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Joint analysis of Dark Energy Survey Year 3 data and CMB lensing from SPT and Planck . I. Construction of CMB lensing maps and modeling choices

Joint analyses of cross-correlations between measurements of galaxy positions, galaxy lensing, and lensing of the cosmic microwave background (CMB) offer powerful constraints on the large-scale structure of the Universe. In a forthcoming analysis, we will present cosmological constraints from the analysis of such cross-correlations measured using Year 3 data from the Dark Energy Survey (DES), and CMB data from the South Pole Telescope (SPT) and Planck. Here we present two key ingredients of this analysis: (1) an improved CMB lensing map in the SPT-SZ survey footprint and (2) the analysis methodology that will be used to extract cosmological information from the cross-correlation measurements. Relative to previous lensing maps made from the same CMB observations, we have implemented techniques to remove contamination from the thermal Sunyaev Zel’dovich effect, enabling the extraction of cosmological information from smaller angular scales of the cross-correlation measurements than in previous analyses with DES Year 1 data. We describe our model for the cross-correlations between these maps and DES data, and validate our modeling choices to demonstrate the robustness of our analysis. We then forecast the expected cosmological constraints from the galaxy survey-CMB lensing auto and cross-correlations. We find that the galaxy-CMB lensing and galaxy shear-CMB lensing correlations will on their own provide a constraint on S 8 =σ 8 $\sqrt{Ωm/0.3}$ at the few percent level, providing a powerful consistency check for the DES-only constraints. Finally, we explore scenarios where external priors on shear calibration are removed, finding that the joint analysis of CMB lensing cross-correlations can provide constraints on the shear calibration amplitude at the 5% to 10% level.

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BEYONDPLANCK XIV. Polarized foreground emission between 30 and 70 GHz

We constrain polarized foreground emission between 30 and 70 GHz with the Planck Low Frequency Instrument (LFI) and WMAP data within the global Bayesian BeyondPlanck framework. We combine for the first time full-resolution Planck LFI time-ordered data with low-resolution WMAP sky maps at 33, 40 and 61 GHz. Spectral parameters are fit with a likelihood defined at the native resolution of each frequency channel. This analysis represents the first implementation of true multi-resolution component separation applied to CMB observations for both amplitude and spectral energy distribution (SED) parameters. For synchrotron emission, we approximate the SED as a power-law in frequency and find that the low signal-to-noise ratio of the current data strongly limits the number of free parameters that may be robustly constrained. We partition the sky into four large disjoint regions (High Latitude; Galactic Spur; Galactic Plane; and Galactic Center), each associated with its own power-law index. We find that the High Latitude region is prior-dominated, while the Galactic Center region is contaminated by residual instrumental systematics. The two remaining regions appear to be signal-dominated, and for these we derive spectral indices of $β$ S Spur = -3.17 ± 0.06 and $β$ S Plane = -3.03 ± 0.07, in good agreement with previous results. For thermal dust emission we assume a modified blackbody model and we fit a single power-law index across the full sky. We find $β$ d = 1.64 ± 0.03, which is slightly steeper than reported from Planck HFI data, but still statistically consistent at the 2σ confidence level.

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A Simulation-based Method for Correcting Mode Coupling in CMB Angular Power Spectra

Modern cosmic microwave background (CMB) analysis pipelines regularly employ complex time-domain filters, beam models, masking, and other techniques during the production of sky maps and their corresponding angular power spectra. However, these processes can generate couplings between multipoles from the same spectrum and from different spectra, in addition to the typical power attenuation. Within the context of pseudo-C ℓ based, MASTER-style analyses, the net effect of the time-domain filtering is commonly approximated by a multiplicative transfer function, F ℓ , that can fail to capture mode mixing and is dependent on the spectrum of the signal. To address these shortcomings, we have developed a simulation-based spectral correction approach that constructs a two-dimensional transfer matrix, ${J}_{{\ell }{\ell }^{\prime} }$, which contains information about mode mixing in addition to mode attenuation. We demonstrate the application of this approach on data from the first flight of the Spider balloon-borne CMB experiment.

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Cosmological preference for a negative neutrino mass

The most precise determination of the sum of neutrino masses from cosmological data, derived from analysis of the cosmic microwave background (CMB) and baryon acoustic acoustic oscillations (BAO) from the Dark Energy Spectroscopic Instrument (DESI), favors a value below the minimum inferred from neutrino flavor oscillation experiments. We explore which data is most responsible of this puzzling aspect of the current constraints on neutrino mass and whether it is related to other anomalies in cosmology. We demonstrate conclusively that the preference for negative neutrino masses is a consequence of larger than expected lensing of the CMB in both the two- and four-point lensing statistics. Furthermore, we show that this preference is robust to changes in likelihoods of the BAO and CMB optical depth analyses given the available data. We then show that this excess clustering is not easily explained by changes to the expansion history and is likely distinct from the preference for for dynamical dark energy in DESI BAO data. Finally, we discuss how future data may impact these results, including an analysis of Planck CMB with mock DESI 5-year data. Here, we conclude that the negative neutrino mass preference is likely to persist even as more cosmological data is collected in the near future.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Hubble constant difference between CMB lensing and BAO measurements

We apply a tension metric QUDM, the update difference in mean parameters, to understand the source of the difference in the measured Hubble constant H0 inferred with cosmic microwave background lensing measurements from the Planck satellite (H 0 = $67.9$ $^{+1.1}_{–1.3}$ km/s/Mpc) and from the South Pole Telescope (H 0 = $72.0$ $^{+2.1}_{–2.5}$ km/s/Mpc) when both are combined with baryon acoustic oscillation (BAO) measurements with priors on the baryon density (BBN). Q UDM isolates the relevant parameter directions for tension or concordance where the two data sets are both informative, and aids in the identification of subsets of data that source the observed tension. With Q UDM , we uncover that the difference in H 0 is driven by the tension between Planck lensing and BAO+BBN, at probability-to-exceed of 6.6%. Most of this mild tension comes from the galaxy BAO measurements parallel to the line of sight in the redshift range 0.2 < z < 0.75. Here, the redshift dependence of the parallel BAOs pulls both the matter density Ω m and H 0 high in Λ CDM, but these parameter anomalies are usually hidden when the BAO measurements are combined with other cosmological data sets with much stronger Ω m constraints.

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Early dark sector, the Hubble tension, and the swampland

We consider the interplay of the Early Dark Energy (EDE) model, the Swampland Distance Conjecture (SDC), and cosmological parameter tensions. EDE is a proposed resolution of the Hubble tension relying upon a near-Planckian scalar field excursion, while the SDC predicts an exponential sensitivity of masses of other fields to such an excursion, m ∝ e –c |ΔΦ|/Mpl with c ~ 0(1). Meanwhile, EDE is in tension with large-scale structure (LSS) data, due to shifts in the standard ΛCDM parameters necessary to fit the cosmic microwave background (CMB). One might hope that a proper treatment of the model, e.g., accounting for the SDC, may ameliorate the tension with LSS. Motivated by these considerations, we introduce the Early Dark Sector (EDS) model, wherein the mass of dark matter is exponentially sensitive to super-Planckian field excursions of the EDE scalar. The EDS model exhibits new phenomenology in both the early and late universe, the latter due to an EDE-mediated dark matter self-interaction. This dark matter-philic "fifth force", while constrained to be small, remains active in the late universe and is not screened in virialized halos. We find that the new interaction with dark matter partially resolves the LSS tension. However, the marginalized posteriors are nonetheless consistent with f EDE = 0 at 95% CL once the Dark Energy Survey Year 3 measurement of S 8 is included. We study constraints on the model from Atacama Cosmology Telescope data, and find a factor of two improvement on the error bar on the SDC parameter c, along with an increased preference for the EDE component. Here, we discuss the implications of these constraints for the SDC, and find the tightest observational constraints to date on a swampland parameter, suggesting that an EDE description of cosmological data is in tension with the SDC.

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No ν s is Good News

The baryon acoustic oscillation (BAO) analysis from the first year of data from the Dark Energy Spectroscopic Instrument (DESI), when combined with data from the cosmic microwave background (CMB), has placed an upper-limit on the sum of neutrino masses, ∑m ν < 70 meV (95%). In addition to excluding the minimum sum associated with the inverted hierarchy, the posterior is peaked at ∑m ν = 0 and is close to excluding even the minumum sum, 58 meV at 2σ. In this paper, we explore the implications of this data for cosmology and particle physics. The sum of neutrino mass is determined in cosmology from the suppression of clustering in the late universe. Allowing the clustering to be enhanced, we extended the DESI analysis to ∑m ν < 0 and find ∑m ν =160 ± 90 meV (68%), and that the suppression of power from the minimum sum of neutrino masses is excluded at 99% confidence. We show this preference for negative masses makes it challenging to explain the result by a shift of cosmic parameters, such as the optical depth or matter density. We then show how a result of ∑m ν = 0 could arise from new physics in the neutrino sector, including decay, cooling, and/or time-dependent masses. These models are consistent with current observations but imply new physics that is accessible in a wide range of experiments. In addition, we discuss how an apparent signal with ∑m ν < 0 can arise from new long range forces in the dark sector or from a primordial trispectrum that resembles the signal of CMB lensing.

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Symmetry of Cosmological Observables, a Mirror World Dark Sector, and the Hubble Constant

We find that a uniform scaling of the gravitational free-fall rates and photon-electron scattering rate leaves most dimensionless cosmological observables nearly invariant. This result opens up a new approach to reconciling cosmic microwave background and large-scale structure observations with high values of the Hubble constant H0: Find a cosmological model in which the scaling transformation can be realized without violating any measurements of quantities not protected by the symmetry. A “mirror world” dark sector allows for effective scaling of the gravitational free-fall rates while respecting the measured mean photon density today. Further model building might bring consistency with the two constraints not yet satisfied: the inferred primordial abundances of deuterium and helium.

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Backlighting extended gas halos around luminous red galaxies: Kinematic Sunyaev-Zel’dovich effect from DESI Y1 and ACT data

The gas density profile around galaxies, shaped by feedback and affecting the galaxy lensing signal, is imprinted on the cosmic microwave background (CMB) by the kinematic Sunyaev-Zel’dovich effect (kSZ). We precisely measure this effect (𝑆/𝑁 ≈ 10) via velocity stacking with 825,283 spectroscopically confirmed luminous red galaxies (LRG) from the Dark Energy Spectroscopic Instrument Year 1 (DESI Y1) survey, which overlap with the Atacama Cosmology Telescope (ACT) Data Release 6 temperature maps over ≥ 4,000 deg 2 . We explore the kSZ dependence with various galaxy parameters and find no significant trend with redshift but clear trends with stellar mass and absolute magnitude in 𝑔, 𝑟, and 𝑧 bands. Our analysis suggests that the gas extends beyond the dark matter halo (99.5% confidence level, i.e., probability to exceed (PTE)⁢ = 0.005). We find a tentative preference for hydrodynamical simulation models with stronger feedback that drives gas further out (Illustris 𝑧 = 0.5, PTE⁢ = 0.37) over weaker-feedback cases (IllustrisTNG 𝑧 = 0.8, PTE⁢ = 0.045), though with limited statistical significance. In all cases, a free multiplicative amplitude was fit to the simulated profiles, and further modeling work is required to firm up these conclusions. We find consistency between kSZ profiles around spectroscopic and photometric LRG, with comparable statistical power, thus increasing our confidence in the photometric analysis. Additionally, we present the first kSZ measurement around the DESI Y1 bright galaxy sample (BGS) and the emission-line galaxies (ELG) whose features match qualitative expectations. Finally, we forecast 𝑆/𝑁 ∼ 50 for future stacked kSZ measurements using data from the ACT, the DESI Y3, and the Rubin Observatory. Furthermore, these measurements will serve as an input for galaxy formation models and baryonic uncertainties in galaxy lensing.

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Using Host Galaxy Photometric Redshifts to Improve Cosmological Constraints with Type Ia Supernovae in the LSST Era

We perform a rigorous cosmology analysis on simulated Type Ia supernovae (SNe Ia) and evaluate the improvement from including photometric host galaxy redshifts compared to using only the "z spec " subset with spectroscopic redshifts from the host or SN. We use the Deep Drilling Fields (~50 deg 2 ) from the Photometric LSST Astronomical Time-Series Classification Challenge (PLAsTiCC) in combination with a low-z sample based on Data Challenge2. The analysis includes light-curve fitting to standardize the SN brightness, a high-statistics simulation to obtain a bias-corrected Hubble diagram, a statistical+systematics covariance matrix including calibration and photo-z uncertainties, and cosmology fitting with a prior from the cosmic microwave background. Compared to using the z spec subset, including events with SN+host photo-z results in (i) more precise distances for z > 0.5, (ii) a Hubble diagram that extends 0.3 further in redshift, and (iii) a 50% increase in the Dark Energy Task Force figure of merit (FoM) based on the w 0 w a CDM model. Analyzing 25 simulated data samples, the average bias on w 0 and w a is consistent with zero. The host photo-z systematic of 0.01 reduces FoM by only 2% because (i) most z < 0.5 events are in the z spec subset, (ii) the combined SN+host photo-z has ×2 smaller bias, and (iii) the anticorrelation between fitted redshift and color self-corrects distance errors. To prepare for analyzing real data, the next SN Ia cosmology analysis with photo-zs should include non–SN Ia contamination and host galaxy misassociations.

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Beyond – ΛCDM constraints from the full shape clustering measurements from BOSS and eBOSS

We analyse the full shape of anisotropic clustering measurements from the extended Baryon Oscillation Spectroscopic Survey quasar sample together with the combined galaxy sample from the Baryon Oscillation Spectroscopic Survey. We obtain constraints on the cosmological parameters independent of the Hubble parameter h for the extensions of the Lambda cold dark matter (ΛCDM) models, focusing on cosmologies with free dark energy equation of state parameter w. We combine the clustering constraints with those from the latest cosmic microwave background data from Planck to obtain joint constraints for these cosmologies for w and the additional extension parameters – its time evolution w a , the physical curvature density ω K and the neutrino mass sum Σm ν . Our joint constraints are consistent with a flat ΛCDM cosmological model within 68 per cent confidence limits. We demonstrate that the Planck data are able to place tight constraints on the clustering amplitude today, σ 12 , in cosmologies with varying w and present the first constraints for the clustering amplitude for such cosmologies, which is found to be slightly higher than the ΛCDM value. Additionally, we show that when we vary w and allow for non-flat cosmologies and the physical curvature density is used, Planck prefers a curved universe at 4σ significance, which is ~2σ higher than when using the relative curvature density Ω K . Finally, when w is varied freely, clustering provides only a modest improvement (of 0.021 eV) on the upper limit of Σm ν .

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Multiprobe cosmology from the abundance of SPT clusters and DES galaxy clustering and weak lensing

Cosmic shear, galaxy clustering, and the abundance of massive halos each probe the large-scale structure of the Universe in complementary ways. We present cosmological constraints from the joint analysis of the three probes, building on the latest analyses of the lensing-informed abundance of clusters identified by the South Pole Telescope (SPT) and of the auto- and cross-correlation of galaxy position and weak lensing measurements (3 × 2 ⁢pt) in the Dark Energy Survey (DES). We consider the cosmological correlation between the different tracers and we account for the systematic uncertainties that are shared between the large-scale lensing correlation functions and the small-scale lensing-based cluster mass calibration. Marginalized over the remaining Λ cold dark matter (Λ ⁢CDM) parameters (including the sum of neutrino masses) and 52 astrophysical modeling parameters, we measure Ω m = 0.300 ± 0.017 and 𝜎 8 = 0.797 ± 0.026. Compared to constraints from Planck primary cosmic microwave background (CMB) anisotropies, our constraints are only 15% wider with a probability to exceed of 0.22 (1.2⁢𝜎) for the two-parameter difference. We further obtain 𝑆 8 ≡𝜎 8 ⁢(Ω m /0.3) 0.5 = 0.796 ± 0.013 which is lower than the Planck measurement at the 1.6⁢𝜎 level. The combined SPT cluster, DES 3 ×2 ⁢pt, and Planck datasets mildly prefer a nonzero positive neutrino mass, with a 95% upper limit ∑ 𝑚 𝜈 < 0.25 eV on the sum of neutrino masses. Assuming a 𝑤⁢CDM model, we constrain the dark energy equation of state parameter 𝑤 = −1.1⁢5$^{+0.23}_{−0.17}$ and when combining with Planck primary CMB anisotropies, we recover 𝑤 = −1.2⁢0$^{+0.15}_{−0.09}$, a 1.7⁢𝜎 difference with a cosmological constant. The precision of our results highlights the benefits of multiwavelength multiprobe cosmology and our analysis paves the way for upcoming joint analyses of next-generation datasets.

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Measurements of the temperature and $E$-mode polarization of the cosmic microwave background from the full 500-square-degree SPTpol dataset

Using the full four-year SPTpol 500 deg 2 dataset in both the 95 and 150 GHz frequency bands, we present measurements of the temperature and E-mode polarization of the cosmic microwave background (CMB), as well as the E-mode polarization autopower spectrum (EE) and temperature-E-mode cross-power spectrum (TE) in the angular multipole range 50 < ℓ < 8000. We find the SPTpol dataset to be self-consistent, passing several internal consistency tests based on maps, frequency bands, bandpowers, and cosmological parameters. The full SPTpol dataset is well-fit by the ΛCDM model, for which we find H 0 = 70.48 ± 2.16 km s -1 Mpc -1 and Ω m = 0.271 ± 0.026, when using only the SPTpol data and a Planck-based prior on the optical depth to reionization. The ΛCDM parameter constraints are consistent across the 95 GHz-only, 150 GHz-only, TE-only, and EE-only data splits. Between the ℓ < 1000 and ℓ > 1000 data splits, the ΛCDM parameter constraints are borderline consistent at the ∼2σ level. This consistency improves when including a parameter A L , the degree of lensing of the CMB inferred from the smearing of acoustic peaks. When marginalized over A L , the ΛCDM parameter constraints from SPTpol are consistent with those from Planck. In conclusion, the power spectra presented here are the most sensitive measurements of the lensed CMB damping tail to date for roughly ℓ > 1700 in TE and ℓ > 2000 in EE.

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DESI 2024: Constraints on physics-focused aspects of dark energy using DESI DR1 BAO data

Baryon acoustic oscillation data from the first year of the Dark Energy Spectroscopic Instrument (DESI) provide near percent-level precision of cosmic distances in seven bins over the redshift range z=0.1–4.2. Here, this paper is the follow-up to the original DESI BAO cosmology paper [A. G. Adame et al. (DESI Collaboration), arXiv:2404.03002], which considered the conventional w 0 w a cold dark matter (CDM) model. We use the novel DESI data, together with other cosmic probes, to constrain the background expansion history using some well-motivated physical classes of dark energy. In particular, we explore three physics-focused behaviors of dark energy from the equation of state and energy density perspectives: the thawing class (matching many simple quintessence potentials), emergent class (where dark energy comes into being recently, as in phase transition models), and mirage class [where phenomenologically the distance to cosmic microwave background (CMB) last scattering is close to that from a cosmological constant Λ despite dark energy dynamics]. All three classes fit the data at least as well as Λ ⁢CDM, and indeed can improve on it by Δ⁢χ 2 ≈ –5 to –17 for the combination of DESI BAO with CMB and supernova data while having one more parameter. The mirage class does essentially as well as w 0 ⁢w a CDM and exhibits moderate to strong Bayesian evidence preference with respect to Λ⁢ CDM. These classes of dynamical behaviors highlight worthwhile avenues for further exploration into the nature of dark energy.

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Extended dark energy analysis using DESI DR2 BAO measurements

We conduct an extended analysis of dark energy constraints, in support of the findings of the Dark Energy Spectroscopic Instrument (DESI) second data release cosmology key paper, including DESI data, Planck cosmic microwave background observations, and three different supernova compilations. Using a broad range of parametric and nonparametric methods, we explore the dark energy phenomenology and find consistent trends across all approaches, in good agreement with the 𝑤 0⁢ 𝑤 𝑎⁢ CDM (cold dark matter) key paper results. Even with the additional flexibility introduced by nonparametric approaches, such as binning and Gaussian processes, we find that extending Λ⁢ CDM to include a two-parameter 𝑤⁡(𝑧) is sufficient to capture the trends present in the data. Finally, we examine three dark energy classes with distinct dynamics, including quintessence scenarios satisfying 𝑤 ≥ −1, to explore what underlying physics can explain such deviations. The current data indicate a clear preference for models that feature a phantom crossing; although alternatives lacking this feature are disfavored, they cannot yet be ruled out. Our analysis confirms that the evidence for dynamical dark energy, particularly at low redshift (𝑧 ≲ 0.3), is robust and stable under different modeling choices.

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Strong detection of the CMB lensing and galaxy weak lensing cross-correlation from ACT-DR4, Planck Legacy, and KiDS-1000

Here we measured the cross-correlation between galaxy weak lensing data from the Kilo Degree Survey (KiDS-1000, DR4) and cosmic microwave background (CMB) lensing data from the Atacama Cosmology Telescope (ACT, DR4) and the Planck Legacy survey. We used two samples of source galaxies, selected with photometric redshifts, (0.1 < z B < 1.2) and (1.2 < z B < 2), which produce a combined detection significance of the CMB lensing and weak galaxy lensing cross-spectrum of 7.7σ. With the lower redshift galaxy sample, for which the cross-correlation was detected at a significance of 5.3σ, we present joint cosmological constraints on the matter density parameter, Ω m , and the matter fluctuation amplitude parameter, σ 8 , marginalising over three nuisance parameters that model our uncertainty in the redshift and shear calibration as well as the intrinsic alignment of galaxies. We find our measurement to be consistent with the best-fitting flat ΛCDM cosmological models from both Planck and KiDS-1000. We demonstrate the capacity of CMB weak lensing cross-correlations to set constraints on either the redshift or shear calibration by analysing a previously unused high-redshift KiDS galaxy sample (1.2 < z B < 2), with the cross-correlation detected at a significance of 7σ. This analysis provides an independent assessment for the accuracy of redshift measurements in a regime that is challenging to calibrate directly owing to known incompleteness in spectroscopic surveys.

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What is flat ΛCDM, and may we choose it?

The Universe is neither homogeneous nor isotropic, but it is close enough that we can reasonably approximate it as such on suitably large scales. The inflationary-Λ-Cold Dark Matter (ΛCDM) concordance cosmology builds on these assumptions to describe the origin and evolution of fluctuations. With standard assumptions about stress-energy sources, this system is specified by just seven phenomenological parameters, whose precise relations to underlying fundamental theories are complicated and may depend on details of those fields. Nevertheless, it is common practice to set the parameter that characterizes the spatial curvature, Ω K , exactly to zero. This parameter-fixed ΛCDM is awarded distinguished status as separate model, "flat ΛCDM." Ipso facto this places the onus on proponents of "curved ΛCDM" to present sufficient evidence that Ω K ≠ 0, and is needed as a parameter. While certain inflationary model Lagrangians, with certain values of their parameters, and certain initial conditions, will lead to a present-day universe well-described as containing zero curvature, this does not justify distinguishing that subset of Lagrangians, parameters and initial conditions into a separate model. Absent any theoretical arguments, we cannot use observations that suggest small Ω K to enforce Ω K = 0. Our track record in picking inflationary models and their parameters a priori makes such a choice dubious, and concerns about tensions in cosmological parameters and large-angle cosmic-microwave-background anomalies strengthens arguments against this choice. We argue that Ω K must not be set to zero, and that ΛCDM remains a phenomenological model with at least 7 parameters.

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

In this work, 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 32 μK-arcmin across an observation area of 670 square degrees. We measure the EE power spectrum over the angular multipole range 500 ≤ ℓ < 3000, tracing the third to seventh acoustic peaks with high sensitivity. The statistical uncertainty on E-mode bandpowers is ~2.3 μK 2 at ℓ ~ 1000, with a systematic uncertainty of 0.5 mK 2 . Furthermore, 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 H0 = 67.20 ±0.57 km s -1 Mpc -1 . When allowing the number of relativistic species (Neff ) to vary, we find N eff = 2.94 ±0.16, which is in good agreement with the standard value of 3.046. Instead allowing the primordial helium abundance (Y He ) to vary, the data favor Y He = 0.248 ±0.012. This is very close to the expectation of 0.2467 from big bang nucleosynthesis. When varying both Y He and N eff , we find N eff = 2.70 ±0.26 and Y He = 0.262 ±0.015.

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