Exact Solution in Chaotic Inflation Model with Negative Potential

New exact solution to the Einstein equations that describe the evolution of cosmological chaotic inflation model is derived. The inflation is driven by the evolution of scalar field with negative potential V() = -V₀ + 1/2m^{2 2}. This includes the solution which is exponential inflation for ₀ > > _f, and then develops smoothly towards the radiation-like evolution for < _f. The spectral indices of the scalar density n_s and the gravitational wave fluctuations n_g are computed. The value of n_s lies well inside the limits set by the cosmic background explorer satellite.