Polarization Power Spectra Research Articles

A power spectrum approach to the search for axion-like particles from resolved galaxy clusters using CMB as a backlight

Axions or axion-like particles (ALPs) are hypothetical particles predicted by beyond standard model theories, which make one of the dark matter candidates. These particles can convert into photons and vice-versa in the presence of a magnetic field, with a probability decided by its coupling strength gaγ . One of the ways to detect these particles is by using the Cosmic Microwave Background (CMB) as a backlight. As the CMB photons pass through a galaxy cluster, they can get converted into ALPs in the mass range 10-15 eV to 10-11 eV through resonant conversion in the presence of cluster magnetic fields. This leads to a polarized spectral distortion (α-distortion) in the CMB as the photon polarization parallel to the magnetic field in the galaxy cluster is involved in the conversion. The fluctuations in the magnetic field and electron density in a galaxy cluster lead to spatially varying α-distortion around the cluster, with a power spectrum that is different from the lensed E-mode and B-mode CMB polarization power spectrum for the standard model of cosmology. By measuring the difference in the polarization power spectrum around a galaxy cluster from the all-sky signal, one can find new α-distortion in the sky. For the resolved galaxy clusters, if the redshift, electron density, and magnetic field profiles of the cluster can be constrained using optical, X-ray, and radio observations, one can measure the coupling strength gaγ from the ALP power spectrum. The contamination from CMB and galactic foregrounds such as synchrotron and dust can be mitigated by using multiple frequency bands by leveraging on the difference in the spectral shape of the signal from foregrounds. Using the ILC technique to clean the foregrounds, we show that the new power spectrum-based approach of the resolved galaxy clusters from upcoming CMB experiments such as Simons Observatory and CMB-S4 can detect (or put constraints) on the ALP-photon coupling strength of gaγ < 5.2 × 10-12 GeV-1 and gaγ < 3.6 × 10-12 GeV-1 at 95% C.I. respectively for ALPs of masses 10-13 eV or for smaller gaγ for lighter ALP masses.

High-accuracy emulators for observables in ΛCDM, Neff, Σmν, and w cosmologies

ABSTRACT We use the emulation framework CosmoPower to construct and publicly release neural network emulators of cosmological observables, including the cosmic microwave background (CMB) temperature and polarization power spectra, matter power spectrum, distance-redshift relation, baryon acoustic oscillation (BAO) and redshift-space distortion (RSD) observables, and derived parameters. We train our emulators on Einstein–Boltzmann calculations obtained with high-precision numerical convergence settings, for a wide range of cosmological models including ΛCDM, wCDM, ΛCDM + Neff, and ΛCDM + Σmν. Our CMB emulators are accurate to better than 0.5 per cent out to ℓ = 104, which is sufficient for Stage-IV data analysis, and our P(k) emulators reach the same accuracy level out to $k=50 \, \, \mathrm{Mpc}^{-1}$, which is sufficient for Stage-III data analysis. We release the emulators via an online repository (CosmoPower Organisation), which will be continually updated with additional extended cosmological models. Our emulators accelerate cosmological data analysis by orders of magnitude, enabling cosmological parameter extraction analyses, using current survey data, to be performed on a laptop. We validate our emulators by comparing them to class and camb and by reproducing cosmological parameter constraints derived from Planck TT, TE, EE, and CMB lensing data, as well as from the Atacama Cosmology Telescope Data Release 4 CMB data, Dark Energy Survey Year-1 galaxy lensing and clustering data, and Baryon Oscillation Spectroscopic Survey Data Release 12 BAO and RSD data.

Current data are consistent with flat spatial hypersurfaces in the ΛCDM cosmological model but favor more lensing than the model predicts

We study the performance of three pairs of tilted $\Lambda$CDM cosmological models, two pairs allowing for non-flat spatial hypersurfaces with CMB temperature and polarization power spectrum data (P18) from Planck, P18 lensing (lensing), and non-CMB data (non-CMB). For the six models, we measure cosmological parameters and study whether or not pairs of the data sets are mutually consistent in these models. Half of these models allow the lensing consistency parameter $A_L$ to be an additional free parameter, while the other three have $A_L = 1$. The tilted spatially-flat models assume the usual primordial spatial inhomogeneity power spectrum. The tilted non-flat models assume either the primordial power spectrum used in the Planck group analyses [Planck $P(q)$] or a recently computed power spectrum [new $P(q)$]. In the tilted non-flat models with $A_L=1$ we find differences between P18 data and non-CMB data cosmological parameter constraints, which are large enough to rule out the Planck $P(q)$ model at 3$\sigma$ but not the new $P(q)$ model. While both P18 data and non-CMB data separately favor a closed geometry when P18+non-CMB data are jointly analyzed the evidence in favor of non-flat hypersurfaces subsides. Differences between P18 data and non-CMB data cosmological constraints subside when $A_L$ is allowed to vary. From the most restrictive P18+lensing+non-CMB data combination we get almost model-independent constraints and find that the $A_L>1$ option is preferred over the $\Omega_k<0$ one, with the $A_L$ parameter, for all models, being larger than unity by $\sim 2.5\sigma$. According to the deviance information criterion, in the P18+lensing+non-CMB analysis, the varying $A_L$ option is on the verge of being strongly favored over the $A_L=1$ one, which could indicate a problem for the standard tilted flat $\Lambda$CDM model (Abridged abstract).

Emergent universe: tensor perturbations within the CSL framework

We calculate the primordial power spectrum of tensor perturbations, within the emergent universe scenario, incorporating a version of the Continuous Spontaneous Localization (CSL) model as a mechanism capable of: breaking the initial symmetries of the system, generating the perturbations, and also achieving the quantum-to-classical transition of such perturbations. We analyze how the CSL model modifies the characteristics of the B-mode CMB polarization power spectrum, and we explore their differences with current predictions from the standard concordance cosmological model. We have found that, regardless of the CSL mechanism, a confirmed detection of primordial B-modes that fits to a high degree of precision the shape of the spectrum predicted from the concordance Lambda CDM model, would rule out one of the distinguishing features of the emergent universe. Namely, achieving a best fit to the data consistent with the suppression observed in the low multipoles of the angular power spectrum of the temperature anisotropy of the CMB. On the contrary, a confirmed detection that accurately exhibits a suppression of the low multipoles in the B-modes, would be a new feature that could be considered as a favorable evidence for the emergent scenario. In addition, we have been able to establish an upper bound on the collapse parameter of the specific CSL model used.

Distinguishing primordial magnetic fields from inflationary tensor perturbations in the cosmic microwave background

A claimed detection of cosmological tensor perturbations from inflation via $B$-mode polarization of the cosmic microwave background requires distinguishing other possible $B$-mode sources. One such potential source of confusion is primordial magnetic fields. For sufficiently low-amplitude $B$-mode signals, the microwave background temperature and polarization power spectra from power-law tensor perturbations and from a power-law primordial magnetic field are indistinguishable. However, we show that such a magnetic field will induce a small-scale Faraday rotation which is detectable using four-point statistics analogous to gravitational lensing of the microwave background. The Faraday rotation signal will distinguish a magnetic-field-induced $B$-mode polarization signal from tensor perturbations for effective tensor-to-scalar ratios larger than 0.001, detectable in upcoming polarization experiments.

Note on interacting holographic dark energy with a Hubble-scale cutoff

Holographic dark energy with the Hubble radius as infrared cutoff has been considered as a candidate to explain the late-time cosmic acceleration and it can solve the coincidence problem. In this scenario, a nonzero equation of state is only possible if there is an interaction between dark energy and cold dark matter. In this paper, a set of phenomenological interactions is assumed and a detailed analysis of the possible values of the coupling constants is carried out, however the resulting matter power spectrum and cosmic microwave background temperature and polarization power spectra have a shape very far from the observed ones. These results rule out any value for the free parameters and it seems to indicate that the assumed interacting holographic dark energy with a Hubble-scale cutoff is not viable to explain the accelerated expansion of the Universe, when cosmological data are taken into account.

Polarization power spectra and dust cloud morphology

Context In the framework of studying cosmic microwave background polarization and characterizing its Galactic foregrounds, the angular power spectrum analysis of the thermal dust polarization map has led to intriguing evidence of an E/B asymmetry and a positive TE correlation. The interpretation of these observations is the subject of theoretical and simulation-driven studies in which the correlation between the density structure of the interstellar medium (ISM) and the magnetic field appears to be a key aspect. In this context, and when the magnetized ISM structures are modeled in three dimensions, dust clouds are generally considered to be filamentary structures only, but both filamentary and sheet-like shapes are supported by observational and theoretical evidence. Aims. We aim to study the influence of the cloud shape and its connection to the local magnetic field, as well as the influence from the viewing angle, on the angular power spectra measured on thermal dust polarization maps; we specifically focus on the dependence of the E/B power asymmetry and TE correlation. Methods. To this end, we simulated realistic interstellar clouds with both filament-like and sheet-like shapes using the software Asterion, which also allowed us to generate synthetic maps of thermal dust polarized emission with an area of 400 square degrees. Then, we computed their polarization power spectra in the multipole range ℓ ϵ [100, 500] and focused on the E/B power asymmetry, quantified through the ℛEB ratio, and the correlation coefficient rTE between Τ and Ε modes. We quantified the dependence of ℛEB and rTE values on the offset angle (between the longest cloud axis and local magnetic field lines) and inclination angle (between the line of sight and the magnetic field) for both types of cloud shapes, either embedded in a regular magnetic field or coupled to a nonregular field to mimic turbulence. Results. We find that both types of cloud shapes cover the same regions of the (ℛEB, rTE) parameter space. The dependence on the inclination and offset angles is similar for both shapes, although sheet-like structures generally show larger scatter than filamentary structures. In addition to the known dependence on the offset angle, we find a strong dependence of ℛEB and rTE on the inclination angle. Conclusions. The very fact that filament-like and sheet-like structures may lead to polarization power spectra with similar (ℛEB,rTE) values complicates their interpretation. We argue that interpreting them solely in terms of filament characteristics is risky, and in future analyses, this degeneracy should be accounted for, as should the connection to the magnetic field geometry. Our results based on maps of 400 square degrees clarify that the overall geometrical arrangement of the magnetized ISM surrounding the observer leaves its marks on polarization power spectra.

Reionization process dependence of the ratio of CMB polarization power spectra at low-ℓ

We investigate how much the ratio of cosmic microwave background (CMB) polarization power spectra CBB ℓ /CEE ℓ at low-ℓ (ℓ ≲ 10) depends on the process of reionization.Both such low-ℓ B-mode and E-mode polarization powers are dominantly produced by Thomson scattering of CMB photons off the free electrons which are produced in the process of reionization.Since the reionization should be finished until at least the redshift z ≃ 6 and the low-ℓ polarization powers are produced at late time, the ratio is rather insensitive by the ionization process at higher redshifts, but it is sensitive to the value of optical depth.The value of the ratio at ℓ = 2, however, is almost insensitive to the reionization process including the value of optical depth, and the value is approximately half of the value of tensor-to-scalar ratio.This fact can be utilized for future determination of tensor-to-scalar ratio in spite of the ambiguity due to cosmic variance.

Effects of boosting on extragalactic components: methods and statistical studies

ABSTRACT In this work, we examine the impact of our motion with respect to the Cosmic Microwave Background (CMB) rest frame on statistics of CMB maps by examining the one-, two-, three-, and four- point statistics of simulated maps of the CMB and Sunyaev–Zeldovich (SZ) effects. We validate boosting codes by comparing their outcomes for temperature and polarization power spectra up to ℓ ≃ 6000. We derive and validate a new analytical formula for the computation of the boosted power spectrum of a signal with a generic frequency dependence. As an example we show how this increases the boosting correction to the power spectrum of CMB intensity measurements by ${\sim}30{{\ \rm per\ cent}}$ at 150 GHz. We examine the effect of boosting on thermal and kinetic SZ power spectra from semianalytical and hydrodynamical simulations; the boosting correction is generally small for both simulations, except when considering frequencies near the tSZ null. For the non-Gaussian statistics, in general we find that boosting has no impact with two exceptions. We find that, whilst the statistics of the CMB convergence field are unaffected, quadratic estimators that are used to measure this field can become biased at the $O(1){{\ \rm per\ cent}}$ level by boosting effects. We present a simple modification to the standard estimators that removes this bias. Second, bispectrum estimators can receive a systematic bias from the Doppler induced quadrupole when there is anisotropy in the sky – in practice this anisotropy comes from masking and inhomogeneous noise. This effect is unobservable and already removed by existing analysis methods.

Computing microwave background polarization power spectra from cosmic birefringence

We present a new publicly available code, class_rot, which modifies class to enable fast nonperturbative calculation of cosmic microwave background polarization power spectra due to both isotropic and anisotropic polarization rotation from cosmic birefringence. Cosmic birefringence can arise from new parity-violating physics such as axion dark matter with a Chern-Simons coupling to photons or Faraday rotation due to a primordial magnetic field. Constraints on these effects can be obtained by comparing measurements to precise numerical calculations of the polarization power spectra. We describe the implementation of class_rot in terms of both mathematical formalism and coding architecture.

Polarization of CMB and possible time dependence of dark energy

Dark energy has been introduced to explain the present accelerating expansion of the universe. In the LambdaCDM model, the present standard model of cosmology, dark energy is described as a cosmological constant which is time independent. The possibility of the time dependence of dark energy has been investigated to obtain deeper understanding of it by looking redshit-magnitude relation of type Ia supernova, for example. We investigate the constraints to the time dependence of dark energy with several phenomenological models by fitting their parameters to the redshit-magnitude relation of the Pantheon supernova catalog, and confirm that little time dependence can not be excluded by the goodness-of-fit criterion only. Such a non-trivial time dependence causes different expansion rate in the period of reionization, which affects the low-l polarization power spectrum of CMB. We investigate the possibility to detect the effect in future probe like LiteBIRD, for example. We find that the low-l EE polarization power spectrum is enhanced in general, but it will be difficult to be detected as far as looking the EE polarization power spectrum only because of the limitation by cosmic variance.

The effect of cosmic variance on the characteristics of dust polarization power spectra

In the context of cosmic microwave background polarization studies and the characterization of the Galactic foregrounds, the power spectrum analysis of the thermal dust polarization sky has led to intriguing evidence of an E∕B asymmetry and a positive TE correlation. In this work, we produce synthesized dust polarization maps from a set of global magneto-hydrodynamic (MHD) simulations of Milky-Way-sized galaxies, and analyze their power spectra at intermediate angular scales (intermediate angular multipoles ℓ∈[60, 140]). We study the role of the initial configuration of the large-scale magnetic field, its strength, and the feedback on the power spectrum characteristics. Using full-galaxy MHD simulations, we were able to estimate the variance induced by the peculiar location of the observer in the galaxy. We find that the polarization power spectra sensitively depend on the observer’s location, impeding a distinction between different simulation setups. In particular, there is a clear statistical difference between the power spectra measured from within the spiral arms and those measured from the inter-arm regions. Also, power spectra from within supernova-driven bubbles share common characteristics, regardless of the underlying model. However, no correlation was found between the statistical properties of the polarization power spectra and the local (with respect to the observer) mean values of physical quantities such as the density and the strength of the magnetic field. Finally, we find some indications that the global strength of the magnetic field may play a role in shaping the power spectrum characteristics; as the global magnetic field strength increases, the E∕B asymmetry and the TE correlation increase, whereas the viewpoint-induced variance decreases. However, we find no direct correlation with the strength of the local magnetic field that permeates the mapped region of the interstellar medium.

Dark energy with oscillatory tracking potential: observational constraints and perturbative effects

ABSTRACT The cosmological models exhibiting tracker properties have great significance in the context of dark energy as they can reach the present value of dark energy density from a wide range of initial conditions, thereby alleviating both the fine-tuning and the cosmic coincidence problem. The α-attractors, which are originally discussed in the context of inflation, can exhibit the properties of dark energy as they can behave like cosmological trackers at early times and show the late-time behaviour of a cosmological constant. In this paper, we study the oscillatory tracker model (OTM), which belongs to the family of α-attractor dark energy models. Using the current observational data sets like cosmic microwave background (CMB), baryon acoustic oscillation, and type 1a supernova data (Pantheon compilation), we constrain the parameters of the model and estimate both the mean and best-fitting values. Although the OTM contains a larger set of parameters than the usual lambda cold dark matter (LCDM) model, the common set of parameters of both agree within $1\, \sigma$ error limits. Our observations using both high redshift and low redshift data support Hubble parameter value H0 = 67.4 Km s−1 Mpc−1. We study the effect of the OTM on the CMB temperature and polarization power spectra, matter power spectrum and fσ8. Our analysis of the CMB power spectrum and matter power spectrum suggests that the oscillatory tracker dark energy model has noticeable differences from usual LCDM predictions. Yet, in most cases, the agreement is very close.

Baryonic feedback biases on fundamental physics from lensed CMB power spectra

Upcoming measurements of the small-scale primary cosmic microwave background (CMB) temperature and polarization power spectra ($TT$/$TE$/$EE$) are anticipated to yield transformative constraints on new physics, including the effective number of relativistic species in the early universe ($N_{\rm eff}$). However, at multipoles $\ell \gtrsim 3000$, the primary CMB power spectra receive significant contributions from gravitational lensing. While these modes still carry primordial information, their theoretical modeling requires knowledge of the CMB lensing convergence power spectrum, $C_L^{\kappa\kappa}$, including on small scales where it is affected by nonlinear gravitational evolution and baryonic feedback processes. Thus, the high-$\ell$ primary CMB is sensitive to these late-time, nonlinear effects. Here, we show that inaccuracies in the modeling of $C_L^{\kappa\kappa}$ can yield surprisingly large biases on cosmological parameters inferred from the primary CMB power spectra measured by the upcoming Simons Observatory and CMB-S4 experiments. For CMB-S4, the biases can be as large as $1.6\sigma$ on the Hubble constant $H_0$ in a fit to $\Lambda$CDM and $1.2\sigma$ on $N_{\rm eff}$ in a fit to $\Lambda$CDM+$N_{\rm eff}$. We show that these biases can be mitigated by explicitly discarding all $TT$ data at $\ell>3000$ or by marginalizing over parameters describing baryonic feedback processes, both at the cost of slightly larger error bars. We also discuss an alternative, data-driven mitigation strategy based on delensing the CMB $T$ and $E$-mode maps. Finally, we show that analyses of upcoming data will require Einstein-Boltzmann codes to be run with much higher numerical precision settings than is currently standard, so as to avoid similar -- or larger -- parameter biases due to inaccurate theoretical predictions.

Interplanetary Dust as a Foreground for the LiteBIRD CMB Satellite Mission

As ever-more sensitive experiments are made in the quest for primordial CMB B Modes, the number of potentially significant astrophysical contaminants becomes larger as well. Thermal emission from interplanetary dust, for example, has been detected by the Planck satellite. While the polarization fraction of this Zodiacal, or interplanetary dust emission (IPDE) is expected to be low, it is bright enough to be detected in total power. Here, estimates of the magnitude of the effect as it might be seen by the LiteBIRD satellite are made. The COBE IPDE model from Kelsall et al. (1998) is combined with a model of the LiteBIRD experiment's scanning strategy to estimate potential contamination of the CMB in both total power and in polarization power spectra. LiteBIRD should detect IPDE in temperature across all of its bands, from 40 through 402 GHz, and should improve limits on the polarization fraction of IPDE at the higher end of this frequency range. If the polarization fraction of IPDE is of order 1%, the current limit from ISO/CAM measurements in the mid-infrared, it may induce large-scale polarization B Modes comparable to cosmological models with an r of order 0.001. In this case, the polarized IPDE would also need to be modeled and removed. As a CMB foreground, IPDE will always be subdominant to Galactic emissions, though because it caused by emission from grains closer to us, it appears variable as the Earth travels around the Sun, and may thereby complicate the data analysis somewhat. But with an understanding of some of the symmetries of the emission and some flexibility in the data processing, it should not be the primary impediment to the CMB polarization measurement.

Current and future constraints on single-field α -attractor models

We study here the observational constraints on single-field inflationary models achievable with the next generation of CMB experiments. We particularly focus on a Stage-IV like experiment and forecasts its constraints on inflationary parameters in the context of $\alpha$-attractor inflation comprising a large class of single-field models. To tailor our forecasts we use as a fiducial model the results obtained with current CMB and LSS data, assuming the $\alpha$-model a priori. We found that current CMB data are able to place a tight bound on the ratio of the tensor-to-scalar ratio with the alpha parameter $r/\alpha = 3.87^{+0.78}_{-0.94}\cdot 10^{-3}$ and on the running of the scalar index $\alpha_S = -6.4^{+1.6}_{-1.3}\cdot 10^{-4}$ with a value of the scalar index consistent with current constraints. In the optimistic scenario of detection of primordial gravitational waves in the CMB B-mode polarization power spectra, we found that CMB-S4 will be able to achieve a $15\%$ bound on the value of the parameter $\alpha = 1.01^{+0.14}_{-0.18}$. This bound clearly show the ability of CMB-S4 to constrain not only the energy scale of inflation but also the shape of its potential. Enlarging the baseline model to also include the neutrino sector merely reduce the accuracy of $5\%$ leading to $\alpha = 1.07^{+0.18}_{-0.23}$ so that our main conclusions are still valid.

Measurements of the E -mode polarization and temperature- E -mode correlation of the CMB from SPT-3G 2018 data

We present measurements of the $E$-mode ($EE$) polarization power spectrum and temperature-$E$-mode ($TE$) cross-power spectrum of the cosmic microwave background using data collected by SPT-3G, the latest instrument installed on the South Pole Telescope. This analysis uses observations of a 1500 deg$^2$ region at 95, 150, and 220 GHz taken over a four month period in 2018. We report binned values of the $EE$ and $TE$ power spectra over the angular multipole range $300 \le \ell < 3000$, using the multifrequency data to construct six semi-independent estimates of each power spectrum and their minimum-variance combination. These measurements improve upon the previous results of SPTpol across the multipole ranges $300 \le \ell \le 1400$ for $EE$ and $300 \le \ell \le 1700$ for $TE$, resulting in constraints on cosmological parameters comparable to those from other current leading ground-based experiments. We find that the SPT-3G dataset is well-fit by a $\Lambda$CDM cosmological model with parameter constraints consistent with those from Planck and SPTpol data. From SPT-3G data alone, we find $H_0 = 68.8 \pm 1.5 \mathrm{km\,s^{-1}\,Mpc^{-1}}$ and $\sigma_8 = 0.789 \pm 0.016$, with a gravitational lensing amplitude consistent with the $\Lambda$CDM prediction ($A_L = 0.98 \pm 0.12$). We combine the SPT-3G and the Planck datasets and obtain joint constraints on the $\Lambda$CDM model. The volume of the 68% confidence region in six-dimensional $\Lambda$CDM parameter space is reduced by a factor of 1.5 compared to Planck-only constraints, with only slight shifts in central values. We note that the results presented here are obtained from data collected during just half of a typical observing season with only part of the focal plane operable, and that the active detector count has since nearly doubled for observations made with SPT-3G after 2018.

Impacts of dark energy on constraining neutrino mass after Planck 2018

Considering the mass splittings of three active neutrinos, we investigate how the properties of dark energy affect the cosmological constraints on the total neutrino mass using the latest cosmological observations. In this paper, several typical dark energy models, including ΛCDM, wCDM, CPL, and HDE models, are discussed. In the analysis, we also consider the effects from the neutrino mass hierarchies, i.e. the degenerate hierarchy (DH), the normal hierarchy (NH), and the inverted hierarchy (IH). We employ the current cosmological observations to do the analysis, including the Planck 2018 temperature and polarization power spectra, the baryon acoustic oscillations (BAO), the type Ia supernovae (SNe), and the Hubble constant H 0 measurement. In the ΛCDM+ model, we obtain the upper limits of the neutrino mass (DH), (NH), and (IH) at the 95% C.L., using the Planck+BAO+SNe data combination. For the wCDM+ model and the CPL+ model, larger upper limits of are obtained compared to those of the ΛCDM+ model. The most stringent constraint on the neutrino mass, (DH), is derived in the HDE+ model. In addition, we find that the inclusion of the local measurement of the Hubble constant in the data combination leads to tighter constraints on the total neutrino mass in all these dark energy models.

A Measurement of the CMB E-mode Angular Power Spectrum at Subdegree Scales from 670 Square Degrees of POLARBEAR Data

Abstract We report a measurement of the E-mode polarization power spectrum of the cosmic microwave background (CMB) using 150 GHz data taken from 2014 July to 2016 December with the Polarbear experiment. We reach an effective polarization map noise level of - across an observation area of 670 square degrees. We measure the EE power spectrum over the angular multipole range , tracing the third to seventh acoustic peaks with high sensitivity. The statistical uncertainty on E-mode bandpowers is ∼2.3 at , with a systematic uncertainty of 0.5 . The data are consistent with the standard ΛCDM cosmological model with a probability-to-exceed of 0.38. We combine recent CMB E-mode measurements and make inferences about cosmological parameters in ΛCDM as well as in extensions to ΛCDM. Adding the ground-based CMB polarization measurements to the Planck data set reduces the uncertainty on the Hubble constant by a factor of 1.2 to . When allowing the number of relativistic species ( ) to vary, we find , which is in good agreement with the standard value of 3.046. Instead allowing the primordial helium abundance ( ) to vary, the data favor . This is very close to the expectation of 0.2467 from big bang nucleosynthesis. When varying both and , we find and .

Simultaneous determination of the cosmic birefringence and miscalibrated polarization angles II: Including cross-frequency spectra

Abstract We develop a strategy to determine the cosmic birefringence and miscalibrated polarization angles simultaneously using the observed $EB$ polarization power spectra of the cosmic microwave background and the Galactic foreground emission. We extend the methodology of Y. Minami et al. (Prog. Theor. Exp. Phys. 2019, 083E02, 2019), which was developed for auto-frequency power spectra, by including cross-frequency spectra. By fitting one global birefringence angle and independent miscalibration angles at different frequency bands, we determine both angles with significantly smaller uncertainties (by more than a factor of two) compared to the auto spectra.