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Register a new userCMB lensing bi-spectrum: assessing analytical predictions against full-sky lensing simulations
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Cosmic microwave background (CMB) lensing is an integrated effect whose kernel is greater than half the peak value in the range $1<z<5$. Measuring this effect offers a powerful tool to probe the large-scale structure of the Universe at high redshifts. With the increasing precision of ongoing CMB surveys, other statistics than the lensing power spectrum, in particular the lensing bi-spectrum, will be measured at high statistical significance. This will provide ways to improve the constraints on cosmological models and lift degeneracies. Following on an earlier paper, we test analytical predictions of the CMB lensing bi-spectrum against full-sky lensing simulations, and discuss their validity and limitation in detail. The tree-level prediction of perturbation theory agrees with the simulation only up to $ellsim 200$, but the one-loop order allows capturing the simulation results up to $ellsim 600$. We also show that analytical predictions based on fitting formulas for the matter bi-spectrum agree reasonably well with simulation results, although the precision of the agreement depends on the configurations and scales considered. For instance, the agreement is at the $10%$-level for the equilateral configuration at multipoles up to $ellsim2000$, but the difference in the squeezed limit raises to more than a factor of two at $ellsim2000$. This discrepancy appears to come from limitations in the fitting formula of the matter bi-spectrum. We also find that the analytical prediction for the post-Born correction to the bi-spectrum is in good agreement with the simulation. We conclude by discussing the bi-spectrum prediction in some theories of modified gravity.
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Cosmological structures grow differently in theories of gravity which are modified as compared to Einsteins General relativity (GR). Cosmic microwave background (CMB) fluctuation patterns at the last scattering surface are lensed by these structures along the photon path to the observer. The observed CMB pattern therefore keeps trace of the growth history of structures. We show that observations of the CMB lensing bi-spectrum offer an interesting way to constrain deviations from GR in a broad class of scalar-tensor theories of gravity called beyond Horndeski. We quantify how the constraints on generic parameters describing the deviations from GR depend on the effective multipole range of the analysis. Our results further indicate that an accurate nonlinear correction of the matter bi-spectrum in the modified gravity considered is necessary when the bi-spectrum is used to probe scales beyond a multipole $ell_{rm max} gtrsim 1500$. We also found that the results are insensitive to details of the implementation of the screening mechanism, at very small scales. We finally demonstrate the potential of the lensing bi-spectrum to provide a blind reconstruction of the redshift evolution of our modified gravity parameters by combining the analysis of CMB and low-z source lensing data.
We present a full-sky derivation of weak lensing observables in the Post-Friedmann (PF) formalism. Weak lensing has the characteristic of mixing small scales and large scales since it is affected by inhomogeneities integrated along the photon trajectory. With the PF formalism, we develop a modelling of lensing observables which encompasses both leading order relativistic effects and effects that are due to the fully non-linear matter distribution at small scales. We derive the reduced shear, convergence and rotation up to order $1/c^4$ in the PF approximation, accounting for scalar, vector and tensor perturbations, as well as galaxies peculiar velocities. We discuss the various contributions that break the Kaiser-Squires relation between the shear and the convergence at different orders. We pay particular attention to the impact of the frame-dragging vector potential on lensing observables and we discuss potential ways to measure this effect in future lensing surveys.
We propose a novel bias-free method for reconstructing the power spectrum of the weak lensing deflection field from cosmic microwave background (CMB) observations. The proposed method is in contrast to the standard method of CMB lensing reconstruction where a reconstruction bias needs to be subtracted to estimate the lensing power spectrum. This bias depends very sensitively on the modeling of the signal and noise properties of the survey, and a misestimate can lead to significantly inaccurate results. Our method obviates this bias and hence the need to characterize the detailed noise properties of the CMB experiment. We illustrate our method with simulated lensed CMB maps with realistic noise distributions. This bias-free method can also be extended to create much more reliable estimators for other four-point functions in cosmology, such as those appearing in primordial non-Gaussianity estimators.
Detailed measurements of the CMB lensing signal are an important scientific goal of ongoing ground-based CMB polarization experiments, which are mapping the CMB at high resolution over small patches of the sky. In this work we simulate CMB polarization lensing reconstruction for the $EE$ and $EB$ quadratic estimators with current-generation noise levels and resolution, and show that without boundary effects the known and expected zeroth and first order $N^{(0)}$ and $N^{(1)}$ biases provide an adequate model for non-signal contributions to the lensing power spectrum estimators. Small sky areas present a number of additional challenges for polarization lensing reconstruction, including leakage of $E$ modes into $B$ modes. We show how simple windowed estimators using filtered pure-$B$ modes can greatly reduce the mask-induced mean-field lensing signal and reduce variance in the estimators. This provides a simple method (used with recent observations) that gives an alternative to more optimal but expensive inverse-variance filtering.
Based on realistic simulations, we propose an hybrid method to reconstruct the lensing potential power spectrum, directly on PLANCK-like CMB frequency maps. It implies using a large galactic mask and dealing with a strong inhomogeneous noise. For l < 100, we show that a full-sky inpainting method, already described in a previous work, still allows a minimal variance reconstruction, with a bias that must be accounted for by a Monte-Carlo method, but that does not couple to the deflection field. For l>100 we develop a method based on tiling the cut-sky with local 10x10 degrees overlapping tangent planes (referred to in the following as patches). It requires to solve various issues concerning their size/position, non-periodic boundaries and irregularly sampled data after the sphere-to-plane projection. We show how the leading noise term of the quadratic lensing estimator applied onto an apodized patch can still be taken directly from the data. To not loose spatial accuracy, we developed a tool that allows the fast determination of the complex Fourier series coefficients from a bi-dimensional irregularly sampled dataset, without performing an interpolation. We show that the multi-patch approach allows the lensing power spectrum reconstruction with a very small bias, thanks to avoiding the galactic mask and lowering the noise inhomogeneities, while still having almost a minimal variance. The data quality can be assessed at each stage and simple bi-dimensional spectra build, which allows the control of local systematic errors.
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