We have considered the existence of a dependence of the entanglement entropy on the cosmological horizon surface area also in several accelerating models of the current universe both for a quintessence scalar field and for a phantom-energy scenario. It is shown that if a quintessence vacuum cosmic field is considered then, though the case for w > À1 satisfies a second law for entanglement entropy, when w < À1 such a law is violated. It is finally noted that the entanglement entropy and the distinct formulations of cosmic holography share common future surfaces which are optimal screen for the latter descriptions. [7]). Actually, entanglement entropy measures a degree of the correlation between subsystems of a given quantum system All the above results allow us to confidently extrapolate the above horizon area-entanglement entropy proportionality law to any system where quantum entanglement takes place in a cosmic space-time. The results that we are going to get later on are all consistent with that extrapolation. In fact, in this brief report we are going to extend the existence of such a dependence of entanglement entropy on the cosmological horizon surface area also in accelerating models for the current universe both for a quintessence scalar dark-energy field and for a phantom-energy scenario. It will be shown that if an usual quintessence vacuum cosmic field is considered [11], then, though the case for w > À1 (note that along this report we shall only consider an equation of state for the Universe with the perfect-fluid form p ¼ w, with p the pressure and the energy density) satisfies a second law for entanglement entropy, when w < À1 such a law would be violated. We want to estimate the entanglement entropy that corresponded to a quantum field in an accelerating spacetime which is inexorable endowed with a future event horizon where w ¼ p= is the parameter of the equation of state, a 0 and t 0 are the initial values of the scale factor and time, and the constant C is given by C ¼ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 8G=3 p , with an integration constant. We introduce then a conformal time defined by so tha
