Cosmic microwave background (CMB) experiments that constrain the tensor-to-scalar ratio $r$ are now approaching the sensitivity at which delensing---removing the $B$ modes induced by the gravitational lensing of large-scale structure---is necessary. We consider the improvement in delensing that maps of large-scale structure from tomographic line intensity mapping (IM) experiments targeting $2 < z < 10$ could provide. Compared to a nominal baseline of cosmic infrared background and internal delensing at CMB-S4 sensitivity, we find that the addition of high-redshift IM data could improve delensing performance by ~11%. Achieving the requisite sensitivity in the IM data is feasible with next-generation experiments that are now being planned. However, these results are contingent on the ability to measure low-$k$ modes along the line of sight. Without these modes, IM datasets are unable to to correlate with the lensing kernel and do not aid in delensing.
One of the primary scientific targets of current and future CMB polarization experiments is the search for a stochastic background of gravity waves in the early universe. As instrumental sensitivity improves, the limiting factor will eventually be B-mode power generated by gravitational lensing, which can be removed through use of so-called delensing algorithms. We forecast prospects for delensing using lensing maps which are obtained externally to CMB polarization: either from large-scale structure observations, or from high-resolution maps of CMB temperature. We conclude that the forecasts i…
We present a first internal delensing of CMB maps, both in temperature and polarization, using the public foreground-cleaned (SMICA) Planck 2015 maps. After forming quadratic estimates of the lensing potential, we use the corresponding displacement field to undo the lensing on the same data. We build differences of the delensed spectra to the original data spectra specifically to look for delensing signatures. After taking into account reconstruction noise biases in the delensed spectra, we find an expected sharpening of the power spectrum acoustic peaks with a delensing efficiency of $29\,\%$…
The delensing procedure is an effective tool for removing lensing-induced $B$-mode polarization in the Cosmic Microwave Background to allow for deep searches of primordial $B$-modes. However, the delensing algorithm existing in the literature breaks down if the target $B$-mode signals overlap significantly with the lensing $B$-mode ($\sim 300<l<2000$) in multipole-$l$ space. In this paper, we identify the cause of the breakdown to be correlations between the input $B$-map and the deflection field estimator ($EB$). The amplitude of this bias is quantified by numerical simulations and compared t…
As confusion with lensing B-modes begins to limit experiments that search for primordial B-mode polarization, robust methods for delensing the CMB polarization sky are becoming increasingly important. We investigate in detail the possibility of delensing the CMB with the cosmic infrared background (CIB), emission from dusty star-forming galaxies that is an excellent tracer of the CMB lensing signal, in order to improve constraints on the tensor-to-scalar ratio $r$. We find that the maps of the CIB, such as current Planck satellite maps at 545 GHz, can be used to remove more than half of the le…
A detection of excess cosmic microwave background (CMB) B-mode polarization on large scales allows the possibility of measuring not only the amplitude of these fluctuations but also their scale dependence, which can be parametrized as the tensor tilt $n_T$. Measurements of this scale dependence will be hindered by the secondary B-mode polarization anisotropy induced by gravitational lensing. Fortunately, these contaminating B modes can be estimated and removed with a sufficiently good estimate of the intervening gravitational potential and a good map of CMB E-mode polarization. We present fore…
We present a demonstration of delensing the observed cosmic microwave background (CMB) B-mode polarization anisotropy. This process of reducing the gravitational-lensing generated B-mode component will become increasingly important for improving searches for the B modes produced by primordial gravitational waves. In this work, we delens B-mode maps constructed from multi-frequency SPTpol observations of a 90 deg$^2$ patch of sky by subtracting a B-mode template constructed from two inputs: SPTpol E-mode maps and a lensing potential map estimated from the $\textit{Herschel}$ $500\,μm$ map of th…
We present a new method for delensing $B$ modes of the cosmic microwave background (CMB) using a lensing potential reconstructed from the same realization of the CMB polarization (CMB internal delensing). The $B$-mode delensing is required to improve sensitivity to primary $B$ modes generated by, e.g., the inflationary gravitational waves, axion-like particles, modified gravity, primordial magnetic fields, and topological defects such as cosmic strings. However, the CMB internal delensing suffers from substantial biases due to correlations between observed CMB maps to be delensed and that used…
The B-mode polarization of the cosmic microwave background on large scales has been considered as a probe of gravitational waves from the cosmic inflation. Ongoing and future experiments will, however, suffer from contamination due to the B-modes of non-primordial origins, one of which is the lensing induced B-mode polarization. Subtraction of the lensing B-modes, usually referred to as delensing, will be required for further improvement of detection sensitivity of the gravitational waves. In such experiments, knowledge of statistical properties of the B-modes after delensing is indispensable …
The search for primordial $B$-mode polarization of the CMB is limited by the sample variance of $B$-modes produced at later times by gravitational lensing. Constraints can be improved by `delensing': using some proxy of the matter distribution to partially remove the lensing-induced $B$-modes. Current and soon-upcoming experiments will infer a matter map -- at least in part -- from the temperature anisotropies of the CMB. These reconstructions are contaminated by extragalactic foregrounds: radio-emitting galaxies, the cosmic infrared background, or the Sunyaev--Zel'dovich effects. Using the We…
Delensing is an increasingly important technique to reverse the gravitational lensing of the cosmic microwave background (CMB) and thus reveal primordial signals the lensing may obscure. We present a first demonstration of delensing on Planck temperature maps using the cosmic infrared background (CIB). Reversing the lensing deflections in Planck CMB temperature maps using a linear combination of the 545 and 857GHz maps as a lensing tracer, we find that the lensing effects in the temperature power spectrum are reduced in a manner consistent with theoretical expectations. In particular, the char…
Impacts of observational systematic errors on the lensing analysis of the cosmic microwave background (CMB) polarization are investigated by numerical simulations. We model errors of gain, angle, and pointing in observation of the CMB polarization and simulate polarization fields modulated by the errors. We discuss the response of systematics-induced $B$-modes to amplitude and spatial scale of the imposed errors and show that the results of the lensing reconstruction and delensing analysis behave according to it. It is observed that error levels expected in the near future lead to no significa…
We develop the first algorithm able to jointly compute the maximum {\it a posteriori} estimate of the Cosmic Microwave Background (CMB) temperature and polarization fields, the gravitational potential by which they are lensed, and cosmological parameters such as the tensor-to-scalar ratio, $r$. This is an important step towards sampling from the joint posterior probability function of these quantities, which, assuming Gaussianity of the CMB fields and lensing potential, contains all available cosmological information and would yield theoretically optimal constraints. Attaining such optimal con…
Using only cosmic microwave background polarization data from the POLARBEAR experiment, we measure $B$-mode polarization delensing on subdegree scales at more than $5σ$ significance. We achieve a 14% $B$-mode power variance reduction, the highest to date for internal delensing, and improve this result to 2% by applying for the first time an iterative maximum a posteriori delensing method. Our analysis demonstrates the capability of internal delensing as a means of improving constraints on inflationary models, paving the way for the optimal analysis of next-generation primordial $B$-mode experi…
Efforts to detect a primordial $B$-mode of CMB polarization generated by inflationary gravitational waves ought to mitigate the large variance associated with the $B$-modes produced by gravitational lensing, a process known as delensing. A popular approach to delensing entails building a lensing $B$-mode template by mimicking the lensing operation, either at gradient order or non-perturbatively, using high-resolution $E$-mode observations and some proxy of the lensing potential. By explicitly calculating all contributions to two-loop order in lensing to the power spectrum of $B$-modes delensed…
The next-generation CMB experiments are expected to constrain the tensor-to-scalar ratio $r$ with high precision. Delensing is an important process as the observed CMB $B$-mode polarization that contains the primordial tensor perturbation signal is dominated by a much larger contribution due to gravitational lensing. To do so successfully, it is useful to explore methods for lensing reconstruction beyond the traditional quadratic estimator (QE) (which will become suboptimal for the next-generation experiments), and the maximum a posterior estimator (which is still currently under development).…
Gravitational lensing by large-scale structure significantly impacts observations of the cosmic microwave background (CMB): it smooths the acoustic peaks in temperature and $E$-mode polarization power spectra, correlating previously uncorrelated modes; and it converts $E$-mode polarization into $B$-mode polarization. The act of measuring and removing the effect of lensing from CMB maps, or delensing, has been well studied in the context of $B$ modes, but little attention has been given to the delensing of the temperature and $E$ modes. In this paper, we model the expected delensed $T$ and $E$ …
Next generation CMB experiments such as CMB-S4 aim at measuring the CMB lensing potential at sub-percent precision where most of the constraining power will come from CMB polarization. We investigate the prospects of achieving this goal in the presence of large-scale, diffuse galactic foreground emission by using non-Gaussian sky simulations and exploit multi-frequency information to clean those. We show that, while prior to foreground cleaning, cosmological parameter estimates from the contaminated lensing potential estimation can be significantly biased, these can be successfully mitigated b…
We present a method to delens the acoustic peaks of the CMB temperature and polarization power spectra internally, using lensing maps reconstructed from the CMB itself. We find that when delensing CMB acoustic peaks with a lensing potential map derived from the same CMB sky, a large bias arises in the delensed power spectrum. The cause of this bias is that the noise in the reconstructed potential map is derived from, and hence correlated with, the CMB map when delensing. This bias is more significant relative to the signal than an analogous bias found when delensing CMB B modes. We calculate t…
The search for primordial gravitational waves in the Cosmic Microwave Background (CMB) will soon be limited by our ability to remove the lensing contamination to $B$-mode polarization. The often-used quadratic estimator for lensing is known to be suboptimal for surveys that are currently operating and will continue to become less and less efficient as instrumental noise decreases. While foregrounds can in principle be mitigated by observing in more frequency bands, progress in delensing hinges entirely on algorithmic advances. We demonstrate here a new inference method that solves this problem…
We explore the potential use of the Radio Continuum (RC) survey conducted by the Square Kilometre Array (SKA) to remove (delens) the lensing-induced B-mode polarization and thus enhance future cosmic microwave background (CMB) searches for inflationary gravitational waves. Measurements of large-scale B-modes of the CMB are considered to be the best method for probing gravitational waves from the cosmic inflation. Future CMB experiments will, however, suffer from contamination by non-primordial B-modes, one source of which is the lensing B-modes. Delensing, therefore, will be required for furth…
The primordial B-modes component of the cosmic microwave background (CMB) polarization is a promising experimental dataset to probe the inflationary paradigm. B-modes are indeed a direct consequence of the presence of gravitational waves in the early universe. However, several secondary effects in the low redshift universe will produce \textit{non-primordial} B-modes. In particular, the gravitational interactions of CMB photons with large-scale structures will distort the primordial E-modes, adding a lensing B-mode component to the primordial signal. Removing the lensing component ("delensing"…
One of the major targets for next-generation cosmic microwave background (CMB) experiments is the detection of the primordial B-mode signal. Planning is under way for Stage-IV experiments that are projected to have instrumental noise small enough to make lensing and foregrounds the dominant source of uncertainty for estimating the tensor-to-scalar ratio $r$ from polarization maps. This makes delensing a crucial part of future CMB polarization science. In this paper we present a likelihood method for estimating the tensor-to-scalar ratio $r$ from CMB polarization observations, which combines th…
The effects of gravitational lensing of the cosmic microwave background (CMB) have been measured at high significance with existing data and will be measured even more precisely in future surveys. Reversing the effects of lensing on the observed CMB temperature and polarization maps provides a variety of benefits. Delensed CMB spectra have sharper acoustic peaks and more prominent damping tails, allowing for improved inferences of cosmological parameters that impact those features. Delensing reduces $B$-mode power, aiding the search for primordial gravitational waves and allowing for lower var…
The most promising avenue for detecting primordial gravitational waves from cosmic inflation is through measurements of degree-scale CMB $B$-mode polarisation. This approach must face the challenge posed by gravitational lensing of the CMB, which obscures the signal of interest. Fortunately, the lensing effects can be partially removed by combining high-resolution $E$-mode measurements with an estimate of the projected matter distribution. For near-future experiments, the best estimate of the latter will arise from co-adding internal reconstructions (derived from the CMB itself) with external …
Delensing CMB B-modes using galaxy surveys: the effect of galaxy bias and matter clustering non-linearities
Berkeley Center for Cosmological Physics, UC Berkeley（加州大学伯克利分校宇宙学物理中心）；Department of Physics, University of California, Berkeley（加州大学伯克利分校物理系）；Lawrence Berkeley National Laboratory（劳伦斯伯克利国家实验室）；Instituto de Física de Cantabria (IFCA), CSIC-Univ. de Cantabria（坎塔布里亚物理研究所（IFCA），西班牙高等科学研究委员会-坎塔布里亚大学）
The next generation of ground-based CMB experiments aim to measure temperature and polarization fluctuations up to $\ell_{\rm max} \approx 5000$ over half of the sky. Combined with Planck data on large scales, this will provide improved constraints on primordial non-Gaussianity. However, the impressive resolution of these experiments will come at a price. Besides signal confusion from galactic foregrounds, extra-galactic foregrounds and late-time gravitational effects, gravitational lensing will introduce large non-Gaussianity that can become the leading contribution to the bispectrum covarian…
We present a constraint on the tensor-to-scalar ratio, $r$, derived from measurements of cosmic microwave background (CMB) polarization $B$-modes with "delensing," whereby the uncertainty on $r$ contributed by the sample variance of the gravitational lensing $B$-modes is reduced by cross-correlating against a lensing $B$-mode template. This template is constructed by combining an estimate of the polarized CMB with a tracer of the projected large-scale structure. The large-scale-structure tracer used is a map of the cosmic infrared background derived from Planck satellite data, while the polari…
At linear order the only expected source of a curl-like, B mode, polarization pattern in the cosmic microwave background (CMB) is primordial gravitational waves. At second-order B modes are also produced from purely scalar, density, initial conditions. Unlike B modes from primordial gravitational waves, these B modes are expected to be non-Gaussian and not independent from the temperature and gradient-like polarization, E mode, CMB anisotropies. We find that the three point function between a second-order B mode and two first-order T/E modes is a powerful probe of second-order B modes and shou…
Lensing of the CMB is an important effect, and is usually modelled by remapping the unlensed CMB fields by a lensing deflection. However the lensing deflections also change the photon path so that the emission angle is no longer orthogonal to the background last-scattering surface. We give the first calculation of the emission-angle corrections to the standard lensing approximation from dipole (Doppler) sources for temperature and quadrupole sources for temperature and polarization. We show that while the corrections are negligible for the temperature and E-mode polarization, additional large-…
We present a novel mathematical formalism that allows to easily compute the expected kinetic Sunyaev Zeldovich (kSZ) signal in intensity and polarization due to an anisotropic primordial Cosmic Microwave Background (CMB). We derive the expected intensity and polarization distortions in the direction of non-moving galaxy clusters and then we generalize our calculations for non-zero peculiar velocity. We show that, in the direction of moving clusters, low CMB multipoles impose intensity and polarization spectral distortions with different frequency dependences. The polarization signal primarily …
Cosmic polarization rotation, which may result from parity-violating new physics or the presence of primordial magnetic fields, converts $E$-mode polarization of the cosmic microwave background (CMB) into $B$-mode polarization. Anisotropic cosmic polarization rotation leads to statistical anisotropy in CMB polarization and can be reconstructed with quadratic estimator techniques similar to those designed for gravitational lensing of the CMB. At the sensitivity of upcoming CMB surveys, lensing-induced $B$-mode polarization will act as a limiting factor in the search for anisotropic cosmic polar…
Gravitational lensing of the CMB is a valuable cosmological signal that correlates to tracers of large-scale structure and acts as a important source of confusion for primordial $B$-mode polarization. State-of-the-art lensing reconstruction analyses use quadratic estimators, which are easily applicable to data. However, these estimators are known to be suboptimal, in particular for polarization, and large improvements are expected to be possible for high signal-to-noise polarization experiments. We develop a method and numerical code, $\rm{LensIt}$, that is able to find efficiently the most pr…
The lensing signals involved in CMB polarization maps have already been measured with ground-based experiments such as SPTpol and POLARBEAR, and would become important as a probe of cosmological and astrophysical issues in the near future. Sizes of polarization maps from ground-based experiments are, however, limited by contamination of long wavelength modes of observational noise. To further extract the lensing signals, we explore feasibility of measuring lensing signals from a collection of small sky maps each of which is observed separately by a ground-based large telescope, i.e., lensing r…
The primordial CMB $B$-mode search is on the spotlight of the scientific community due to the large amount of cosmological information that is encoded in the primeval signal. However, the detection of this signal is challenging from the data analysis point of view, due to the relative low amplitude compared to the foregrounds, the lensing contamination coming from the leakage of $E$-modes, and the instrumental noise. Here, we studied the viability of the detection of the primordial polarization $B$-mode with a ground-based telescope operating in the microwave low-frequency regime (i.e., from 1…
[Abridged] Recent results from the BICEP, Keck Array and Planck Collaborations demonstrate that Galactic foregrounds are an unavoidable obstacle in the search for evidence of inflationary gravitational waves in the cosmic microwave background (CMB) polarization. Beyond the foregrounds, the effect of lensing by intervening large-scale structure further obscures all but the strongest inflationary signals permitted by current data. With a plethora of ongoing and upcoming experiments aiming to measure these signatures, careful and self-consistent consideration of experiments' foreground- and lensi…
We have studied the implications of high sensitivity polarization measurements of objects from the WMAP point source catalogue made using the VLA at 8.4, 22 and 43 GHz. The fractional polarization of sources is almost independent of frequency with a median of ~2 per cent and an average, for detected sources, of ~3.5 per cent. These values are also independent of the total intensity over the narrow range of intensity we sample. Using a contemporaneous sample of 105 sources detected at all 3 VLA frequencies, we have investigated the spectral behaviour as a function of frequency by means of a 2-c…
We study the signatures of local type primordial non-Gaussianity, parametrized by $\fnl$, of scalar perturbations in CMB polarization using the probability distribution functions, Minkowski Functionals and Betti numbers. We show that the lowest order non-Gaussian deviation of the PDF of the total polarization intensity is at order $(\fnlσ)^2$. We calculate the non-Gaussian deviations of Minkowski Functionals and Betti numbers from simulated polarization maps. We find that $E$ mode polarization provides independent and equally strong constraint on $\fnl$ as temperature fluctuations. The non-Gau…
We present ECLIPSE (Efficient Cmb poLarization and Intensity Power Spectra Estimator), an optimized implementation of the Quadratic Maximum Likelihood (QML) method for the estimation of the power spectra of the Cosmic Microwave Background (CMB). This approach allows one to reduce significantly the computational costs associated to this technique, allowing to estimate the power spectra up to higher multipoles than previous implementations. In particular, for a resolution of $N_\mathrm{side}=64$, $\ell_{\mathrm{max}}=192$ and a typical Galactic mask, the number of operations can be reduced by ap…
Deep convolutional neural networks have been a popular tool for image generation and restoration. The performance of these networks is related to the capability of learning realistic features from a large dataset. In this work, we applied the problem of inpainting non-Gaussian signal, in the context of Galactic diffuse emissions at the millimetric and sub-millimetric regimes, specifically Synchrotron and Thermal Dust emission. Both of them are affected by contamination at small angular scales due to extra-galactic radio sources (the former) and to dusty star-forming galaxies (the latter). We c…
Within the framework of a flat cosmological model a propagation of an instantaneous burst of nonpolarized isotropic radiation is considered from the moment of its beginning at some initial redshift z0 to the moment of its registration now (at z=0). Thomson (Rayleigh) scattering by free electrons is considered as the only source of opacity. Spatial distributions of the mean (over directions) radiation intensity are calculated as well as angular distributions of radiation intensity and polarization at some different distances from the center of the burst. It is shown that for redshifts z0 large …
Nearby galaxy clusters can potentially induce sub-microkelvin polarization signals in the cosmic microwave background (CMB) at characteristic scales of a few arcminutes. We explore four such polarization signals induced in a rich nearby fiducial cluster and calculate the likelihood of their detection by a telescope project with capabilities such as those of the Simons Observatory (SO). In our feasibility analysis, we include instrumental noise, primordial CMB anisotropy, statistical thermal Sunyaev-Zeldovich (SZ) cluster signal, and point source confusion, assuming a few percent of the nominal…
The C-Band All-Sky Survey (C-BASS) is an experiment to image the whole sky in intensity and polarization at 5 GHz. The primary aim of C-BASS is to provide low-frequency all-sky maps of the Galactic emission which will enable accurate component separation analysis of both existing and future CMB intensity and polarization imaging surveys. Here we present an overview of the experiment and an update on the current status of observations. We present simulation results showing the expected improvement in the recovery of CMB and foreground signals when including C-BASS data as an additional low-freq…
Large-scale magnetic fields reveal themselves through diffuse synchrotron sources observed in galaxy clusters such as radio halos. Total intensity filaments of these sources have been observed in polarization as well, but only in three radio halos out of about one hundred currently known. In this paper we analyze new polarimetric Very Large Array data of the diffuse emission in the galaxy cluster Abell 523 in the frequency range 1-2 GHz. We find for the first time evidence of polarized emission on scales of ~ 2.5 Mpc. Total intensity emission is observed only in the central part of the source,…
With the increasing number of experiments dedicated to the observation of the Cosmic Microwave Background, interest on the detailed properties of the foreground Galactic emission has risen. In particular the focus is shifting towards polarized microwave emission with the goal of detecting signature from primordial gravitational waves and inflation. This review describes the Galactic polarized and unpolarized emissions in the microwave range : free-free, synchrotron, thermal dust and anomalous emission.
