Constraining the dark energy dynamics with the cosmic microwave background bispectrum

Abstract

We consider the influence of the dark energy dynamics at the onset of cosmic acceleration on the cosmic microwave background (CMB) bispectrum, through the weak lensing effect induced by structure formation. We study the line of sight behavior of the contribution to the bispectrum signal at a given angular multipole l: we show that it is nonzero in a narrow interval centered at a redshift z satisfying the relation $l/r(z)\ensuremath{\simeq}{k}_{\mathrm{NL}}(z),$ where the wave number corresponds to the scale entering the nonlinear phase and r is the cosmological comoving distance. The relevant redshift interval is in the range $0.1\ensuremath{\lesssim}z\ensuremath{\lesssim}2$ for multipoles $1000\ensuremath{\gtrsim}l\ensuremath{\gtrsim}100;$ the signal amplitude, reflecting the perturbation dynamics, is a function of the cosmological expansion rate at those epochs, probing the dark energy equation of state redshift dependence independent of its present value. We provide a working example by considering tracking inverse power law and supergravity quintessence scenarios, having sensibly different redshift dynamics and respecting all the present observational constraints. For scenarios having the same present equation of state, we find that the effect described above induces a projection feature which makes the bispectra shifted by several tens of multipoles, about ten times more than the corresponding effect on the ordinary CMB angular power spectrum.