Unexpected features have been observed in the cosmic microwave background (CMB) temperature on large scales. We revisit these CMB anomalies using new foreground-cleaned CMB temperature maps derived in a companion paper from WMAP and Planck data, which are tailored to low-resolution analysis and require only minimal masking of 1% of the sky. These maps allow us to assess the impact of foreground-cleaning methods and the choice of sky cut on the significance of five commonly studied CMB anomalies. We find a notable impact of the choice of galactic mask on the significance of two anomalies: the significance of the low real-space correlation function and of the local-variance asymmetry reduces from ∼3 σ for the Planck common mask with 26% masked fraction to ∼2 σ for the 1% mask. We find good agreement between the two sky cuts for the low northern variance, ∼3 σ , and the parity asymmetry, ∼2 σ . For the quadrupole-octopole alignment, we find good agreement between the 1% mask result and the full-sky results in the literature, ∼3 σ . Thus, using a larger fraction of the sky enabled by improved foreground cleaning reduces the significance of two commonly studied CMB anomalies. Overall, for an alternative physical model to be convincingly favored over Λ cold dark matter (CDM) with statistically isotropic Gaussian fluctuations, it would need to explain multiple CMB anomalies, or better describe some other type of measurement in addition to a CMB anomaly.

We present a cosmic microwave background (CMB) temperature power spectrum measurement at large angular scales from WMAP and Planck maps that were cleaned of foregrounds using a template-based approach described in the first paper of this series. We recover essentially the full-sky CMB information at multipoles ℓ < 30 with only 1% of pixels near the Galactic plane masked and with no inpainting. Notable features continue to appear: (a) a low quadrupole power compared to the best-fit Planck 2018 ΛCDM spectrum at 2.2 σ , (b) a dip in the range 20 ≤ ℓ ≤ 27, and (c) an overall ℓ < 30 power level low of the ΛCDM prediction derived from higher multipole moments. Given the different methodology from previous analyses and the nearly full-sky solution presented here, these features do not plausibly arise from foreground contamination, systematic errors, masking, or mode mixing. Our overall ℓ < 30 amplitude constraint is consistent with published WMAP (77% sky fraction) and Planck (86%) results at 1.2 σ and 0.6 σ , respectively, accounting for the improvement in statistical precision. We present a new ℓ < 30 likelihood for use with the Cobaya package. Parameter constraints from joint fits with the higher-multipole Planck data are consistent with the published Planck results; for example, we find H _0 = 67.35 ± 0.54 km s ^−1 Mpc ^−1 in a joint ΛCDM fit.

Studies of cosmic microwave background (CMB) are often limited by foreground contamination. Foreground cleaning is performed in either harmonic or pixel space after data cuts have excluded sky areas of strong contamination. We present a nearly full-sky CMB temperature map with only 1% of pixels masked. To derive this map, we make use of six full-sky template maps at foreground-dominated frequencies from different experiments smoothed to 1° and rely on the combination of these weighted maps to trace the morphology of foreground contamination. We do not impose any spectral index constraints but only fit for template amplitudes at each target frequency. We clean Wilkinson Microwave Anisotropy Probe and Planck maps at a set of target frequencies and conduct quality tests at the level of the maps, pixel histograms, and power spectra to select four CMB maps that are cleaned with negligible foreground contamination and only 1% masked pixels and no inpainting. We recommend use of these cleaned CMB maps for low-multipole ( ℓ < 30) studies.

The current standard model of cosmology successfully describes a variety of measurements, but the nature of its main ingredients, dark matter and dark energy, remains unknown. Euclid is a medium-class mission in the Cosmic Vision 2015-2025 programme of the European Space Agency (ESA) that will provide high-resolution optical imaging, as well as near-infrared imaging and spectroscopy, over about 14,000 deg^2 of extragalactic sky. In addition to accurate weak lensing and clustering measurements that probe structure formation over half of the age of the Universe, its primary probes for cosmology, these exquisite data will enable a wide range of science. This paper provides a high-level overview of the mission, summarising the survey characteristics, the various data-processing steps, and data products. We also highlight the main science objectives and expected performance.

We introduce a method for removing cosmic microwave background (CMB) and anomalous microwave emission (AME, or spinning dust) intensity signals at high to intermediate Galactic latitudes in temperature sky maps at frequencies roughly between 5 and 40 GHz. The method relies on the assumption of a spatially uniform combined dust (AME and thermal) rms spectral energy distribution for these regions but is otherwise model independent. A difference map is produced from input maps at two different frequencies in thermodynamic temperature: the two frequencies are chosen such that the rms AME signal in the lower-frequency (∼5−40 GHz) map is equivalent to the thermal dust emission rms in the higher-frequency (∼95−230 GHz) map. Given the high spatial correlation between AME and thermal dust, the resulting difference map is dominated by synchrotron and free–free foreground components and can thus provide useful insight into the morphology and possible spectral variations of these components at high latitudes. We show examples of these difference maps obtained with currently available WMAP and Planck data and demonstrate the efficacy of CMB and dust mitigation using this method. We also use these maps, in conjunction with Haslam 408 MHz and Wisconsin H-Alpha Mapper H α observations, to form an estimate of the diffuse synchrotron spectral index in brightness temperature on degree scales. The hybrid analysis approach we describe is advantageous in situations where frequency coverage is insufficient to break spectral degeneracies between AME and synchrotron.

We use new cosmic microwave background (CMB) primary temperature and polarization anisotropy measurements from the Atacama Cosmology Telescope (ACT) Data Release 6 (DR6) to test foundational assumptions of the standard cosmological model, Lambda CDM, and set constraints on extensions to it. We derive constraints from the ACT DR6 power spectra alone, as well as in combination with legacy data from the Planck mission. To break geometric degeneracies, we include ACT and Planck CMB lensing data and baryon acoustic oscillation data from DESI Year-1. To test the dependence of our results on non-ACT data, we also explore combinations replacing Planck with WMAP and DESI with BOSS, and further add supernovae measurements from Pantheon+ for models that affect the late-time expansion history. We verify the near-scale-invariance (running of the spectral index dn(s)/d ln k = 0.0062 +/- 0.0052) and adiabaticity of the primordial perturbations. Neutrino properties are consistent with Standard Model predictions: we find no evidence for new light, relativistic species that are free-streaming (N-eff = 2.86 +/- 0.13, which combined with astrophysical measurements of primordial helium and deuterium abundances becomes N-eff = 2.89 +/- 0.11), for non-zero neutrino masses (Sigma m(nu) < 0.089 eV at 95% CL), or for neutrino self-interactions. We also find no evidence for self-interacting dark radiation (N-idr < 0.134), or for early-universe variation of fundamental constants, including the fine-structure constant (alpha(EM)/alpha(EM,0) = 1.0043 +/- 0.0017) and the electron mass (m(e)/m(e,0) = 1.0063 +/- 0.0056). Our data are consistent with standard big bang nucleosynthesis (we find Y-p = 0.2312 +/- 0.0092), the COBE/FIRAS-inferred CMB temperature (we find T-CMB = 2.698 +/- 0.016 K), a dark matter component that is collisionless and with only a small fraction allowed as axion-like particles, a cosmological constant (w = -0.986 +/- 0.025), and the late-time growth rate predicted by general relativity (gamma = 0.663 +/- 0.052). We find no statistically significant preference for a departure from the baseline Lambda CDM model. In fits to models invoking early dark energy, primordial magnetic fields, or an arbitrary modified recombination history, we find H-0 = 69.9(-1.5)(+0.8), 69.1 +/- 0.5, or 69.6 +/- 1.0 km/s/Mpc, respectively; using BOSS instead of DESI BAO data reduces the central values of these constraints by 1-1.5 km/s/Mpc while only slightly increasing the error bars. In general, models introduced to increase the Hubble constant or to decrease the amplitude of density fluctuations inferred from the primary CMB are not favored over Lambda CDM by our data.

JWST provides new opportunities to cross-check the HST Cepheid/SNeIa distance ladder, which yields the most precise local measure of H0. We analyze early JWST subsamples (~1/4 of the HST sample) from the SH0ES and CCHP groups, calibrated by a single anchor (N4258). We find HST Cepheid distances agree well (~1 sigma) with all 8 combinations of methods, samples, and telescopes: JWST Cepheids, TRGB, and JAGB by either group, plus HST TRGB and Miras. The comparisons explicitly include the measurement uncertainty of each method in N4258, an oft-neglected but dominant term. Mean differences are ~0.03 mag, far smaller than the 0.18 mag "Hubble tension." Combining all measures produces the strongest constraint yet on the linearity of HST Cepheid distances, 0.994+-0.010, ruling out distance-dependent bias or offset as the source of the tension at ~7 sigma. Yet, measurements of H0 from current JWST subsamples produce large sampling differences whose size and direction we can directly estimate from the full HST set. We show that Delta(H0)~2.5 km/s/Mpc between the CCHP JWST program and the full HST sample is entirely consistent with differences in sample selection. Combining all JWST samples produces a new, distance-limited set of 16 SNeIa at D<25 Mpc and more closely resembles the full sample thanks to "reversion to the mean" of larger samples. Using JWST Cepheids, JAGB, and TRGB, we find 73.4+-2.1, 72.2+-2.2, and 72.1+-2.2 km/s/Mpc, respectively. Explicitly accounting for SNe in common, the combined-sample three-method result from JWST is H0=72.6+-2.0, similar to H0=72.8 expected from HST Cepheids in the same galaxies. The small JWST sample trivially lowers the Hubble tension significance due to small-sample statistics and is not yet competitive with the HST set (42 SNeIa and 4 anchors), which yields 73.2+-0.9. Still, the joint JWST sample provides important crosschecks which the HST data passes.

We introduce a method for removing CMB and anomalous microwave emission (AME, or spinning dust) intensity signals at high to intermediate Galactic latitudes in temperature sky maps at frequencies roughly between 5 and 40 GHz. The method relies on the assumption of a spatially uniform combined dust (AME and thermal) rms spectral energy distribution for these regions, but is otherwise model independent. A difference map is produced from input maps at two different frequencies in thermodynamic temperature: the two frequencies are chosen such that the rms AME signal in the lower frequency (~5 - 40 GHz) map is equivalent to the thermal dust emission rms in the higher frequency (~95 - 230 GHz) map. Given the high spatial correlation between AME and thermal dust, the resulting difference map is dominated by synchrotron and free-free foreground components, and can thus provide useful insight into the morphology and possible spectral variations of these components at high latitudes. We show examples of these difference maps obtained with currently available WMAP and Planck data and demonstrate the efficacy of CMB and dust mitigation using this method. We also use these maps, in conjunction with Haslam 408 MHz and WHAM H-alpha observations, to form an estimate of the diffuse synchrotron spectral index in temperature on degree scales. The hybrid analysis approach we describe is advantageous in situations where frequency coverage is insufficient to break spectral degeneracies between AME and synchrotron.

We revisit the lensing anomaly in the Planck 2018 temperature (TT) data and examine its robustness to frequency selection and additional sky masking. Our main findings are: (1) The phenomenological lensing amplitude parameter, $A_L$, varies with ecliptic latitude, with a $2.9\sigma$ preference for $A_L>1$ near the ecliptic, and $1.0\sigma$ preference near the ecliptic poles, compared to $2.5\sigma$ on the original masks. This behavior is largely or solely from 217 GHz and suggestive of some non-random effect given the Planck scan strategy. (2) The 217 GHz TT data also show a stronger preference for $A_L>1$ than the lower frequencies. The shifts in $A_L$ from 217 GHz with additional Galactic dust masking are too large to be explained solely by statistical fluctuations, indicating some connection with the foreground treatment. Overall, the Planck $A_L$ anomaly does not have a single simple cause. Removing the 217 GHz TT data leaves a $1.8\sigma$ preference for $A_L>1$. The low-multipole ($\ell<30$) TT data contribute to the preference for $A_L>1$ through correlations with $\Lambda$CDM parameters. The 100 and 143 GHz data at $\ell\geq30$ prefer $A_L>1$ at $1.3\sigma$, and this appears robust to the masking tests we performed. The lensing anomaly may impact fits to alternative cosmological models. Marginalizing over $A_L$, optionally applied only to Planck TT spectra, can check this. Models proposed to address cosmological tensions should be robust to removal of the Planck 217 GHz TT data.

We cross-check the Hubble Space Telescope (HST) Cepheid/Type Ia supernova (SN Ia) distance ladder, which yields the most precise local H 0, against early James Webb Space Telescope (JWST) subsamples (similar to 1/4 of the HST sample) from SH0ES and CCHP, calibrated only with NGC 4258. We find HST Cepheid distances agree well (similar to 1 sigma) with all combinations of methods, samples, and telescopes. The comparisons explicitly include the measurement uncertainty of each method in NGC 4258, an oft-neglected but dominant term. Mean differences are similar to 0.03 mag, far smaller than the 0.18 mag "Hubble tension." Combining all measures produces the strongest constraint yet on the linearity of HST Cepheid distances, 0.994 +/- 0.010, ruling out distance-dependent bias or offset as the source of the tension at similar to 7 sigma. However, current JWST subsamples produce large sampling differences in H0 whose size and direction we can directly estimate from the full HST set. We show that Delta H 0 similar to 2.5 km s-1 Mpc-1 between the CCHP JWST program and the full HST sample is entirely consistent with differences in sample selection. We combine all JWST samples into a new distance-limited set of 16 SNe Ia at D <= 25 Mpc. Using JWST Cepheids, JAGB, and tip of the red giant branch, we find 73.4 +/- 2.1, 72.2 +/- 2.2, and 72.1 +/- 2.2 km s-1 Mpc-1, respectively. Explicitly accounting for common supernovae, the three-method JWST result is H 0 = 72.6 +/- 2.0, similar to H 0 = 72.8 expected from HST Cepheids in the same galaxies. The small JWST sample trivially lowers the Hubble tension significance due to small-sample statistics and is not yet competitive with the HST set (42 SNe Ia and 4 anchors), which yields 73.2 +/- 0.9. Still, the joint JWST sample provides important cross-checks that the HST data pass.

We revisit the claimed detection of a new cosmic microwave background (CMB) foreground based on the correlation between low-redshift 2MASS Redshift Survey (2MRS) galaxies and CMB temperature maps from the Planck and WMAP missions. We reproduce the reported measurements but argue that the original analysis significantly underestimated the uncertainties. We cross-correlate the 2MRS galaxy positions with simulated CMB maps and show that the correlation measured with the real data for late-type spiral galaxies at angular scales $\theta\geq0.1^{\circ}$ and redshift $cz<4500$ km s$^{-1}$ is consistent with zero at the $1.7\sigma$ level or less, depending on the exact CMB map and simulation construction. This was the sample that formed the basis for the original detection claim. For smaller angular separations the results are not robust to galaxy type or CMB cleaning method, and we are unable to draw firm conclusions. The original analysis did not propose a specific, falsifiable physical correlation mechanism, and it is impossible to rule out any contribution from an underlying physical effect. However, given our calculations, the lack of signal from expanding the redshift range, and the lack of corroboration from other galaxy surveys, we do not find the evidence for a new CMB foreground signal compelling.

In this follow-up analysis, we update previous constraints on the transitional Planck mass (TPM) modified gravity model using the latest version of EFTCAMB and provide new constraints using South Pole Telescope (SPT) and Planck anisotropy data along with Planck cosmic microwave background lensing, baryon acoustic oscillations, and Type Ia supernovae data and a Hubble constant, H 0 , prior from local measurements. We find that large shifts in the Planck mass lead to large suppression of power on small scales that is disfavored by both the SPT and Planck data. Using only the SPT temperature-polarization–polarization-polarization (TE-EE) data, this suppression of power can be compensated for by an upward shift of the scalar index to n s = 1.003 ± 0.016, resulting in H 0 = 71.94 − 0.85 + 0.86 km m −1 Mpc −1 and a ∼7% shift in the Planck mass. Including the Planck temperature-temperature (TT) ℓ ≤ 650 and Planck TE-EE data restricts the shift to be <5% at 2 σ with H 0 = 70.65 ± 0.66 km m −1 Mpc −1 . Excluding the H 0 prior, the SPT and Planck data constrain the shift in the Planck mass to be <3% at 2 σ with a best-fit value of 0.04%, consistent with the Λ cold dark matter limit. In this case H 0 = 69.09 − 0.68 + 0.69 km s −1 Mpc −1 , which is partially elevated by the dynamics of the scalar field in the late Universe. This differs from early dark energy models that prefer higher values of H 0 when the high- ℓ Planck TT data are excluded. We additionally constrain TPM using redshift space distortion data from BOSS DR12 and cosmic shear, galaxy–galaxy lensing, and galaxy clustering data from DES Y1, finding both disfavor transitions close to recombination, but earlier Planck mass transitions are allowed.

This Snowmass 2021 White Paper describes the Cosmic Microwave Background Stage 4 project CMB-S4, which is designed to cross critical thresholds in our understanding of the origin and evolution of the Universe, from the highest energies at the dawn of time through the growth of structure to the present day. We provide an overview of the science case, the technical design, and project plan.

Polarized Galactic synchrotron emission is an undesirable foreground for cosmic microwave background experiments observing at frequencies <150 GHz. We perform a combined analysis of observational data at 1.4, 2.3, 23, 30, and 33 GHz to quantify the spatial variation of the polarized synchrotron spectral index, β pol , on ∼3.°5 scales. We compare results from different data combinations to address limitations and inconsistencies present in these public data, and form a composite map of β pol . Data quality masking leaves 44% sky coverage (73% for ∣ b ∣ > 45°). Generally −3.2 < β pol ≲ −3 in the inner Galactic plane and spurs, but the Fan Region in the outer galaxy has a flatter index. We find a clear spectral index steepening with increasing latitude south of the Galactic plane with Δ β pol = 0.4, and a smaller steepening of 0.25 in the north. Near the south Galactic pole the polarized synchrotron spectral index is β pol ≈ −3.4. Longitudinal spectral index variations of Δ β pol ∼ 0.1 about the latitudinal mean are also detected. Within the BICEP2/Keck survey footprint, we find consistency with a constant value, β pol = −3.25 ± 0.04 (statistical) ±0.02 (systematic). We compute a map of the frequency at which synchrotron and thermal dust emission contribute equally to the total polarized foreground. The limitations and inconsistencies among data sets encountered in this work make clear the value of additional independent surveys at multiple frequencies, especially between 10 and 20 GHz, provided these surveys have sufficient sensitivity and control of instrumental systematic errors.

CMB-S4—the next-generation ground-based cosmic microwave background (CMB) experiment—is set to significantly advance the sensitivity of CMB measurements and enhance our understanding of the origin and evolution of the universe. Among the science cases pursued with CMB-S4, the quest for detecting primordial gravitational waves is a central driver of the experimental design. This work details the development of a forecasting framework that includes a power-spectrum-based semianalytic projection tool, targeted explicitly toward optimizing constraints on the tensor-to-scalar ratio, r, in the presence of Galactic foregrounds and gravitational lensing of the CMB. This framework is unique in its direct use of information from the achieved performance of current Stage 2–3 CMB experiments to robustly forecast the science reach of upcoming CMB-polarization endeavors. The methodology allows for rapid iteration over experimental configurations and offers a flexible way to optimize the design of future experiments, given a desired scientific goal. To form a closed-loop process, we couple this semianalytic tool with map-based validation studies, which allow for the injection of additional complexity and verification of our forecasts with several independent analysis methods. We document multiple rounds of forecasts for CMB-S4 using this process and the resulting establishment of the current reference design of the primordial gravitational-wave component of the Stage-4 experiment, optimized to achieve our science goals of detecting primordial gravitational waves for r > 0.003 at greater than 5σ, or in the absence of a detection, of reaching an upper limit of r < 0.001 at 95% CL.

We study a step-like transition in the value of the effective Planck mass (or effective gravitational constant) on cosmological scales prior to recombination. We employ cosmic microwave background, baryon acoustic oscillations, and Type Ia supernova data and find they are sufficient to strongly constrain our implementation of the effective field theory of dark energy and modified gravity, used to model the transition, to a limited parameter space. The data prefer a ∼5% shift in the value of the effective Planck mass (<10% at 2σ) prior to recombination. This Transitional Planck Mass (TPM) model is free to undergo its transition at any point over multiple decades of scale factor prior to recombination, log10(a)=−5.32−0.72+0.96 (68% confidence level). This lowers the sound horizon at last scattering, which increases the Hubble constant to 71.09 ± 0.75 km s−1 Mpc−1 with a combination of local measurements as prior and to 69.22−0.86+0.67 km s−1 Mpc−1 when the prior is excluded. The TPM model improves χ 2 with respect to ΛCDM by Δχ 2 = −23.72 with the H 0 prior and Δχ 2 = −4.8 without the prior. The model allows for both H 0 > 70 kms−1 Mpc−1 and S 8 < 0.80 simultaneously with lower values of S 8 due to a reduction in the matter density Ω m to offset the increase in H 0 relative to ΛCDM. While this is a particular modified gravity model, studying other variants of modified gravity may be a productive path for potentially resolving cosmological tensions while avoiding the need for a cosmological constant.

Using Planck polarization data, we search for and constrain spatial variations of the polarized dust foreground for cosmic microwave background (CMB) observations, specifically in its spectral index, $\beta_d$. Failure to account for such variations will cause errors in the foreground cleaning that propagate into errors on cosmological parameter recovery from the cleaned CMB map. It is unclear how robust prior studies of the Planck data which constrained $\beta_d$ variations are due to challenges with noise modeling, residual systematics, and priors. To clarify constraints on $\beta_d$ and its variation, we employ two pixel space analyses of the polarized dust foreground at $>3.7^{\circ}$ scales on $\approx 60\%$ of the sky at high Galactic latitudes. A template fitting method, which measures $\beta_d$ over three regions of $\approx 20\%$ of the sky, does not find significant deviations from an uniform $\beta_d = 1.55$, consistent with prior Planck determinations. An additional analysis in these regions, based on multifrequency fits to a dust and CMB model per pixel, puts limits on $\sigma_{\beta_d}$, the Gaussian spatial variation in $\beta_d$. At the highest latitudes, the data support $\sigma_{\beta_d}$ up to $0.45$, $0.30$ at mid-latitudes, and $0.15$ at low-latitudes. We also demonstrate that care must be taken when interpreting the current Planck constraints, $\beta_d$ maps, and noise simulations. Due to residual systematics and low dust signal to noise at high latitudes, forecasts for ongoing and future missions should include the possibility of large values of $\sigma_{\beta_d}$ as estimated in this paper, based on current polarization data.

The E-mode (EE) CMB power spectra measured by Planck, ACTPol, and SPTpol constrain the Hubble constant to be 70.0 ± 2.7, , and km s−1 Mpc−1 within the standard ΛCDM model (posterior mean and central 68% interval bounds). These values are higher than the constraints from the Planck temperature (TT) power spectrum, and consistent with the Cepheid-supernova distance ladder measurement H 0 = 73.2 ± 1.3 km s−1 Mpc−1. If this preference for a higher value was strengthened in a joint analysis it could provide an intriguing hint at the resolution of the Hubble disagreement. We show, however, that combining the Planck, ACTPol, and SPTpol EE likelihoods yields H 0 = 68.7 ± 1.3 km s−1 Mpc−1, 2.4σ lower than the distance ladder measurement. This is due to different degeneracy directions across the full parameter space, particularly involving the baryon density, Ω b h 2, and scalar tilt, n s , arising from sensitivity to different multipole ranges. We show that the E-mode ΛCDM constraints are consistent across the different experiments within 1.4σ, and with the Planck TT results at 0.8σ. Combining the Planck, ACTPol, and SPTpol EE data constrains the phenomenological lensing amplitude, A L = 0.89 ± 0.10, consistent with the expected value of unity.

Consistency checks of Lambda cold dark matter (?CDM) predictions with current cosmological data sets may illuminate the types of changes needed to resolve cosmological tensions. To this end, we modify the CLASS Boltzmann code to create phenomenological amplitudes, similar to the lensing amplitude parameter A(L), for the Sachs-Wolfe, Doppler, early Integrated Sachs-Wolfe (eISW), and polarization contributions to the cosmic microwave background temperature anisotropy, and then we include these additional amplitudes in fits to the Planck TT power spectrum. We find that allowing one of these amplitudes to vary at a time results in little improvement over ?CDM alone suggesting that each of these physical effects are being correctly accounted for given the current level of precision. Further, we find that the only pair of phenomenological amplitudes that results in a significant improvement to the fit to Planck temperature data results from varying the amplitudes of the Sachs-Wolfe and Doppler effects simultaneously. However, we show that this model is really just refinding the ?CDM + A(L) solution. We test adding our phenomenological amplitudes as well as N-eff, Y-He, and n(run) to ?CDM + A(L) and find that none of these model extensions provide significant improvement over ?CDM + A(L) when fitting Planck temperature data. Finally, we quantify the contributions of both the eISW effect and lensing on the constraint of the physical matter density from Planck temperature data by allowing the phenomenological amplitude from each effect to vary. We find that these effects play a relatively small role (the uncertainty increases by 3.5% and 16% respectively) suggesting that the overall photon envelope has the greatest constraining power.

We present the temperature and polarization angular power spectra of the CMB measured by the Atacama Cosmology Telescope (ACT) from 5400 deg2of the 2013–2016 survey, which covers >15000 deg2at 98 and 150 GHz. For this analysis we adopt a blinding strategy to help avoid confirmation bias and, related to this, show numerous checks for systematic error done before unblinding. Using the likelihood for the cosmological analysis we constrain secondary sources of anisotropy and foreground emission, and derive a “CMB-only” spectrum that extends to ℓ=4000. At large angular scales, foreground emission at 150 GHz is ∼1% of TT and EE within our selected regions and consistent with that found byPlanck. Using the same likelihood, we obtain the cosmological parameters for ΛCDM for the ACT data alone with a prior on the optical depth of τ=0.065±0.015. ΛCDM is a good fit. The best-fit model has a reduced χ2of 1.07 (PTE=0.07) withH0=67.9±1.5 km/s/Mpc. We show that the lensing BB signal is consistent with ΛCDM and limit the celestial EB polarization angle to ψP =−0.07̂±0.09̂. We directly cross correlate ACT withPlanckand observe generally good agreement but with some discrepancies in TE. All data on which this analysis is based will be publicly released.