Tracking dark energy with the integrated Sachs-Wolfe effect: Short and long-term predictions

We present an analysis of the constraining power of future measurements of the integrated Sachs-Wolfe (ISW) effect on models of the equation of state of dark energy as a function of redshift, w(z). To achieve this, we employ a new parametrization of w, which utilizes the mean value of w(z) (< w >) as an explicit parameter. This helps to separate the information contained in the estimation of the distance to the last scattering surface (from the cosmic microwave background (CMB)) from the information contained in the ISW effect. We then use Fisher analysis to forecast the expected uncertainties in the measured parameters from future ISW observations for two models of dark energy with very different time evolution properties. For example, we demonstrate that the cross correlation of Planck CMB data and large synoptic survey telescope (LSST) galaxy catalogs will provide competitive constraints on w(z), compared to a supernovae acceleration probe (SNAP)-like supernovae (SNe) project, for models of dark energy with a rapidly changing equation of state (e.g. Kink models). Our work confirms that, while SNe measurements are more suitable for constraining variations in w(z) at low redshift, the ISW effect can provide important independent constraints on w(z) at high z.