  The one-loop effective action for non-minimal scalar modified gravity on de
Sitter background with a constant scalar field is found. The corresponding
induced cosmological constant is evaluated. It is shown that quantum effects in
non-minimal modified gravity may induce an early-time de Sitter universe even
in the situation when such solution does not occur on the classical level.
Classical reconstruction of the theory is presented in such a way that the
resulting theory has a cosmological solution unifying early-time inflation with
late-time acceleration.
