Avoidance of big rip in phantom cosmology by gravitational back reaction

The effects of the gravitational back reaction of cosmological perturbations are investigated in a cosmological model where the universe is dominated by phantom energy. We assume a COBE normalized spectrum of cosmological fluctuations at the present time and calculate the effective energy-momentum tensor of the gravitational back-reactions of cosmological perturbations whose wavelengths at the time when the back-reactions are evaluated are larger than the Hubble radius. Our results reveal that the effects of gravitational back-reactions will counteract that of phantom energy sooner or later and can become large enough to terminate the phantom dominated phase before the big rip as the universe evolves. This arises because the phase space of infrared modes grows very rapidly as we come close to the big rip