Cosmic microwave background tests of inflation

Future observations of cosmic microwave background (CMB) polarisation have the potential to answer some of the most fundamental questions of modern physics and cosmology, including: what physical process gave birth to the Universe we see today? What are the dark matter and dark energy that seem to constitute 95% of the energy density of the Universe? Do we need extensions to the standard model of particle physics and fundamental interactions? Is the ΛCDM cosmological scenario correct, or are we missing an essential piece of the puzzle? In this paper, we list the requirements for a future CMB polarisation survey addressing these scientific objectives, and discuss the design drivers of the COREmfive space mission proposed to ESA in answer to the “M5” call for a medium-sized mission. The rationale and options, and the methodologies used to assess the mission's performance, are of interest to other future CMB mission design studies. COREmfive has 19 frequency channels, distributed over a broad frequency range, spanning the 60–600 GHz interval, to control astrophysical foreground emission. The angular resolution ranges from 2′ to 18′, and the aggregate CMB sensitivity is about 2 μK⋅arcmin. The observations are made with a single integrated focal-plane instrument, consisting of an array of 2100 cryogenically-cooled, linearly-polarised detectors at the focus of a 1.2-m aperture cross-Dragone telescope. The mission is designed to minimise all sources of systematic effects, which must be controlled so that no more than 10−4 of the intensity leaks into polarisation maps, and no more than about 1% of E-type polarisation leaks into B-type modes. COREmfive observes the sky from a large Lissajous orbit around the Sun-Earth L2 point on an orbit that offers stable observing conditions and avoids contamination from sidelobe pick-up of stray radiation originating from the Sun, Earth, and Moon. The entire sky is observed repeatedly during four years of continuous scanning, with a combination of three rotations of the spacecraft over different timescales. With about 50% of the sky covered every few days, this scan strategy provides the mitigation of systematic effects and the internal redundancy that are needed to convincingly extract the primordial B-mode signal on large angular scales, and check with adequate sensitivity the consistency of the observations in several independent data subsets. COREmfive is designed as a “near-ultimate” CMB polarisation mission which, for optimal complementarity with ground-based observations, will perform the observations that are known to be essential to CMB polarisation science and cannot be obtained by any other means than a dedicated space mission. It will provide well-characterised, highly-redundant multi-frequency observations of polarisation at all the scales where foreground emission and cosmic variance dominate the final uncertainty for obtaining precision CMB science, as well as 2′ angular resolution maps of high-frequency foreground emission in the 300–600 GHz frequency range, essential for complementarity with future ground-based observations with large telescopes that can observe the CMB with the same beamsize.

The contribution of one loop milli-charged fermion vacuum polarization in cosmic magnetic field to the cosmic microwave background (CMB) polarization is considered. Exact and perturbative solution of the density matrix equations of motion in terms of the Stokes parameters are presented. For linearly polarized CMB at decoupling time, it is shown that propagation of CMB photons in cosmic magnetic field would generate elliptic polarization (circular and linear) of the CMB due to milli-charged fermion vacuum polarization. Analytic expressions for the degree of circular polarization and rotation angle of polarization plane of the CMB are presented. Depending on the ratio of milli-charged fermion relative charge to mass, $\epsilon/m_\epsilon$, and CMB observation frequency, it is shown that the acquired CMB degree of circular polarization could be of the order of magnitude $P_C(T_0)\sim 10^{-10}- 10^{-6}$ in the best scenario. The effect studied generates CMB polarization even in the case when the CMB is initially in thermal equilibrium. Limits on the magnetic field amplitude due to prior decoupling CMB polarization are presented.

A stochastic gravitational wave background (SGWB) would gravitationally lens the cosmic microwave background (CMB) photons. We correct the results provided in existing literature for modifications to the CMB polarization power spectra due to lensing by gravitational waves. Weak lensing by gravitational waves distorts all four CMB power spectra; however, its effect is most striking in the mixing of power between the E mode and B mode of CMB polarization. This suggests the possibility of using measurements of the CMB angular power spectra to constrain the energy density (Ω(GW)) of the SGWB. Using current data sets (QUAD, WMAP, and ACT), we find that the most stringent constraints on the present Ω(GW) come from measurements of the angular power spectra of CMB temperature anisotropies. In the near future, more stringent bounds on Ω(GW) can be expected with improved upper limits on the B modes of CMB polarization. Any detection of B modes of CMB polarization above the expected signal from large scale structure lensing could be a signal for a SGWB.

The polarization of the cosmic microwave background (CMB) is widely recognized as a potential source of information about primordial gravitational waves. The gravitational wave contribution can be separated from the dominant CMB polarization created by density perturbations at the times of recombination and reionization because it generates both E and B polarization modes, whereas the density perturbations create only E polarization. The limits of our ability to measure gravitational waves are thus determined by statistical and systematic errors from CMB experiments, foregrounds, and nonlinear evolution effects such as gravitational lensing of the CMB. Usually it is assumed that most foregrounds can be removed because of their frequency dependence, however Thomson scattering of the CMB quadrupole by electrons in the Galaxy or nearby structures shares the blackbody frequency dependence of the CMB. If the optical depth from these nearby electrons is anisotropic, the polarization generated can include B modes even if no tensor perturbations are present. We estimate this effect for the Galactic disk and nearby extragalactic structures, and find that it contributes to the B polarization at the level of similar to(1-2) x 10(-4) mu K per logarithmic interval in multipole l for l < 30. This is well below the detectability level even for a future CMB polarization satellite and hence is negligible. Depending on its structure and extent, the Galactic corona may be a source of B-modes comparable to the residual large-scale lensing B-mode after the latter has been cleaned using lensing reconstruction techniques. For an extremely ambitious post-Planck CMB experiment, Thomson scattering in the Galactic corona is thus a potential contaminant of the gravitational wave signal; conversely, if the other foregrounds can be cleaned out, such an experiment might be able to constrain models of the corona.

The coming flood of CMB polarization experiments, spurred by the recent detection of CMB polarization by DASI and WMAP, will be confronted by many new analysis tasks specific to polarization. For the analysis of CMB polarization data sets, the devil is truly in the details. With this in mind, we present the details of the data analysis for the POLAR experiment, which recently led to the tightest upper limits on the polarization of the Cosmic Microwave Background Radiation at large angular scales. We discuss the data selection process, mapmaking algorithms, offset removal, and the likelihood analysis which were used to find upper limits on the polarization. Stated using the modern convention for reporting CMB Stokes parameters, these limits are 5.0 \uK on both E-type and B-type polarization at 95% confidence. Finally, we discuss simulations used to test our analysis techniques and to probe the fundamental limitations of the experiment.

Tangled, primordial cosmic magnetic fields create small rotational velocity perturbations on the last scattering surface (LSS) of the cosmic microwave background radiation (CMBR). Such perturbations can contribute significantly to the CMBR temperature and polarization anisotropies at large l > 1000 or so, like the excess power detected by the Cosmic Background Imager (CBI) experiment. The magnetic contribution can be distinguished from most conventional signals, as they lead to CMBR polarization dominated by the odd-parity, B-type signal. Experiments like the Degree Angular Scale Interferometer (DASI) and the Wilkinson Microwave Anisotropy Probe (WMAP) have detected evidence for CMBR polarization at low l. Many experiments will also probe the large l regime. Therefore we calculate the polarization signals due to primordial magnetic fields for different spectra and different cosmological parameters. A scale-invariant spectrum of tangled fields which redshifts to a present value of B0= 3 × 10−9 G produces B-type polarization anisotropies of ∼0.3–0.4 μK between l∼ 1000 and 5000. Larger signals result if the spectral index of magnetic tangles is steeper, n > −3. The peak of the signal shifts to larger l for a Λ-dominated universe or if the baryon density is larger. The signal will also have non-Gaussian statistics. We also predict the much smaller E-type polarization and T–E cross-correlations for these models.

One of the key steps in Cosmic Microwave Background (CMB) data analysis is component separation to recover the CMB signal from multi-frequency observations contaminated by foreground emissions. Needlet Internal Linear Combination (NILC) is one of the successful methods that applies the minimum variance estimation technique to a set of needlet-filtered frequency maps to recover CMB. In this work, we develop a deep convolutional neural network (CNN) model to recover CMB temperature map from needlet-filtered frequency maps over the full sky. The network operates on a multi-resolution representation of spherical data, capturing localised features in both pixel and harmonic space, and is designed to preserve the rotational invariance of the CMB signal. The network model is trained on realistic simulations at Planck frequencies, which include CMB temperature maps generated using cosmological parameters sampled within a 2σ standard deviation around the Planck best-fit values. We demonstrate the network performance for simulations that exhibit different foreground complexities. The recovered CMB temperature map closely follows the true signal with some residual leakage near the Galactic plane. The TT power spectrum is accurately reconstructed up to multipoles of approximately ℓ ∼ 1100. A minor residual systematics remain at smaller scales. Compared to the NILC method, the network shows reduced residual foreground contamination in the recovered CMB map. Once validated on the simulations, the network is applied to Planck PR3 intensity data. The resulting CMB map is consistent with the CMB maps from the Planck legacy products, including those produced using the NILC and SMICA pipelines. This work demonstrates a powerful component separation method to clean spherical signal data from multi-resolution wavelet-filtered maps.

Inflation predicts a stochastic background of gravitational waves over a broad range of frequencies, from those accessible with cosmic microwave background (CMB) measurements, to those accessible directly with gravitational-wave detectors, like NASA's Big-Bang Observer (BBO), currently under study. In a previous paper [Phys. Rev. D 73, 023504 (2006)] we connected CMB constraints to the amplitude and tensor spectral tilt of the inflationary gravitational-wave background (IGWB) at BBO frequencies for four classes of models of inflation by directly solving the inflationary equations of motion. Here we extend that analysis by including results obtained in the Wilkinson Microwave Anisotropy Probe third-year data release as well as by considering two additional classes of inflationary models. As often noted in the literature, the recent indication that the primordial density power spectrum has a red spectral index implies (with some caveats) that the amplitude of the IGWB may be large enough to be observable in the CMB polarization. Here we also explore the implications for the direct detection of the IGWB.

Future measurements of the polarization of the cosmic microwave background (CMB) are very powerful tools for cosmological studies and may help in extracting cosmological parameters from the observational data. In particular, the polarization is quite sensitive to the presence of primordial gravitational waves. In this talk we analyse the geometrical and statistical properties of the polarization of the CMB. This analysis was performed in our recent work. Singular points of the vector field which describes CMB polarization are found and classified. A possible signature of primordial gravitational waves in CMB polarization is discussed. We also discuss some other new methods of analysis of CMB anisotropy and polarization.

We model the effect of photon and ultra-light pseudoscalar mixing on the propagation of electromagnetic radiation through the extragalactic medium. The medium is modelled as a large number of magnetic domains, uncorrelated with one another. We obtain an analytic expression for the different Stokes parameters in the limit of small mixing angle. The different Stokes parameters are found to increase linearly with the number of domains. We also verify this result by direct numerical simulations. We use this formalism to estimate the effect of pseudoscalar-photon mixing on the Cosmic Microwave Background (CMB) polarization. We impose limits on the model parameters by the CMB observations. We find that the currently allowed parameter range admits a CMB circular polarization up to order $10^{-7}$.

In this work, the use of a calibration satellite (L2-CalSat) flying in formation with a Cosmic Microwave Background (CMB) polarization mission in an orbit located at the second Lagrange point, is proposed. The new generation of CMB telescopes are expected to reach unprecedented levels of sensitivity to allow a very precise measurement of the B-mode of polarization, the curl-like polarization component expected from gravitational waves coming from Starobinski inflationary models. Due to the CMB polarized signal weakness, the instruments must be subjected to very precise calibration processes before and after launching. Celestial sources are often used as external references for calibration after launch, but these sources are not perfectly characterized. As a baseline option, L2-CalSat is based on the CubeSat standard and serves as a perfectly known source of a reference signal to reduce polarization measurements uncertainty. A preliminary design of L2-CalSat is described and, according to the scanning strategy followed by the telescope, the influence of the relative position between the spacecrafts in the calibration process is studied. This new calibration element will have a huge impact on the performance of CMB space missions, providing a significant improvement in the measurements accuracy without requiring new and costly technological developments.

Recent Chandra observations have revealed the presence of cold fronts in many clusters of galaxies. The cold fronts are believed to be produced by the bulk motions of massive, dense, cold gas clouds with respect to the hotter, more rarefied ambient gas at velocities that can be as high as the speed of sound. This phenomenon may produce a significant contamination of both the kinetic Sunyaev-Zel'dovich (SZ) effect and the cosmic microwave background (CMB) polarization pattern observed in the direction of a cluster. We estimate the contributions to the kinetic SZ effect and to the CMB polarization toward galaxy clusters produced by the bulk motions of the gas in the inner parts of galaxy clusters. The observed cold fronts probe the absolute velocities of the gas motion, while the induced polarization and the kinetic SZ effect probe the transverse and the radial components, respectively. We show that these signals may be easily detected with sensitive future experiments, opening an exciting new window for studies of galaxy cluster internal dynamics and eventually facilitating reconstruction of the intrinsic cluster polarization of the CMB and the associated measure of the local CMB quadrupole.

The contribution from the residuals of the foreground can have a significant impact on the temperature maps of the Cosmic Microwave Background (CMB). Mostly, the focus has been on the galactic plane, when foreground cleaning has taken place. However, in this paper, we will investigate the possible foreground contamination, from sources outside the galactic plane in the CMB maps. We will analyze the correlation between the Faraday rotation map and the CMB temperature map. The Faraday rotation map is dependent on the galactic magnetic field, as well as the thermal electron density, and both may contribute to the CMB temperature. We find that the standard deviation for the mean cross correlation deviate from that of simulations at the 99.9% level. Additionally, a comparison between the CMB temperature extrema and the extremum points of the Faraday rotation is also performed, showing a general overlap between the two. Also we find that the CMB Cold Spot is located at an area of strong negative cross correlation, meaning that it may be explained by a galactic origin. Further, we investigate nearby supernova remnants in the galaxy, traced by the galactic radio loops. These super nova remnants are located at high and low galactic latitude, and thus well outside the galactic plane. We find some correlation between the Faraday Rotation and the CMB temperature, at select radio loops. This indicate, that the galactic foregrounds may affect the CMB, at high galactic latitudes

\n A new map of the sky representing the degree of randomness in the cosmic microwave background (CMB) temperature has been obtained. The map based on estimation of the Kolmogorov stochasticity parameter clearly distinguishes the contribution of the Galactic disk from the CMB and reveals regions of various degrees of randomness that can reflect the properties of inhomogeneities in the Universe. For example, among the high randomness regions is the southern non-Gaussian anomaly, the Cold Spot, with a stratification expected for the voids. Existence of its counterpart, a Northern Cold Spot with almost identical randomness properties among other low-temperature regions is revealed. By its informative power, Kolmogorov's map can be complementary to the CMB temperature and polarization sky maps.\n\n\n

Multifield 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 aforementioned inflation models. We investigate the ability of a future CMB satellite imager like LiteBIRD to measure μT and μE cross-power spectra between anisotropic μ-distortions and CMB temperature and E-mode polarization anisotropies in the presence of foregrounds, and derive LiteBIRD forecasts on ${f_{\rm NL}^\mu (k\simeq 740\, {\rm Mpc^{-1}})}$. We show that μE cross-correlations with CMB polarization provide more constraining power on $f_{\rm NL}^\mu$ than μT cross-correlations in the presence of foregrounds, and the joint combination of μT and μE observables adds further leverage to the detection of small-scale primordial non-Gaussianity. For multifield inflation, we find that LiteBIRD would detect ${f_{\rm NL}^\mu }=4500$ at 5σ significance after foreground removal, and achieve a minimum error of ${\sigma (f_{\rm NL}^\mu =0) \simeq 800}$ at 68 per cent CL by combining CMB temperature and polarization. Due to the huge dynamic range of wavenumbers between CMB and μ-distortion anisotropies, such large $f^\mu _{\rm NL}$ values would still be consistent with current CMB constraints in the case of very mild scale dependence of primordial non-Gaussianity. Anisotropic spectral distortions thus provide a new path, complementary to CMB B-modes, to probe inflation with LiteBIRD.