  A continuous transition from early Friedmann-like radiation era through to
late time cosmic acceleration passing through a long Friedmann-like matter
dominated era followed by a second phase of radiation era has been realized in
modified theory of gravity containing a combination of curvature squared term,
a linear term, a three-half term and an ideal fluid. Thus the history of cosmic
evolution is explained by modified theory of gravity singlehandedly. The second
phase of radiation-like era might provide an explanation to the hydrogen and
helium reionization at low redshift.
