Understanding the origin of CMB constraints on dark energy

We study the observational constraints of cosmic microwave background (CMB) temperature and polarization anisotropies on models of dark energy, with special focus on models with variation in properties of dark energy with time. We demonstrate that the key constraint from CMB observations arises from the location of acoustic peaks. An additional constraint arises from the limits on (NR) from the relative amplitudes of acoustic peaks. Further, we show that the distance to the last scattering surface is not how the CMB observations constrain the combination of parameters for models of dark energy. We also use constraints from supernova observations and show that unlike the gold and silver samples, the Supernova Legacy Survey (SNLS) sample prefers a region of parameter space that has a significant overlap with the region preferred by the CMB observations. This is a verification of a conjecture made by us in an earlier work. We discuss combined constraints from Wilkinson Microwave Anisotropy Probe 5-yr and SNLS observations. We find that models with w similar or equal to - 1 are preferred for models with a constant equation-of-state parameters. In case of models with a time-varying dark energy, we show that constraints on evolution of dark energy density are almost independent of the type of variation assumed for the equation-of-state parameter. This makes it easy to get approximate constraints from CMB observations on arbitrary models of dark energy. Constraints on models with a time-varying dark energy are predominantly due to CMB observations, with supernova constraints playing only a marginal role.