Dark energy records in lensed cosmic microwave background

Abstract

We consider the weak lensing effect induced by linear cosmological perturbations on the cosmic microwave background (CMB) polarization anisotropies. We find that the amplitude of the lensing peak in the BB mode power spectrum is a faithful tracer of the dark energy dynamics at the onset of cosmic acceleration. This is due to two reasons. First, the lensing power is nonzero only at intermediate redshifts between the observer and the source, keeping record of the linear perturbation growth rate at the corresponding epoch. Second, the BB lensing signal is expected to dominate over the other sources. The lensing distortion on the TT and EE spectra do exhibit a similar dependence on the dark energy dynamics, although those are dominated by primary anisotropies. We investigate and quantify the effect by means of exact tracking quintessence models, as well as parameterizing the dark energy equation of state in terms of the present value (${w}_{0}$) and its asymptotic value in the past (${w}_{\ensuremath{\infty}}$); in the interval allowed by the present constraints on dark energy, the variation of ${w}_{\ensuremath{\infty}}$ induces a significant change in the BB mode lensing amplitude. A Fisher matrix analysis, under conservative assumptions concerning the increase of the sample variance due to the lensing non-Gaussian statistics, shows that a precision of order 10% on both ${w}_{0}$ and ${w}_{\ensuremath{\infty}}$ is achievable by the future experiments probing a large sky area with angular resolution and sensitivity appropriate to detect the lensing effect on the CMB angular power spectrum; the forecast precision reaches a few percent for highly dynamic models whose dark energy abundance at the epoch when lensing is most effective is sensibly larger than the present one, i.e. for ${w}_{\ensuremath{\infty}}\ensuremath{\gtrsim}\ensuremath{-}0.5$. These results show that the CMB can probe the differential redshift behavior of the dark energy equation of state, beyond its average.