  An exact scalar field cosmological model is constructed from the exact
solution of the field equations. The solutions are exact and no approximation
like slow roll is used. The model gives inflation, solves horizon and flatness
problems. The model also gives a satisfactory estimate of present vacuum energy
density and solves cosmological constant problem of 120 orders of magnitude
discrepancy of vacuum energy density. Further, this model predicts existence of
dark matter/energy and gives an extremely accurate estimate of present energy
density of dark matter and energy. Alongwith explanations of graceful exit,
radiation era, matter domination, this model also indicates the reason for
present accelerated state of the universe. In this work a method is shown
following which one can construct an infinite number of exact scalar field
inflationary cosmological models.
