New types of inflationary universe

We investigate a range of scalar-field potentials which give rise to slow-roll inflation. The behavior of the scale factor of the Universe is derived in each case. Exact solutions are found which illustrate new types of inflationary behavior that arise when the potential is asymptotically of the form $V=V_0{\phi }^N\exp \left(A{\phi }^M\right)$. The gravitational wave and density perturbation spectral indices arising in these models are derived and discussed. We give a detailed discussion of the interrelationships between our exact solutions and approximate solutions derived in the slow-roll approximation.