We use the lensing potential map from Planck CMB lensing reconstruction analysis and the "Public Cosmic Void Catalog" to measure the stacked void lensing potential. In this profile, four parameters are needed to describe the shape of voids with different characteristic radii R V . However, we have found that after reducing the background noise by subtracting the average background, there is a residue lensing power left in the data. The inclusion of the environment shifting parameter, γ V , is necessary to get a better fit to the data with the residue lensing power. We divide the voids into two redshift bins: cmass1 (0.45 < z < 0.5) and cmass2 (0.5 < z < 0.6). Our best-fit parameters are α = 1.989 ± 0.149, β = 12.61 ± 0.56, δ c = −0.697 ± 0.025, R S /R V = 1.039 ± 0.030, γ v = (−7.034 ± 0.150) × 10 −2 for the cmass1 sample with 123 voids and α = 1.956 ± 0.165, β = 12.91 ± 0.60, δ c = −0.673 ± 0.027, R S /R V = 1.115 ± 0.032, γ v = (−4.512 ± 0.114) × 10 −2 for the cmass2 sample with 393 voids at 68% C.L. The addition of the environment parameter is consistent with the conjecture that the Sloan Digital Sky Survey voids reside in an underdense region.

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.Comment: 8 pages, 5 figures, accepted for publication in Physical Review

Bursts of particle production during inflation provide a well-motivated mechanism for creating bump-like features in the primordial power spectrum. Current data constrains these features to be less than about 5% the size of the featureless primordial power spectrum at wavenumbers of about 0.1 h Mpc −1 . We forecast that the Planck cosmic microwave background experiment will be able to strengthen this constraint to the 0.5% level. We also predict that adding data from a square kilometer array (SKA) galaxy redshift survey would improve the constraint to about the 0.1% level. For features at larger wave-numbers, Planck will be limited by Silk damping and foregrounds. While, SKA will be limited by non-linear effects. We forecast for a Cosmic Inflation Probe (CIP) galaxy redshift survey, similar constraints can be achieved up to about a wavenumber of 1.0 h Mpc −1 .PACS numbers: