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This paper discusses the science case for a sensitive spectro-polarimetric survey of the microwave sky. Such a survey would provide a tomographic and dynamic census of the three-dimensional distribution of hot gas, velocity flows, early metals, dust, and mass distribution in the entire Hubble volume, exploit CMB temperature and polarisation anisotropies down to fundamental limits, and track energy injection and absorption into the radiation background across cosmic times by measuring spectral distortions of the CMB blackbody emission. In addition to its exceptional capability for cosmology and fundamental physics, such a survey would provide an unprecedented view of microwave emissions at sub-arcminute to few-arcminute angular resolution in hundreds of frequency channels, a data set that would be of immense legacy value for many branches of astrophysics. We propose that this survey be carried out with a large space mission featuring a broad-band polarised imager and a moderate resolution spectro-imager at the focus of a 3.5 m aperture telescope actively cooled to about 8K, complemented with absolutely-calibrated Fourier Transform Spectrometer modules observing at degree-scale angular resolution in the 10–2000 GHz frequency range. We propose two observing modes: a survey mode to map the entire sky as well as a few selected wide fields, and an observatory mode for deeper observations of regions of specific interest.

The method of weighted addition of multi-frequency maps, more commonly referred to as ıt Internal Linear Combination (ILC), has been extensively employed in the measurement of cosmic microwave background (CMB) anisotropies and its secondaries along with similar application in 21cm data analysis. Here we argue and demonstrate that ILC methods can also be applied to data from absolutely-calibrated CMB experiments to extract average-sky signals in addition to the conventional CMB anisotropies. The performance of the simple ILC method is, however, limited, but can be significantly improved by adding constraints informed by physics and existing empirical information. In recent work, a moment description has been introduced as a technique of carrying out high precision modeling of foregrounds in the presence of inevitable averaging effects. We combine these two approaches to construct a heavily constrained form of the ILC, dubbed which can be used to recover tiny monopolar spectral distortion signals in the presence of realistic foregrounds and instrumental noise. This is a first demonstration for measurements of the monopolar and anisotropic spectral distortion signals using ILC and extended moment methods. We also show that CMB anisotropy measurements can be improved, reducing foreground biases and signal uncertainties when using the While here we focus on CMB spectral distortions, the scope extends to the 21cm monopole signal and \\(B\\)-mode analysis. We briefly discuss augmentations that need further study to reach the full potential of the method.

Primordial non-Gaussianity can source \\(\\)-distortion anisotropies that are correlated with the large-scale temperature and polarization signals of the cosmic microwave background (CMB). A measurement of \\( T\\) and \\( E\\) correlations can therefore be used to constrain it on wavelengths of perturbations not directly probed by the standard CMB anisotropies. In this work, we carry out a first rigorous search for \\(\\)-type spectral distortion anisotropies with data, applying the well-tested constrained ILC component-separation method combined with the needlet framework. We reconstruct a \\(\\) map from data, which we then correlate with the CMB anisotropies to derive constraints on the amplitude \\(\\) of the local form bispectrum, specifically on the highly squeezed configurations with effective wavenumbers \\(k_s 740Mpc^-1\\) and \\(k_L 0.05Mpc^-1\\). We improve previously estimated constraints by more than an order of magnitude. This enhancement is owing to the fact that for the first time we are able to use the full multipole information by carefully controlling biases and systematic effects in the final analysis. We also for the first time incorporate constraints from measurements of \\( E\\) correlations, which further tighten the limits. A combination of the derived \\( T\\) and \\( E\\) power spectra yields \\(|| 6800\\) (95\\% c.l.) on this highly squeezed bispectrum. This is only \\( 3\\) times weaker than the anticipated constraint from alone. We show that a combination of with will improve the expected future constraint by \\( 20\\%\\) over alone. These limits can be used to constrain multi-field inflation models and primordial black hole formation scenarios, thus providing a promising novel avenue forward in CMB cosmology.

The modeling and removal of foregrounds poses a major challenge to searches for signals from inflation using the cosmic microwave background (CMB). In particular, the modeling of CMB foregrounds including various spatial averaging effects introduces multiple complications that will have to be accounted for in upcoming analyses. In this work, we introduce the generalization of the intensity moment expansion to the spin-2 field of linear polarization: the spin-moment expansion. Within this framework, moments become spin-2 objects that are directly related to the underlying spectral parameters and polarization angle distribution functions. In obtaining the required expressions for the polarization modeling, we highlight the similarities and differences with the intensity moment methods. A spinor rotation in the complex plane with frequency naturally arises from the first order moment when the signal contains both spectral parameters and polarization angle variations. Additional dependencies are introduced at higher order, and we demonstrate how these can be accounted with several illustrative examples. Our new modeling of the polarized signals reveals to be a powerful tool to model the frequency dependence of the polarization angle. As such, it can be immediately applied to numerous astrophysical situations.

Multi-frequency matched filters (MMFs) are routinely used to detect galaxy clusters from CMB data through the thermal Sunyaev-Zeldovich (tSZ) effect, leading to cluster catalogues that can be used for cosmological inference. In order to be applied, MMFs require knowledge of the cross-frequency power spectra of the noise in the maps. This is typically estimated from the data and taken to be equal to the power spectra of the data, assuming the contribution from the tSZ signal of the detections to be negligible. Using both analytical arguments and Planck-like mock observations, we show that doing so causes the MMF noise to be overestimated, inducing a loss of signal-to-noise. Furthermore, the MMF cluster observable (the amplitude \\(y_0\\) or the signal-to-noise \\(q\\)) does not behave as expected, which can potentially bias cosmological inference. In particular, the observable becomes biased with respect to its theoretical prediction and displays a variance that also differs from its predicted value. We propose an iterative MMF (iMMF) approach designed to mitigate these effects. In this approach, after a first standard MMF step, the noise power spectra are reestimated by masking the detections from the data, delivering an updated iterative cluster catalogue. Applying our iMMF to our Planck-like mock observations, we find that the aforementioned effects are completely suppressed. This leads to a signal-to-noise gain relative to the standard MMF, with more significant detections and a higher number of them, and to a cluster observable with the expected theoretical properties, thus eliminating any potential biases in the cosmological constraints.

Cosmological Birefringence (CB) is a phenomenon, caused by parity violating modifications to electrodynamics, whereby the linear polarisation angle of light changes as photons traverse a vacuum. It is possible to use a number of different analysis techniques to constrain this effect using Cosmic Microwave Background (CMB) polarisation observations. We investigate two different methods of constraining direction dependent birefringence for present and future CMB experiments including BICEP/Keck, Simons Observatory (SO), and LiteBIRD . Specifically we compare the constraints placed on anisotropic CB from a quadratic estimator technique to those derived from estimates of the \\(B\\)-mode power-spectrum for the three different experiments. The constraints derived from estimates of the \\(B\\)-mode power spectrum are found to be comparable to those derived from quadratic estimator for BICEP/Keck and SO, but not LiteBIRD due to its larger sky coverage. These forecasted upper bounds for CB are converted to constraints on primordial magnetic fields and the coupling between photons and pseudo Nambu-Goldstone bosons. Finally we show that even with the best constraints on CB, for the respective experiments, the potentially induced \\(B\\)-mode power can act as a significant contaminant in the prospective measurement of primordial \\(B\\)-modes.

The cosmological recombination radiation (CRR) is one of the inevitable \\(\\)CDM spectral distortions of the cosmic microwave background (CMB). While it shows a rich spectral structure across dm-mm wavelengths, it is also one of the smallest signals to target. Here we carry out a detailed forecast for the expected sensitivity levels required to not only detect but also extract cosmological information from the CRR in the presence of foregrounds. We use \\( CosmoSpec\\) to compute the CRR including all important radiative transfer effects and modifications to the recombination dynamics. We confirm that detections of the overall CRR signal are possible with spectrometer concepts like \\(ıt SuperPIXIE\\). However, for real exploitation of the cosmological information, a \\( 50\\) times more sensitive spectrometer is required. While extremely futuristic, this could provide independent constraints on the primordial helium abundance, \\(Y_p\\), and probe the presence of extra relativistic degrees of freedom during BBN and recombination. Significantly improving the constraints on other cosmological parameters requires even higher sensitivity (another factor of \\( 5\\)) when considering a combination of a CMB spectrometer with existing CMB data. To a large part this is due to astrophysical foregrounds which interestingly do not degrade the constraints on \\(Y_p\\) and \\(N_ eff\\) as much. A future CMB spectrometer could thus open a novel way of probing non-standard BBN scenarios, dark radiation and sterile neutrinos. In addition, inflation physics could be indirectly probed using the CRR in combination with existing and forthcoming CMB anisotropy data.

The Cosmological Recombination Radiation (CRR) is one of the guaranteed \\(\\)CDM Spectral Distortion (SD) signals. Even if very small in amplitude, it provides a direct probe of the three recombination eras, opening the path for testing one of the key pillars in our cosmological interpretation of the measured CMB anisotropies. Here we develop a new emulator, CRRfast, to quickly and accurately represent the CRR for a wide range of cosmologies, using the state-of-the-art CosmoSpec code as a reference. CRRfast has been made publicly available both as stand-alone code and as part of CLASS, thereby completing the set of \\(\\)CDM sources of SDs that can be modeled with CLASS. With this newly-developed pipeline we investigate the full constraining power of SDs within \\(\\)CDM and highlight possible future applications to experimental design optimization. Furthermore, we show that the inhomogeneous evolution of the recombination process imprints second-order contributions to the CRR spectrum, leading to a broadening and shifting of the CRR features. These second-order terms are naturally captured by the emulator and allow us to evaluate the \\(\\)CDM contributions to the average CRR as well as to illustrate the effect of perturbed recombination due to Primordial Magnetic Fields (PMFs). As it turns out, while the \\(\\)CDM variance effects can be neglected, they could be significantly enhanced in the beyond-\\(\\)CDM models. In particular in the case of PMFs we demonstrate that through these non-linear terms the parameter space relevant to the Hubble tension could be tested with future CMB spectrometers.

We present the first detailed case study using quadratic estimators (QE) to diagnose and remove systematics present in observed Cosmic Microwave Background (CMB) maps. In this work we focus on the temperature to polarization leakage. We use an iterative QE analysis to remove systematics, in analogy to de-lensing, recovering the primordial B-mode signal and the systematic maps. We introduce a new Gaussian filtering scheme crucial to stable convergence of the iterative cleaning procedure and validate with comparisons to semi-analytical forecasts. We study the limitations of this method by examining its performance both on idealized simulations and on more realistic, non-ideal simulations, where we assume varying de-lensing efficiencies. Finally, we quantify the systematic cleaning efficiency by presenting a likelihood analysis on the tensor to scalar ratio, \\(r\\), and demonstrate that the blind cleaning results in an un-biased measurement of \\(r\\), reducing the systematic induced B-mode power by nearly two orders of magnitude.

We derive full-sky, real-space operators that convert between polarization Stokes Q/U parameters and the coordinate-independent scalar E/B modes that are widely used in Cosmic Microwave Background (CMB) and cosmic shear analysis. We also derive real space operators that decompose the measured Stokes parameters into those corresponding to E-modes and B-modes respectively, without ever evaluating the scalar fields themselves. For all these real space operators we show that the kernels split naturally into angular and radial parts and we show explicitly how the radial extent of these kernels depends on the targeted band-limit. The kernels can be interpreted either as a complex convolving beam or as a Green's function when they are expressed in terms of the forward or inverse rotation Euler angles. We show that an arbitrary radial function can produce E/B-like maps, provided it vanishes at the origin and the antipodal point. These maps are simply filtered versions of the standard E/B maps. We argue that it is possible compute E/B maps in real space with a compactly-supported kernel, an approach that can guarantee the avoidance of known foreground regions and could be employed in a massively-parallel scheme at high-resolution. We show that the spin raising and lowering operators \\(^2\\)/\\(ð^2\\) are special cases of these generalized radial functions, and present their band limited versions. The spatial structure of the real space operators provides great intuition for the E/B structure of polarized, filamentary galactic foregrounds. We predict a non-zero B-mode signature that is expected from polarized filaments in the sky. This paper is the first part in a series of papers that explore real-space computation of polarization modes and their applications.