Phantom Energy with Variable G and Lambda

Abstract

We have investigated a cosmological model of a phantom energy with a variable cosmological constant ($\Lambda$) depending on the energy density ($\rho$) as $\Lambda\propto \rho^{-\alpha}$, $\alpha=\rm const.$ and a variable gravitational constant ($G$). The model requires $\alpha<0$ and a negative gravitational constant. A negative gravitational constant may forbid \emph{black holes} to form a particle horizon in a background of phantom energy. This implies that black holes are naked, and consequently the \emph{Cosmic Censorship} theorem is violated. The cosmological constant evolves with time as, $\Lambda\propto t^{-2}$. 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 $\Lambda>0$.