  We propose a 3 + 1 dimensional model of gravity which results in inflation at
early times, followed by radiation- and matter-dominated epochs and a
subsequent acceleration at late times. Both the inflation and late time
acceleration are nearly de Sitter with a large hierarchy between the effective
cosmological constants. There is no scalar field agent of inflation, and the
transition from the inflation to the radiation-dominated period is smooth. This
model is designed so that it yields, at the cost of giving up on Lorentz
invariance in the gravitational sector, the Dirac-Born-Infeld type conformal
scalar theory when the universe is conformally flat. It, however, resembles
Einstein's gravity with the Gibbons-Hawking-York boundary term in weakly curved
space-times.
