ON THE QUINTESSENCE SCALAR FIELD POTENTIAL

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 = p gamma/rho gamma and the quintessence, w plp are constants, it is shown that the potential for the flat case is V(phi) = Ap phi(0), sinh(B) (lambda phi), where A, B and lambda are functions of gamma and w. 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. A formula yielding the transition redshift from a decelerating to an accelerating regime is also determined and compared to the ACDM case.