Abstract
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 ΛCDM 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.
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