Chinese Acad Sci, Inst High Energy Phys, Beijing 100039, Peoples R China
; Brown Univ, Dept Phys, Providence, RI 02912 USA
We study the effects of gravitational back reaction in models of quintessence. The effective energy-momentum tensor with which cosmological fluctuations back react on the background metric will in some cases lead to a termination of the phase of acceleration. The fluctuations we make use of are the perturbations in our present Universe. Their amplitude is normalized by recent measurements of anisotropies in the cosmic microwave background; their slope is taken to be either scale invariant or characterized by a slightly blue tilt. In the latter case, we find that the back-reaction effect of fluctuations whose present wavelength is smaller than the Hubble radius but which are stretched beyond the Hubble radius by the accelerated expansion during the era of quintessence domination can become large. Since the back-reaction effects of these modes oppose acceleration, back reaction will lead to a truncation of the period of quintessence domination. This result impacts on the recent discussions of the potential incompatibility between string theory and quintessence.