  Exact analytic solutions for a class of scalar-tensor gravity theories with a
hyperbolic scalar potential are presented. Using an exact solution we have
successfully constructed a model of inflation that produces the spectral index,
the running of the spectral index and the amplitude of scalar perturbations
within the constraints given by the WMAP 7 years data. The model simultaneously
describes the Big Bang and inflation connected by a specific time delay between
them so that these two events are regarded as dependent on each other. In
solving the Fridemann equations, we have utilized an essential Weyl symmetry of
our theory in 3+1 dimensions which is a predicted remaining symmetry of
2T-physics field theory in 4+2 dimensions. This led to a new method of
obtaining analytic solutions in 1T field theory which could in principle be
used to solve more complicated theories with more scalar fields. Some
additional distinguishing properties of the solution includes the fact that
there are early periods of time when the slow roll approximation is not valid.
Furthermore, the inflaton does not decrease monotonically with time, rather it
oscillates around the potential minimum while settling down, unlike the slow
roll approximation. While the model we used for illustration purposes is
realistic in most respects, it lacks a mechanism for stopping inflation. The
technique of obtaining analytic solutions opens a new window for studying
inflation, and other applications, more precisely than using approximations.
