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We consider the influence of the dark energy dynamics at the onset of cosmicacceleration on the Cosmic Microwave Background (CMB) bispectrum, through theweak lensing effect induced by structure formation. We study the line of sightbehavior of the contribution to the bispectrum signal at a given angularmultipole $l$: we show that it is non-zero in a narrow interval centered at aredshift $z$ satisfying the relation $l/r(z)\simeq k_{NL}(z)$, where thewavenumber corresponds to the scale entering the non-linear phase, and $r$ isthe cosmological comoving distance. The relevant redshift interval is in therange $0.1\lsim z\lsim 2$ for multipoles $1000\gsim\ell\gsim 100$; the signalamplitude, reflecting the perturbation dynamics, is a function of thecosmological expansion rate at those epochs, probing the dark energy equationof state redshift dependence independently on its present value. We provide aworked example by considering tracking inverse power law and SUGRA Quintessencescenarios, having sensibly different redshift dynamics and respecting all thepresent observational constraints. For scenarios having the same presentequation of state, we find that the effect described above induces a projectionfeature which makes the bispectra shifted by several tens of multipoles, about10 times more than the corresponding effect on the ordinary CMB angular powerspectrum.

Constraining the dark energy dynamics with the cosmic microwave background bispectrum