explanations for the cosmic acceleration, the different being the approach with $f(R)$ gravity, where $R$ is the scalar curvature. Other forms of $R$ along with $R$ in the Lagrangian can explain the observed acceleration without considering other additional components (the review [@f71] is useful). Among other existing theories $f(R)$ gravity models can be shown to be compatible with a matter dominated epoch transiting into an accelerating phase [@f88]. Also the forms of $f(R)$ with positive powers of curvature support the inflationary epoch and forms with negative powers of curvature serve as the effective DE responsible for cosmic acceleration and compatible with solar system experiments [@f89]. Also it is worth mentioning that these models face some challenges in the line of argument discussed in [@asph1; @asph2; @asphadd1; @asphadd2; @f103].

The idea that the uncertainty principle could be affected by gravity was given by Mead [@new19]. In the regime when the gravity is strong enough, conventional Heisenberg uncertainty relation is no longer satisfactory (though approximately but perfectly valid in low gravity regimes). Later modified commutation relations between position and momenta commonly known as Generalized Uncertainty Principle (GUP) were given by candidate theories of quantum gravity (String Theory, Doubly Special Relativity Theory and 