The Equivalence between Different Dark (Matter) Energy Scenarios

We have shown that the phenomenological models with a cosmological constant of the type $\Lambda=\beta(\frac{\ddot R}{R})$ and $\Lambda=3\alpha H^2$, where $R$ is the scale factor of the universe and $H$ is the Hubble constant, are equivalent to a quintessence model with a scalar ($\phi$) potential of the form $V\propto \phi^{-n}, n$ = constant. The equation of state of the cosmic fluid is described by these parameters ($\alpha, \beta, n$) only. The equation of state of the cosmic fluid (dark energy) can be determined by any of these parameters. The actual amount of dark energy will define the equation of state of the cosmic fluid. All of the three forms can give rise to cosmic acceleration depending the amount of dark energy in the universe.