Cosmological models based on a complex scalar field with a power-law potential associated with a polytropic equation of state

We construct cosmological models based on a complex scalar field with a power-law potential V = K/gamma-1 (m/h)(2 gamma)vertical bar phi vertical bar(2 gamma) associated with a polytropic equation of state P = K rho(gamma) (the potential associated with an isothermal equation of state P = rho k(B)T/m is V = mk(B)T/h(2)vertical bar phi vertical bar(2)[ln(m(2)vertical bar phi vertical bar(2)/rho(*)h(2)) - 1] and the potential associated with a logotropic equation of state P = A ln(rho/rho(P)) is V = -A[ln(m(2)vertical bar phi vertical bar(2)/h(2)rho(P)) + 1]. We consider a fast oscillation regime of "spintessence" where the equations of the problem can be simplified. We study all possible cases with arbitrary (positive and negative) values of the polytropic constant and polytropic index. The ACDM model, the Chaplygin gas model, and the Bose-Einstein condensate model are recovered as particular cases of our study corresponding to a constant potential (gamma = 0), an inverse square-law potential (gamma = -1), and a quartic potential (gamma = 2). We also derive the two-fluid representation of the Chaplygin gas model.