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

Vacuum energy fluctuations, the induced cosmological constant and cosmological reconstruction in non-minimal modified gravity models