Cosmological parameter constraints from CMB lensing with cosmic voids

We investigate the potential of using cosmic voids as a probe to constrain cosmological parameters through the gravitational lensing effect of the cosmic microwave background (CMB) and make predictions for the next generation surveys. By assuming the detection of a series of $\approx 5 - 10$ voids along a line of sight within a square-degree patch of the sky, we found that they can be used to break the degeneracy direction of some of the cosmological parameter constraints (for example $\omega_b$ and $\Omega_\Lambda$) in comparison with the constraints from random CMB skies with the same size area for a survey with extensive integration time. This analysis is based on our current knowledge of the average void profile and analytical estimates of the void number function. We also provide combined cosmological parameter constraints between a sky patch where series of voids are detected and a patch without voids (a randomly selected patch). The full potential of this technique relies on an accurate determination of the void profile to $\approx 10$% level. For a small-area CMB observation with extensive integration time and a high signal-to-noise ratio, CMB lensing with such series of voids will provide a complementary route to cosmological parameter constraints to the CMB observations. Example of parameter constraints with a series of five voids on a $1.0^{\circ} \times 1.0^{\circ}$ patch of the sky are $100\omega_b = 2.20 \pm 0.27$, $\omega_c = 0.120 \pm 0.022$, $\Omega_\Lambda = 0.682 \pm 0.078$, $\Delta_{\mathcal{R}}^2 = \left(2.22 \pm 7.79\right) \times 10^{-9}$, $n_s = 0.962 \pm 0.097$ and $\tau = 0.925 \pm 1.747$ at 68% C.L.