Inflation with a Negative Cosmological Constant
  We find a unique way of realizing inflation through cyclic phases in an
universe with negative vacuum energy. According to the second law of
thermodynamics entropy monotonically increases from cycle to cycle, typically
by a constant factor. This means that the scale factor at the same energy
density in consecutive cycles also increases by a constant factor. If the time
period of the oscillations remain approximately constant then this leads to an
``over all'' exponential growth of the scale factor, mimicking inflation. A
graceful exit from this inflationary phase is possible as a dynamical scalar
field can take us from the negative to a positive energy vacuum during the last
contracting phase.
