On the Quintessence Scalar Field Potential

Understand

In this work we propose a new analytical method for determining the scalar field potential $V(\phi)$ in FRW type cosmologies containing a mixture of perfect fluid plus a quintessence scalar field.

• By assuming that the equation of state parameters of the perfect fluid, $\gamma -1 \equiv p_{\gamma}/\rho_{\gamma}$ and the quintessence, $\omega \equiv p/\rho$ are constants, it is shown that the potential for the flat case is $V(\phi) = A\rho_{\phi_{0}}\sinh^{B}(\lambda \phi)$, where $A$, $B$ and $\lambda$ are functions of $\gamma$ and $\omega$.
• This general result is a pure consequence of the Einstein field equations and the constancy of the parameters.
• Applying the same method for closed and open universes, the corresponding scalar field potentials are also explicitly obtained for a large set of values of the free parameters $\gamma$ and $\omega$.