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The gravitational lensing signal from the Cosmic Microwave Background is highly valuable to constrain the growth of the structures in the Universe in a clean and robust manner over a wide range of redshifts. One of the theoretical systematics for lensing reconstruction is the impact of the lensing field non-Gaussianities on its estimators. Non-linear matter clustering and post-Born lensing corrections are known to bias standard quadratic estimators to some extent, most significantly so in temperature. In this work, we explore the impact of non-Gaussian deflections on Maximum a Posteriori lensing estimators, which, in contrast to quadratic estimators, are able to provide optimal measurements of the lensing field. We show that these naturally reduce the induced non- Gaussian bias and lead to unbiased cosmological constraints in $\Lambda$CDM at CMB-S4 noise levels without the need for explicit modelling. We also test the impact of assuming a non-Gaussian prior for the reconstruction; this mitigates the effect further slightly, but generally has little impact on the quality of the reconstruction. This shows that higher-order statistics of the lensing deflections are not expected to present a major challenge for optimal CMB lensing reconstruction in the foreseeable future., Comment: 18 figures

We present $\texttt{cunusht}$, a general-purpose Python package that wraps a highly efficient CUDA implementation of the nonuniform spin-$0$ spherical harmonic transform. The method is applicable to arbitrary pixelization schemes, including schemes constructed from equally-spaced iso-latitude rings as well as completely nonuniform ones. The algorithm has an asymptotic scaling of $\mathrm{O}{(\ell_{\rm max}^3)}$ for maximum multipole $\ell_{\rm max}$ and achieves machine precision accuracy. While $\texttt{cunusht}$ is developed for applications in cosmology in mind, it is applicable to various other interpolation problems on the sphere. We outperform the fastest available CPU algorithm by a factor of up to 5 for problems with a nonuniform pixelization and $\ell_{\rm max}>4\cdot10^3$ when comparing a single modern GPU to a modern 32-core CPU. This performance is achieved by utilizing the double Fourier sphere method in combination with the nonuniform fast Fourier transform and by avoiding transfers between the host and device. For scenarios without GPU availability, $\texttt{cunusht}$ wraps existing CPU libraries. $\texttt{cunusht}$ is publicly available and includes tests, documentation, and demonstrations.

The tightest constraints on the tensor-to-scalar ratio $r$ can only be obtained after removing a substantial fraction of the lensing $B$-mode sample variance. The planned CMB-S4 experiment will remove the lensing $B$-mode signal internally by reconstructing the gravitational lenses from high-resolution observations. We document here a first lensing reconstruction pipeline able to achieve this optimally for arbitrary sky coverage. We make it part of a map-based framework to test CMB-S4 delensing performance and its constraining power on $r$, including inhomogeneous noise and two non-Gaussian Galactic polarized foreground models. The framework performs component-separation of the high-resolution maps, followed by the construction of lensing $B$-mode templates, which are then included in a parametric small-aperture maps cross-spectra-based likelihood for $r$. We find that the lensing reconstruction and framework achieve the expected performance, compatible with the target $\sigma(r) \simeq 5\cdot 10^{-4}$ in the absence of a tensor signal, after an effective removal of $92\%$ to $93\%$ of the lensing $B$-mode variance, depending on the simulation set. The code for the lensing reconstruction can also be used for cross-correlation studies with large-scale structures, lensing spectrum reconstruction, cluster lensing, or other CMB lensing-related purposes. As part of our tests we also demonstrate joint optimal reconstruction of the lensing potential with the lensing curl potential mode, second-order in the density fluctuations., Comment: 29 pages, ApJ version

Deep cosmic microwave background polarization experiments allow a very precise internal reconstruction of the gravitational lensing signal in pricinple. For this aim, likelihood-based or Bayesian methods are typically necessary, where very large numbers of lensing and delensing remappings on the sphere are sometimes required before satisfactory convergence. We discuss here an optimized piece of numerical code in some detail that is able to efficiently perform both the lensing operation and its adjoint (closely related to delensing) to arbitrary accuracy, using nonuniform fast Fourier transform technology. Where applicable, we find that the code outperforms current widespread software by a very wide margin. It is able to produce high-resolution maps that are accurate enough for next-generation cosmic microwave background experiments on the timescale of seconds on a modern laptop. The adjoint operation performs similarly well and removes the need for the computation of inverse deflection fields. This publicly available code enables de facto efficient spherical harmonic transforms on completely arbitrary grids, and it might be applied in other areas as well., Comment: 8 pages, 3 figures, final A&A

PICO is a concept for a NASA probe-scale mission aiming to detect or constrain the tensor to scalar ratio $r$, a parameter that quantifies the amplitude of inflationary gravity waves. We carry out map-based component separation on simulations with five foreground models and input $r$ values $r_{in}=0$ and $r_{in} = 0.003$. We forecast $r$ determinations using a Gaussian likelihood assuming either no delensing or a residual lensing factor $A_{\rm lens}$ = 27%. By implementing the first full-sky, post component-separation, map-domain delensing, we show that PICO should be able to achieve $A_{\rm lens}$ = 22% - 24%. For four of the five foreground models we find that PICO would be able to set the constraints $r < 1.3 \times 10^{-4} \,\, \mbox{to} \,\, r <2.7 \times 10^{-4}\, (95\%)$ if $r_{in}=0$, the strongest constraints of any foreseeable instrument. For these models, $r=0.003$ is recovered with confidence levels between $18\sigma$ and $27\sigma$. We find weaker, and in some cases significantly biased, upper limits when removing few low or high frequency bands. The fifth model gives a $3\sigma$ detection when $r_{in}=0$ and a $3\sigma$ bias with $r_{in} = 0.003$. However, by correlating $r$ determinations from many small 2.5% sky areas with the mission's 555 GHz data we identify and mitigate the bias. This analysis underscores the importance of large sky coverage. We show that when only low multipoles $\ell \leq 12$ are used, the non-Gaussian shape of the true likelihood gives uncertainties that are on average 30% larger than a Gaussian approximation., Comment: 34 pages, 13 figures, published in JCAP

This Snowmass 2021 White Paper describes the Cosmic Microwave Background Stage 4 project CMB-S4, which is designed to cross critical thresholds in our understanding of the origin and evolution of the Universe, from the highest energies at the dawn of time through the growth of structure to the present day. We provide an overview of the science case, the technical design, and project plan., Comment: Contribution to Snowmass 2021. arXiv admin note: substantial text overlap with arXiv:1908.01062, arXiv:1907.04473

SCYNet (SUSY Calculating Yield Net) is a tool for testing supersymmetric models against LHC data. It uses neural network regression for a fast evaluation of the profile likelihood ratio. Two neural network approaches have been developed: one network has been trained using the parameters of the 11-dimensional phenomenological Minimal Supersymmetric Standard Model (pMSSM-11) as an input and evaluates the corresponding profile likelihood ratio within milliseconds. It can thus be used in global pMSSM-11 fits without time penalty. In the second approach, the neural network has been trained using model-independent signature-related objects, such as energies and particle multiplicities, which were estimated from the parameters of a given new physics model. While the calculation of the energies and particle multiplicities takes up computation time, the corresponding neural network is more general and can be used to predict the LHC profile likelihood ratio for a wider class of new physics models., Comment: 19 pages, 15 figures; References added for V2, version submitted to EPJC