  We find a class of solutions for a homogeneous and isotropic universe in
which the initially expanding universe stops expanding, experiences
contraction, and then expands again (the "bounce"), in the framework of
Einstein gravity with a real scalar field without violating the null energy
condition nor encountering any singularities. Two essential ingredients for the
bouncing universe are the positive spatial curvature and the scalar potential
which becomes flatter at large field values. Depending on the initial
condition, either the positive curvature or the negative potential stops the
cosmic expansion and begins the contraction phase. The flat potential plays a
crucial role in triggering the bounce. After the bounce, the flat potential
naturally allows the universe to enter the slow-roll inflation regime, thereby
making the bouncing universe compatible with observations. If the e-folding of
the subsequent inflation is just enough, a positive spatial curvature may be
found in the future observations. Our scenario nicely fits with the creation of
the universe from nothing, which leads to the homogeneous and isotropic
universe with positive curvature. As a variant of the mechanism, we also find
solutions representing a cyclic universe.
