  We consider the modified gravity non-minimally coupled with matter Lagrangian
for 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 passes
the local tests and reproduces the $\Lambda$CDM era. For qualitatively similar
choice of non-minimal gravitational coupling function it is shown that the
unified description of early-time inflation and late-time cosmic acceleration
is possible. It is interesting that matter (scalar) which supports the
inflationary era is gravitationally screened at late times. Hence, it may be
effectively invisible at current universe.
