The method of weighted addition of multi-frequency maps, more commonly referred to as {\it 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 \milc, 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 \milc. 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.
We propose a new internal linear combination (ILC) method in the pixel space, applicable on large angular scales of the sky, to estimate a foreground minimized Cosmic Microwave Background (CMB) temperature anisotropy map by incorporating prior knowledge about the theoretical CMB covariance matrix. Usual ILC method in pixel space, on the contrary, does not use any information about the underlying CMB covariance matrix. The new approach complements the usual pixel space ILC technique specifically at low multipole region, using global information available from theoretical CMB covariance matrix a…
We extend the ILC method in harmonic space to include the error in its CMB estimate. This allows parameter estimation routines to take into account the effect of the foregrounds as well as the errors in their subtraction in conjunction with the ILC method. Our method requires the use of a model of the foregrounds which we do not develop here. The reduction of the foreground level makes this method less sensitive to unaccounted for errors in the foreground model. Simulations are used to validate the calculations and approximations used in generating this likelihood function.
The Cosmic Microwave Background (CMB) radiation B mode polarization signal contains the unique signature of primordial metric perturbations produced during the inflation. The separation of the weak CMB B-mode signal from strong foreground contamination in observed maps is a complex task, and proposed new generation low noise satellite missions compete with the weak signal level of this gravitational background. In this article, for the first time, we employ a foreground model-independent internal linear combination (ILC) method to reconstruct the CMB B mode signal using simulated observations …
The `Internal Linear Combination' (ILC) component separation method has been extensively used on the data of the WMAP space mission, to extract a single component, the CMB, from the WMAP multifrequency data. We extend the ILC approach for reconstructing millimeter astrophysical emissions beyond the CMB alone. In particular, we construct a Constrained ILC to extract clean maps of both the CMB or the thermal Sunyaev Zeldovich (SZ) effect, with vanishing contamination from the other. The performance of the Constrained ILC is tested on simulations of Planck mission observations, for which we succe…
The WMAP 7-year temperature maps have been re-analized to extract a CMB map and CMB power spectrum with reduced contamination by astrophysical foregrounds and noise. The method used is based on linear combinations of WMAP data and foreground templates, implemented on a decomposition of the observations onto a needlet frame. We obtain a clean CMB map with low contamination from foregrounds and noise, as well as a new estimate of the CMB temperature power spectrum. The latter is essentially compatible with the power spectrum published by the WMAP collaboration, although it is slightly but system…
We report an improved technique for diffuse foreground minimization from Cosmic Microwave Background (CMB) maps using a new multi-phase iterative internal-linear-combination (ILC) approach in harmonic space. The new procedure consists of two phases. In phase 1, a diffuse foreground cleaned map is obtained by performing a usual ILC operation in the harmonic space in a single iteration over the desired portion of the sky. In phase 2, we obtain the final foreground cleaned map using an iterative ILC approach also in the harmonic space, however, now, during each iteration of foreground minimizatio…
In this work, we formalize a new technique to investigate joint posterior density of Cosmic Microwave Background (CMB) signal and its theoretical angular power spectrum given the observed data, using the global internal-linear-combination (ILC) method first proposed by Sudevan & Saha (2017). We implement the method on low resolution CMB maps observed by WMAP and Planck satellite missions, using Gibbs sampling, assuming that the detector noise is negligible on large angular scales of the sky. The main products of our analysis are best fit CMB cleaned map and its theoretical angular power spectr…
In this article we present a formalism to incorporate the partial-sky maps to the Gibbs ILC algorithm to estimate the joint posterior density of the Cosmic Microwave Background (CMB) signal and the theoretical CMB angular power spectrum given the observed CMB maps. In order to generate the partial-sky maps we mask all the observed CMB maps provided by WMAP and Planck satellite mission using a Gaussian smoothed mask formed on the basis of thermal dust emissions in Planck 353 GHz map. The central galactic region from all the input maps is removed after the application of the smoothed mask. While…
In the recent years, the internal-linear-combination (ILC) method was investigated extensively in the context of reconstruction of Cosmic Microwave Background (CMB) temperature anisotropy signal using observations obtained by WMAP and Planck satellite missions. In this article, we, for the first time, apply the ILC method to reconstruct the large scale CMB E mode polarization signal, which serves as the unique probe of ionization history of the Universe, using simulated observations of 15 frequency CMB polarization maps of future generation COrE satellite mission. We find that usual ILC cleane…
Residual error in calibration coefficients corresponding to observed CMB maps is an important issue while estimating a pure CMB signal. A component separation method, if these errors in the input foreground contaminated CMB maps are not properly taken into account, may lead to bias in the cleaned CMB map and estimated CMB angular power spectrum. But the inability to exactly determine the calibration coefficients corresponding to each observed CMB map from any CMB experiment makes it very difficult to incorporate their exact and actual values in a component separation analysis. Hence the effect…
Internal Linear Combination (ILC) methods are some of the most widely used multi-frequency cleaning techniques employed in CMB data analysis. These methods reduce foregrounds by minimizing the total variance in the coadded map (subject to a signal-preservation constraint), although often significant foreground residuals or biases remain. A modification to the ILC method is the constrained ILC (cILC), which explicitly nulls certain foreground components; however, this foreground nulling often comes at a high price for ground-based CMB datasets, with the map noise increasing significantly on sma…
A detection or non detection of primordial non--Gaussianity (NG) by using the cosmic microwave background radiation (CMB) is a possible way to break the degeneracy of early universe models. Since a single statistical estimator hardly can be sensitive to all possible forms of NG which may be present in the data, it is important to use different statistical estimators to study NG in CMB. Recently, two new large-angle NG indicators based on skewness and kurtosis of spherical caps or spherical cells of CMB sky have been proposed and used in both CMB data and simulated maps. Here, we make a compara…
The separation of emissions from different astrophysical processes is an important step towards the understanding of observational data. This topic of component separation is of particular importance in the observation of the relic Cosmic Microwave Background Radiation, as performed by the WMAP satellite and the more recent Planck mission, launched May 14th, 2009 from Kourou and currently taking data. When performing any sort of component separation, some assumptions about the components must be used. One assumption that many techniques typically use is knowledge of the frequency scaling of on…
Scattering of cosmic microwave background (CMB) radiation in galaxy clusters induces polarization signals determined by the quadrupole anisotropy in the photon distribution at the location of clusters. This "remote quadrupole" derived from the measurements of the induced polarization in galaxy clusters provides an opportunity of reconstruction of local CMB temperature anisotropies. In this {\em Letter} we develop an algorithm of the reconstruction through the estimation of the underlying primordial gravitational potential, which is the origin of the CMB temperature and polarization fluctuation…
Primordial magnetic fields present since before the epoch of matter-radiation equality have an effect on the anisotropies of the cosmic microwave background. The CMB anisotropies due to scalar perturbations are calculated in the gauge invariant formalism for magnetized adiabatic initial conditions. Furthermore the linear matter power spectrum is calculated. Numerical solutions are complemented by a qualitative analysis.
This PhD thesis (defended in 2014) is focused on the estimation of the CMB polarised anisotropies power spectra on a masked sky and on forecasts of constraints set on the primordial universe physics thanks to these anisotropies. After an introduction on the light polarisation, the standard model of cosmology and the CMB properties, I show the results obtained on the use and efficiency of pseudospectrum methods to correct for the so-called E-to-B leakage. Afterwards, I present the forecasts obtained on the detection of the tensor-to-scalar ratio r and on the detection of chiral gravity, using t…
Galactic foregrounds are the main obstacle to observations of the cosmic microwave background (CMB) $B$-mode polarization. In addition to obscuring the inflationary $B$-mode signal by several orders of magnitude, Galactic foregrounds have non-trivial spectral signatures that are partially unknown and distorted by averaging effects along the line-of-sight, within the pixel/beam window, and by various analysis choices (e.g., spherical harmonic transforms and filters). Statistical moment expansion methods provide a powerful tool for modeling the effective Galactic foreground emission resulting fr…
We estimate Cosmic Microwave Background (CMB) polarisation power spectra, and temperature-polarisation cross-spectra, from the 9-year data of the Wilkinson Microwave Anisotropy Probe (WMAP). Foreground cleaning is implemented using minimum variance linear combinations of the coefficients of needlet decompositions of sky maps for all WMAP channels, to produce maps for CMB temperature anisotropies (T-mode) and polarisation (E-mode and B-mode), for 9 different years of observation. The final power spectra are computed from averages of all possible cross-year power spectra obtained using foregroun…
The 'Internal Linear Combination' (ILC) component separation method has been extensively used to extract a single component, the CMB, from the WMAP multifrequency data. We generalise the ILC approach for separating other millimetre astrophysical emissions. We construct in particular a multidimensional ILC filter, which can be used, for instance, to estimate the diffuse emission of a complex component originating from multiple correlated emissions, such as the total emission of the Galactic interstellar medium. The performance of such generalised ILC methods, implemented on a needlet frame, is …
CMB component-separated power spectrum estimation by Spectral Internal Linear Combination (SpILC)
University of Cambridge（剑桥大学）；Kavli Institute for Cosmology Cambridge（卡弗里宇宙学剑桥研究所）；Center for Computational Astrophysics, Flatiron Institute（纽约市立大学富尔顿计算天体物理中心）；Astrophysics Group, Cavendish Laboratory（卡文迪许实验室天体物理学组）
We obtain the non-linear generalization of the Sachs-Wolfe + integrated Sachs-Wolfe (ISW) formula describing the CMB temperature anisotropies. Our formula is valid at all orders in perturbation theory, is also valid in all gauges and includes scalar, vector and tensor modes. A direct consequence of our results is that the maps of the logarithmic temperature anisotropies are much cleaner than the usual CMB maps, because they automatically remove many secondary anisotropies. This can for instance, facilitate the search for primordial non-Gaussianity in future works. It also disentangles the non-…
We investigate the contribution of cosmic string loops to the Cosmic Microwave Background (CMB) anisotropies. This is done by extending the Unconnected Segment Model (USM) to include the contribution of the cosmic string loops created throughout the cosmological evolution of a cosmic string network to the stress-energy tensor. We then implement this extended USM in the publicly available CMBACT code and obtain the linear CDM power spectrum and the CMB angular power spectra generated by cosmic string loops. We find that the shape of the angular power spectra generated by loops is, in general, s…
We consider the impact of a stochastic background of primordial magnetic fields with non-vanishing helicity on CMB anisotropies in temperature and polarization. We compute the exact expressions for the scalar, vector and tensor part of the energy-momentum tensor including the helical contribution, by assuming a power-law dependence for the spectra and a comoving cutoff which mimics the damping due to viscosity. We also compute the parity-odd correlator between the helical and non-helical contribution which generate the TB and EB cross-correlation in the CMB pattern. We finally show the impact …
We propose a framework of Finsler space-time to explain the observed parity asymmetry and the power deficit in the low-$\ell$ ($2\leqslant \ell \leqslant 29$) multipole range of cosmic microwave background (CMB) temperature anisotropies. In the $3+1$ dimensional space-time, the three-dimensional space is described by a Randers-Finsler space, which is spatially irreversible, inducing the parity asymmetry in the CMB angular power spectrum. We estimate the constraints on the two parameters introduced by Finsler space-time via analyzing the low-$\ell$ angular power spectrum in PLANCK 2015 CMB temp…
Multi-field inflation models and non-Bunch-Davies vacuum initial conditions both predict sizeable non-Gaussian primordial perturbations and anisotropic $μ$-type spectral distortions of the cosmic microwave background (CMB) blackbody. While CMB anisotropies allow us to probe non-Gaussianity at wavenumbers $k\simeq 0.05\,{\rm Mpc^{-1}}$, $μ$-distortion anisotropies are related to non-Gaussianity of primordial perturbation modes with much larger wavenumbers, $k\simeq 740\,{\rm Mpc^{-1}}$. Through cross-correlations between CMB and $μ$-distortion anisotropies, one can therefore shed light on the a…
The primordial magnetic fields (PMFs) produced in the early universe are expected to be the origin of the large-scale cosmic magnetic fields. The PMFs are considered to leave a footprint on the cosmic microwave background (CMB) anisotropies due to both the electromagnetic force and gravitational interaction. In this paper, we investigate how the PMFs affect the CMB anisotropies on smaller scales than the mean-free-path of the CMB photons. We solve the baryon Euler equation with Lorentz force due to the PMFs, and we show that the vector-type perturbations from the PMFs induce the CMB anisotropi…
Anisotropies in distortions to the frequency spectrum of the cosmic microwave background (CMB) can be created through spatially varying heating processes in the early Universe. For instance, the dissipation of small-scale acoustic modes does create distortion anisotropies, in particular for non-Gaussian primordial perturbations. In this work, we derive approximations that allow describing the associated distortion field. We provide a systematic formulation of the problem using Fourier-space window functions, clarifying and generalizing previous approximations. Our expressions highlight the fac…
We study the effects of pre-recombination physics on the Stochastic Gravitational Wave Background (SGWB) anisotropies induced by the propagation of gravitons through the large-scale density perturbations and their cross-correlation with Cosmic Microwave Background (CMB) temperature and E-mode polarization ones. As examples of Early Universe extensions to the $Λ$CDM model, we consider popular models featuring extra relativistic degrees of freedom, a massless non-minimally coupled scalar field, and an Early Dark Energy component. Assuming the detection of a SGWB, we perform a Fisher analysis to …
Observations of the temperature anisotropies induced as light from the CMB passes through large scale structures in the late universe are a sensitive probe of the interactions of photons in such environments. In extensions of the Standard Model which give rise to mini-charged particles, photons propagating through transverse magnetic fields can be lost to pair production of such particles. Such a decrement in the photon flux would occur as photons from the CMB traverse the magnetic fields of galaxy clusters. Therefore late time CMB anisotropies can be used to constrain the properties of mini-c…
CMB photons passing through a collapsing texture knot receive an energy shift, creating characteristic cold and hot spots on the sky. We calculate the anisotropy pattern produced by collapsing texture knots of arbitrary shape. The texture dynamics are solved numerically on a Minkowski background.
We investigate models where structure formation is initiated by scaling seeds: We consider rapidly expanding relativistic shells of energy and show that they can fit current CMB and large scale structure data if they expand with super-luminal velocities. These acausally expanding shells provide a viable alternative to inflation for cosmological structure formation with the same minimal number of parameters to characterize the initial fluctuations. Causally expanding shells alone cannot fit present data. Hybrid models where causal shells and inflation are mixed also provide good fits.
For 2442 galaxies of the catalog, compiled based on the NED, SDSS, and CATS survey data with redshifts z, > 0.3 we conducted an analysis of the amplitude of temperature fluctuations in the cosmic microwave background (CMB) in the points, corresponding to the direction to these objects. To this end, we used the ILC map from the WMAP mission seven-year data release. We have estimated the dipole component of the background and tested the hypothesis of Kashlinsky on the existence of a "dark bulk flow", determined for the estimated dipole component of the CMB WMAP by the value of the CMB anisotropy…
While the arcminute-scale Cosmic Microwave Background (CMB) anisotropies are due to secondary effects, point sources dominate the total anisotropy power spectrum. At high frequencies the point sources are primarily in the form of dusty, star-forming galaxies. Both Herschel and Planck have recently measured the anisotropy power spectrum of cosmic infrared background (CIB) generated by dusty, star-forming galaxies from degree to sub-arcminute angular scales, including the non-linear clustering of these galaxies at multipoles of 3000 to 6000 relevant to CMB secondary anisotropy studies. We scale …
Mirror dark matter is a dissipative and self-interacting multiparticle dark matter candidate which can explain the DAMA, CoGeNT and CRESST-II direct detection experiments. This explanation requires photon-mirror photon kinetic mixing of strength $ε\sim 10^{-9}$. Mirror dark matter with such kinetic mixing can potentially leave distinctive signatures on the CMB anisotropy spectrum. We show that the most important effect of kinetic mixing on the CMB anisotropies is the suppression of the height of the third and higher odd peaks. If $ε\stackrel{>}{\sim} 10^{-9}$ then this feature can be observed …
Genetic Algorithm (GA) -- motivated by natural evolution -- is a robust method to estimate the global optimal solutions of problems involving multiple objective functions. In this article, for the first time, we apply GA to reconstruct the CMB temperature anisotropy map over large angular scales of the sky using (internal) linear combination (ILC) of the final-year WMAP and Planck satellite observations. To avoid getting trapped into a local minimum, we implement the GA with generous diversity in the populations by selecting pairs with diverse fitness coefficients and by introducing a small bu…
Searching for the signal of primordial gravitational waves in the B-modes (BB) power spectrum is one of the key scientific aims of the cosmic microwave background (CMB) polarization experiments. However, this could be easily contaminated by several foreground issues, such as the thermal dust emission. In this paper we study another mechanism, the cosmic birefringence, which can be introduced by a CPT-violating interaction between CMB photons and an external scalar field. Such kind of interaction could give rise to the rotation of the linear polarization state of CMB photons, and consequently i…
The Internal Linear Combination (ILC) is widely used to extract the cosmic microwave background (CMB) signal from multi-frequency observation maps, especially for Satellite experiments with quasi-full sky coverage. We extend ILC method to CMB polarization map analysis with a small sky patch which is especially typical for ground-based experiments, by combing ILC with a template cleaning method which can give pure $B$ map free from $EB$ leakage caused by partial sky coverage. The feature of our methods is that we do the ILC analysis on pseudo-scalar $B$ maps, and the advantage is that it totall…
Extragalactic foregrounds in Cosmic Microwave Background (CMB) temperature maps lead to significant biases in CMB lensing reconstruction if not properly accounted for. Combinations of multi-frequency data have been used to minimize the overall map variance (internal linear combination, or ILC), or specifically null a given foreground, but these are not tailored to CMB lensing. In this paper, we derive an optimal multi-frequency combination to jointly minimize CMB lensing noise and bias. We focus on the standard lensing quadratic estimator, as well as the "shear-only" and source-hardened estima…
The anisotropies of the cosmic microwave background (CMB) are computed for the half-turn space E_2 which represents a compact flat model of the Universe, i.e. one with finite volume. This model is inhomogeneous in the sense that the statistical properties of the CMB depend on the position of the observer within the fundamental cell. It is shown that the half-turn space describes the observed CMB anisotropies on large scales better than the concordance model with infinite volume. For most observer positions it matches the temperature correlation function even slightly better than the well studi…
Bulk motions of electrons along the line of sight induce secondary temperature fluctuations in the post-decoupling, reionized universe. In the presence of a magnetic field not only the scalar mode but also the vector mode act as a source for the bulk motion. The resulting angular power spectrum of temperature anisotropies of the cosmic microwave background is calculated assuming a simple model of reionization.Contributions from the standard adiabatic, curvature mode and a non helical magnetic field are included. The contribution due to magnetic fields with field strengths of order nG and negat…
We point out that if quantum field renormalization is taken into account the predictions of slow-roll inflation for both the scalar and tensorial power spectra change significantly for wavelengths that today are at observable scales
We analyze the alignment of the low multipoles (quadrupole and octupole) of various maps of the WMAP 5yr release: the CMB maps obtained with ILC and MCMC methods, the CMB map in the V band after foreground reduction, and, for comparison, the (not cleaned) V band map. We study how much this alignment is polluted by residuals on the Galactic region. Among the considered maps, the WMAP-ILC turns out to be the most clean map from the point of view of the proposed test. This result has been found studying the redistribution (due to the masking process) of each bin of the probability distribution fu…
The cosmic microwave background (CMB) anisotropies in spherical 3-spaces with a non-trivial topology are studied. This paper discusses the special class of the so-called double-action manifolds, which are for the first time analysed with respect to their CMB anisotropies. The CMB anisotropies are computed for all prism double-action manifolds generated by a binary dihedral and a cyclic group with a group order of up to 180 leading to 33 different topologies. Several spaces are found which show a suppression of the CMB anisotropies on large angular distances as it is found on the real CMB sky. …
As well as primary fluctuations, CMB temperature maps contain a wealth of additional information in the form of secondary anisotropies. Secondary effects that can be identified with individual objects, such as the thermal and kinetic Sunyaev-Zel'dovich (SZ) effects due to galaxy clusters, are difficult to unambiguously disentangle from foreground contamination and the primary CMB however. We develop a Bayesian formalism for rigorously characterising anisotropies that are localised on the sky, taking the TSZ and KSZ effects as an example. Using a Gibbs sampling scheme, we are able to efficientl…
The cosmic microwave background (CMB) temperature anisotropies from primordial magnetic fields are studied. In addition to the known passive and the compensated mode we discuss an inflationary magnetic mode in the curvature perturbation, present when magnetic fields are generated during inflation. This mode is absent if the generation mechanism is causal, e.g. a phase transition. We compute and discuss the effect of this mode on the observed CMB anisotropy spectrum, in comparison with the passive and compensated ones. We find that it dominates the CMB anisotropy, and consequently leads to stro…
We present constraints on the patchy reionization by measuring the trispectrum of the Planck 2015 cosmic microwave background (CMB) temperature anisotropies. The patchy reionization leads to anisotropies in the CMB optical depth, and the statistics of the observed CMB anisotropies is altered. We estimate the trispectrum of the CMB temperature anisotropies to constrain spatial variation of the optical depth. We show that the measured trispectrum is consistent with that from the standard lensed CMB simulation at $2σ$. While no evidence of the patchy reionization is found in the Planck 2015 tempe…
We study Gravitational Waves (GWs) in the context of Massive Gravity, an extension to General Relativity (GR) where the fluctuations of the metric have a nonzero mass, and specifically investigate the effect of the tensor modes on the Cosmic Microwave Background (CMB) anisotropies. We first study the time evolution of the tensor modes in Massive Gravity and show that there is a graviton mass limit $m_l=10^{-66}g\sim 10^{-29}cm^{-1}$, so that for masses $m\leq m_l$ the tensor perturbations in Massive Gravity are indistinguishable from the corresponding ones in GR. Also, we show that short wavel…
Spectral distortions and anisotropies of the CMB provide independent and complementary probes to study energy injection processes in the early universe. Here we discuss the synergy between these observables, and show the promising future of spectral distortion missions to constrain both exotic and non-exotic energy injections. We show that conventional probes such as Big Bang Nucleosynthesis and CMB anisotropies can benefit from and even be surpassed by future spectral distortion experiments. For this, we have implemented a unified framework within the Boltzmann code CLASS to consistently trea…
We review the theory of the temperature anisotropy and polarization of the cosmic microwave background (CMB) radiation, and describe what we have learned from current CMB observations. In particular, we discuss how the CMB is being used to provide precise measurements of the composition and geometry of the observable universe, and to constrain the physics of the early universe. We also briefly review the physics of the small-scale CMB fluctuations generated during and after the epoch of reionization, and which are the target of a new breed of arcminute-resolution instruments.
The weak lensing effect on the cosmic microwave background (CMB) induces distortions in spatial pattern of CMB anisotropies, and statistical properties of CMB anisotropies become a weakly non-Gaussian field. We first summarize the weak lensing effect on the CMB (CMB lensing) in the presence of scalar, vector and tensor perturbations. Then we focus on the lensing effect on CMB statistics and methods to estimate deflection angles and their power spectrum. We end by summarizing recent observational progress and future prospect.
Observational searches for large-scale vorticity modes in the late time Universe are underexplored. Within the standard $Λ$CDM model, this is well motivated given the observed properties of the cosmic microwave background (CMB). However, this means that searches for cosmic vorticity modes can serve as a powerful consistency test of our cosmological model. We show that through combining CMB measurements of the kinetic Sunyaev-Zel'dovich and the moving lens effects with galaxy survey data we can constrain vorticity fields independently from the large scale cosmic velocity field. This approach ca…
Measurements of the cosmic microwave background (CMB) spectral distortions (SDs) will open a new window on the very early universe, providing new information complementary to that gathered from CMB temperature and polarization anisotropies. In this paper, we study their synergy as a function of the characteristics of the considered experiments. In particular, we examine a wide range of sensitivities for possible SD measurements, spanning from FIRAS up to noise levels 1000 times better than PIXIE, and study their constraining power when combined with current or future CMB anisotropy experiments…
