerated outwards form the symmetry center, even though the
strong energy condition is satisfied. This behavior is very different from that
observed in the homogeneous and isotropic universe in which the fluid elements
would move outwards with deceleration, if the strong energy conditions are
satisfied. We are thus able to achieve the accelerated expansion of the
universe for the models considered here, without a need to violate the energy
conditions. The cosmological features of the models are examined in some
detail.
