  We introduce a scenario in which the breakdown of conformal symmetry is
responsible for the acceleration of universe in the matter dominant era. In
this regard, we consider a self interacting scalar field non-minimally coupled
to the Ricci scalar and the trace of energy-momentum tensor. For a traceless
energy-momentum tensor in radiation dominant era, the coupling to matter
vanishes and we are left with a conformal invariant gravitational action of
Deser, where the universe may experience a decelerating phase in agreement with
observations. In matter dominant era, the coupling to matter no longer
vanishes, the conformal symmetry is broken down, and the matter inevitably
becomes pressureless. The corresponding field equations are obtained and it is
shown that the universe may have an accelerating phase in this era, provided
that the value of self interaction coupling constant satisfies an specific
lower bound. Moreover, we provide a reasonable solution to the coincidence
problem.
