In the model where Primordial Black Holes (PBHs) form from large primordial curvature (C) perturbations, i.e., CPBHs, constraints on PBH abundance provide in principle constraints on the primordial curvature power spectrum. This connection however depends necessarily on the details of PBH formation mechanism. In this paper we provide, for the first time, constraints on the primordial curvature power spectrum from the latest limits on PBH abundance, taking into account all the steps from gravitational collapse in real space to PBH formation. In particular, we use results from numerical relativity simulations and peak theory to study the conditions for PBH formation for a range of perturbation shapes, including nonlinearities, perturbation profile and a careful treatment of smoothing and filtering scales. We then obtain updated PBH formation conditions and translate that into primordial spectrum constraints for a wide range of shapes and abundances. These updated constraints cover a range of scales not probed by other cosmological observables. Our results show that the correct and accurate modelling of non-linearities, filtering and typical perturbation profile, is crucial for deriving meaningful cosmological implications.

We study the cosmic variance limit on constraining primordial non-Gaussianity for a variety of theory-motivated shapes. We consider general arguments for 2D and 3D surveys, with a particular emphasis on the CMB. A scale-invariant N-point correlator can be measured with a signal-to-noise that naively scales with the square root of the number of observed modes. This intuition generally fails for two reasons. First, the signal-to-noise scaling is reduced due to the blurring of the last scattering surface at short distances. This blurring is caused by the combination of projection and damping, but the loss of signal is not due to exponential decay, as both signal and noise are equally damped. Second, the behavior of the N-point correlator in the squeezed and collapsed (for N > 3) limits can enhance the scaling of the signal-to-noise with the resolution, even with a reduced range of momenta probing these limits. We provide analytic estimates for all N-point correlators. We show that blurring affects equilateral-like shapes much more than squeezed ones. We discuss under what conditions the optimistic scalings in the collapsed limit can be exploited. Lastly, we confirm our analytical estimates with numerical calculations of the signal-to-noise for local, orthogonal and equilateral bispectra, and local trispectra. We also show that adding polarization to intensity data enhances the scaling for equilateral-like spectra.

We introduce and validate a delensing framework for the Simons Observatory (SO), which will be used to improve constraints on inflationary gravitational waves by reducing the lensing noise in measurements of the B modes in CMB polarization. SO will initially observe CMB by using three small aperture telescopes and one large-aperture telescope. While polarization maps from small-aperture telescopes will be used to constrain inflationary gravitational waves, the internal CMB lensing maps used to delens will be reconstructed from data from the large-aperture telescope. Since lensing maps obtained from the SO data will be noise dominated on subdegree scales, the SO lensing framework constructs a template for lensinginduced B modes by combining internal CMB lensing maps with maps of the cosmic infrared background from Planck as well as galaxy density maps from the LSST survey. We construct a likelihood for constraining the tensor-to-scalar ratio r that contains auto and cross spectra between observed B modes and the lensing B-mode template. We test our delensing analysis pipeline on map-based simulations containing survey nonidealities, but that, for this initial exploration, does not include contamination from Galactic and extragalactic foregrounds. We find that the SO survey masking and inhomogeneous and atmospheric noise have very little impact on the delensing performance, and the r constraint becomes σðrÞ ≈ 0.0015 which is close to that obtained from the idealized forecasts in the absence of the Galactic foreground and is nearly a factor of 2 tighter than without delensing. We also find that uncertainties in the external large-scale structure tracers used in our multitracer delensing pipeline lead to bias much smaller than the 1σ statistical uncertainties.