Abstract
We have investigated a cosmological model of a phantom energy with a variable cosmological constant (Lambda) depending on the energy density (rho) as Lambda proportional to rho(-alpha), alpha = const. and a variable gravitational constant (G). The model requires alpha < 0 and a negative gravitational constant. The cosmological constant evolves with time as, Lambda proportional to t(-2). For omega > -1 and alpha < -1 the cosmological constant, Lambda < 0, G > 0 and rho decrease with cosmic expansion. For ordinary matter (or dark matter), i.e., omega > -1 we have -1 < alpha < 0 and beta > 0 so that G > 0 increases with time and rho decreases with time. Cosmic acceleration with dust particles is granted provided -2/3 < alpha < 0 and Lambda > 0.