  In this letter, it is obtained using dual role of the Ricci scalar (physical
as well as geometrical role of the Ricci scalar curvature) in a natural way
without any input in the theory for it. In contrast to other models, where an
idea for dark energy is introduced in the beginning of the theory, here it
emerges from the gravitational sector spontaneously.Dark energy density,
obtained in this model,decreases with scale factor $a(t)$ as $\sim a(t)^{- 3 (1
+ {\rm w}_{\rm de})}$ explaining fall of its value from $1.19 \times 10^{75}
{\rm GeV}^4$ at Planck scale to its present value suggested by recent
experiments. Interestingly, apart from dark energy, dark radiation and dark
matter are also obtained from gravity sector.Moreover, time for transition from
deceleration to acceleration is evaluated. It is found that if dark energy
obeys equation of state for generalized Chaplygin gas and barotropic fluid
simultaneously, evolution of scale factor depends on $cosh (t - t_*)$ ($t$ and
$t_*$ being time and transition time respectively), but after a finite time
expansion will become de-Sitter like.
