We show that many independent scenarios as the ‘accelerated expansion of the universe’, ‘eternal inflation’, ‘eternally oscillating universe’, ‘nonsingular oscillating universe’, and ‘collapse of an oscillating universe’ may occur without modifying the gravity theory or introducing scalar fields of any type. This is achieved by replacing the standard Lagrangian in the Friedmann-Robertson-Walker spacetime model by an exponentially nonstandard Lagrangian which modify the Euler-Lagrange equation although the standard variational approach is used.