Cosmic microwave background constraints on dark energy dynamics: Analysis beyond the power spectrum

We consider the distribution of the non-Gaussian signal induced by weak lensing on the primary total intensity cosmic microwave background (CMB) anisotropies. Our study focuses on the three point statistics exploiting a harmonic analysis based on the CMB bispectrum. By considering the three multipoles as independent variables, we reveal a complex structure of peaks and valleys determined by the reprojection of the primordial acoustic oscillations through the lensing mechanism. We study the dependence of this system on the expansion rate at the epoch in which the weak lensing power injection is relevant, probing the dark energy equation of state at redshift corresponding to the equivalence with matter or higher (w(infinity)). The variation of the latter quantity induces a geometrical feature affecting distances and growth rate of linear perturbations, acting coherently on the whole set of bispectrum coefficients, regardless of the configuration of the three multipoles. We evaluate the impact of the bispectrum observable on the CMB capability of constraining the dark energy dynamics. We perform a maximum likelihood analysis by varying the dark energy abundance, the present equation of state w(0) and w(infinity). We show that the projection degeneracy affecting a pure power spectrum analysis in total intensity is broken if the bispectrum is taken into account. For a Planck-like experiment, assuming nominal performance, no foregrounds or systematics, and fixing all the parameters except w(0), w(infinity) and the dark energy abundance, a percent and ten percent precision measure of w(0) and w(infinity) is achievable from CMB data only. The reason is the enhanced sensitivity of the weak lensing signal to the behavior of the dark energy at high redshifts, which compensates the reduced signal to noise ratio with respect to the primary anisotropies. These results indicate that the detection of the weak lensing signal by the forthcoming CMB probes may be relevant to gain insight into the dark energy dynamics at the onset of cosmic acceleration.