Although cosmic microwave background anisotropy data alone cannot constrain simultaneously the spatial curvature and the equation of state of dark energy, CMB data provide a valuable addition to other experimental results. However computing a full CMB power spectrum with a Boltzmann code is quite slow; for instance if we want to work with many dark energy and/or modified gravity models, or would like to optimize experiments where many different configurations need to be tested, it is possible to adopt a quicker and more efficient approach. In this paper we consider the compression of the projected Planck cosmic microwave background data into four parameters, $R$ (scaled distance to last scattering surface), $l_a$ (angular scale of sound horizon at last scattering), ${\Omega }_b{h}^2$ (baryon density fraction) and $n_s$ (powerlaw index of primordial matter power spectrum), all of which can be computed quickly. We show that, although this compression loses information compared to the full likelihood, such information loss becomes negligible when more data is added. We also demonstrate that the method can be used for canonical scalar-field dark energy independently of the parametrization of the equation of state, and discuss how this method should be used for other kinds of dark energy models.

• Received 13 March 2008

DOI:https://doi.org/10.1103/PhysRevD.78.083529