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We consider the modified gravity non-minimally coupled with matter Lagrangianfor the description of early-time and late-time universe. Such $F(R)$ ($F(G)$)gravity in the absence of non-minimal coupling is viable theory which passesthe local tests and reproduces the $\Lambda$CDM era. For qualitatively similarchoice of non-minimal gravitational coupling function it is shown that theunified description of early-time inflation and late-time cosmic accelerationis possible. It is interesting that matter (scalar) which supports theinflationary era is gravitationally screened at late times. Hence, it may beeffectively invisible at current universe.

From inflation to dark energy in the non-minimal modified gravity