Cosmic scenarios in $f(R)$ gravity: a complete evolution

The paper deals with $f(R)$ gravity theory in the background of inhomogeneous FLRW--type space time model. With proper choice of the inhomogeneous metric function it is possible to have an emergent scenario for the $f(R)$--cosmology. Explicit form of $f(R)$ is obtained for power law expansion. It has been shown that the present $f(R)$ gravity model is equivalent to some particle creation mechanism in Einstein gravity. Further a complete cosmic evolution from inflation to present late time acceleration is possible with proper continuous choices of the $f(R)$--functions. Finally, in the perspective of thermodynamical analysis a form of $f(R)$ has been evaluated using the unified first law.