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  1. Abstract We discuss the model of astrophysical emission at millimeter wavelengths used to characterize foregrounds in the multi-frequency power spectra of the Atacama Cosmology Telescope (ACT) Data Release 6 (DR6), expanding on Louis et al. (2025) (2503.14452). We detail several tests to validate the capability of the DR6 parametric foreground model to describe current observations and complex simulations, and show that cosmological parameter constraints are robust against model extensions and variations. We demonstrate consistency of the model with pre-DR6 ACT data and observations fromPlanckand the South Pole Telescope. We evaluate the implications of using different foreground templates and extending the model with new components and/or free parameters. In all scenarios, the DR6 ΛCDM and ΛCDM+Neffcosmological parameters shift by less than 0.5σrelative to the baseline constraints. Some foreground parameters shift more; we estimate their systematic uncertainties associated with modeling choices. From our constraint on the kinematic Sunyaev-Zel'dovich power, we obtain a conservative limit on the duration of reionization of Δzrei< 4.4, assuming a reionization midpoint consistent with optical depth measurements and a minimal low-redshift contribution, with varying assumptions for this component leading to tighter limits. Finally, we analyze realistic non-Gaussian, correlated microwave sky simulations containing Galactic and extragalactic foreground fields, built independently of the DR6 parametric foreground model. Processing these simulations through the DR6 power spectrum and likelihood pipeline, we recover the input cosmological parameters of the underlying cosmic microwave background field, a new demonstration for small-scale CMB analysis. These tests validate the robustness of the ACT DR6 foreground model and cosmological parameter constraints. 
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    Free, publicly-accessible full text available October 1, 2026
  2. Abstract The Atacama Cosmology Telescope Data Release 6 (ACT DR6) power spectrum is expected to provide state-of-the-art cosmological constraints, with an associated need for precise error modeling. In this paper we design, and evaluate the performance of, an analytic covariance matrix prescription for the DR6 power spectrum that sufficiently accounts for the complicated ACT map properties. We use recent advances in the literature to handle sharp features in the signal and noise power spectra, and account for the effect of map-level anisotropies on the covariance matrix. In including inhomogeneous survey depth information, the resulting covariance matrix prescription is structurally similar to that used in thePlanckCosmic Microwave Background (CMB) analysis. We quantify the performance of our prescription using comparisons to Monte Carlo simulations, finding better than 3% agreement. This represents an improvement from a simpler, pre-existing prescription, which differs from simulations by ∼ 16%. We develop a new method to correct the analytic covariance matrix using simulations, after which both prescriptions achieve better than 1% agreement. This correction method outperforms a commonly used alternative, where the analytic correlation matrix is assumed to be accurate when correcting the covariance. Beyond its use for ACT, this framework should be applicable for future high resolution CMB experiments including the Simons Observatory (SO). 
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    Free, publicly-accessible full text available May 1, 2026
  3. Abstract We present Atacama Cosmology Telescope (ACT) Data Release 6 (DR6) maps of the Cosmic Microwave Background temperature and polarization anisotropy at arcminute resolution over three frequency bands centered on 98, 150 and 220 GHz. The maps are based on data collected with the AdvancedACT camera over the period 2017–2022 and cover 19,000 square degrees with a median combined depth of 10 μK arcmin. We describe the instrument, mapmaking and map properties and illustrate them with a number of figures and tables. The ACT DR6 maps and derived products are available on LAMBDA athttps://lambda.gsfc.nasa.gov/product/act/actadv_prod_table.html. We also provide an interactive web atlas athttps://phy-act1.princeton.edu/public/snaess/actpol/dr6/atlasand HiPS data sets in Aladin (e.g.https://alasky.cds.unistra.fr/ACT/DR4DR6/color_CMB). 
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    Free, publicly-accessible full text available November 1, 2026
  4. ABSTRACT We present a coherent, re-usable python framework building on the CosmoPower emulator code for high-accuracy calculations of cosmological observables with Einstein–Boltzmann codes. For detailed statistical analyses, such codes require high computing power, making parameter space exploration costly, especially for beyond-$$\Lambda$$CDM analyses. Machine learning-enabled emulators of Einstein–Boltzmann codes are becoming an increasingly popular solution to this problem. To enable generation, sharing, and use of emulators for inference, we define standards for robustly describing, packaging, and distributing them. We present software for easily performing these tasks in an automated and replicable manner and provide examples and guidelines for generating emulators and wrappers for using them in popular cosmological inference codes. We demonstrate our framework with a suite of high-accuracy emulators for the CAMB code’s calculations of CMB $$C_\ell$$, $P(k)$, background evolution, and derived parameter quantities. We show these emulators are accurate enough for analysing both $$\Lambda$$CDM and a set of extension models ($$N_{\rm eff}$$, $$\sum m_\nu$$, $$w_0 w_a$$) with stage-IV observatories, recovering the original high-accuracy spectra to tolerances well within the cosmic variance uncertainties. We show our emulators also recover cosmological parameters in a simulated cosmic-variance limited experiment, finding results well within $$0.1 \sigma$$ of the input cosmology, while requiring $$\lesssim 1/50$$ of the evaluation time. 
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  5. Abstract We present power spectra of the cosmic microwave background (CMB) anisotropy in temperature and polarization, measured from the Data Release 6 maps made from Atacama Cosmology Telescope (ACT) data. These cover 19,000 deg2of sky in bands centered at 98, 150 and 220 GHz, with white noise levels three times lower thanPlanckin polarization. We find that the ACT angular power spectra estimated over 10,000 deg2, and measured to arcminute scales in TT, TE and EE, are well fit by the sum of CMB and foregrounds, where the CMB spectra are described by the ΛCDM model. Combining ACT with larger-scalePlanckdata, the joint P-ACT dataset provides tight limits on the ingredients, expansion rate, and initial conditions of the universe. We find similar constraining power, and consistent results, from either thePlanckpower spectra or from ACT combined withWMAPdata, as well as from either temperature or polarization in the joint P-ACT dataset. When combined with CMB lensing from ACT andPlanck, and baryon acoustic oscillation data from the Dark Energy Spectroscopic Instrument (DESI DR1), we measure a baryon density of Ωbh2= 0.0226 ± 0.0001, a cold dark matter density of Ωch2= 0.118 ± 0.001, a Hubble constant ofH0= 68.22 ± 0.36 km/s/Mpc, a spectral index ofns= 0.974 ± 0.003, and an amplitude of density fluctuations ofσ8= 0.813 ± 0.005. Including the DESI DR2 data tightens the Hubble constant toH0= 68.43 ± 0.27 km/s/Mpc; ΛCDM parameters agree between the P-ACT and DESI DR2 data at the 1.6σlevel. We find no evidence for excess lensing in the power spectrum, and no departure from spatial flatness. The contribution from Sunyaev-Zel'dovich (SZ) anisotropy is detected at high significance; we find evidence for a tilt with suppressed small-scale power compared to our baseline SZ template spectrum, consistent with hydrodynamical simulations with feedback. 
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    Free, publicly-accessible full text available November 1, 2026
  6. Abstract 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, ΛCDM, 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 thePlanckmission. To break geometric degeneracies, we include ACT andPlanckCMB 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 replacingPlanckwithWMAPand 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 indexdns/dlnk= 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 (Neff= 2.86 ± 0.13, which combined with astrophysical measurements of primordial helium and deuterium abundances becomesNeff= 2.89 ± 0.11), for non-zero neutrino masses (∑mν< 0.089 eV at 95% CL), or for neutrino self-interactions. We also find no evidence for self-interacting dark radiation (Nidr< 0.134), or for early-universe variation of fundamental constants, including the fine-structure constant (αEMEM,0= 1.0043 ± 0.0017) and the electron mass (me/me,0= 1.0063 ± 0.0056). Our data are consistent with standard big bang nucleosynthesis (we findYp= 0.2312 ± 0.0092), theCOBE/FIRAS-inferred CMB temperature (we findTCMB= 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 (γ= 0.663 ± 0.052). We find no statistically significant preference for a departure from the baseline ΛCDM model. In fits to models invoking early dark energy, primordial magnetic fields, or an arbitrary modified recombination history, we findH0= 69.9+0.8-1.5, 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 ΛCDM by our data. 
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    Free, publicly-accessible full text available November 1, 2026
  7. 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. 
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  8. Abstract We present a reproduction of thePlanck2018 angular power spectra at ℓ > 30, and associated covariance matrices, for intensity and polarization maps at 100, 143 and 217 GHz. This uses a new, publicly available, pipeline that is part of thePSpipepackage. As a test case we use the same input maps, ancillary products, and analysis choices as in thePlanck2018 analysis, and find that we can reproduce the spectra to 0.1σprecision, and the covariance matrices to 10%. We show that cosmological parameters estimated from our re-derived products agree with the publicPlanckproducts to 0.1σ, providing an independent cross-check of thePlanckteam's analysis. Going forward, the publicly-available code can be easily adapted to use alternative input maps, data selections and analysis choices, for future optimal analysis ofPlanckdata with new ground-based Cosmic Microwave Background data. 
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  9. Abstract The increasing statistical power of cosmic microwave background (CMB) datasets requires a commensurate effort in understanding their noise properties. The noise in maps from ground-based instruments is dominated by large-scale correlations, which poses a modeling challenge. This paper develops novel models of the complex noise covariance structure in the Atacama Cosmology Telescope Data Release 6 (ACT DR6) maps. We first enumerate the noise properties that arise from the combination of the atmosphere and the ACT scan strategy. We then prescribe a class of Gaussian, map-based noise models, including a new wavelet-based approach that uses directional wavelet kernels for modeling correlated instrumental noise. The models are empirical, whose only inputs are a small number of independent realizations of the same region of sky. We evaluate the performance of these models against the ACT DR6 data by drawing ensembles of noise realizations. Applying these simulations to the ACT DR6 power spectrum pipeline reveals a ∼ 20% excess in the covariance matrix diagonal when compared to an analytic expression that assumes noise properties are uniquely described by their power spectrum. Along with our public code,mnms, this work establishes a necessary element in the science pipelines of both ACT DR6 and future ground-based CMB experiments such as the Simons Observatory (SO). 
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  10. Abstract We present cosmological constraints from a gravitational lensing mass map covering 9400 deg2reconstructed from measurements of the cosmic microwave background (CMB) made by the Atacama Cosmology Telescope (ACT) from 2017 to 2021. In combination with measurements of baryon acoustic oscillations and big bang nucleosynthesis, we obtain the clustering amplitudeσ8= 0.819 ± 0.015 at 1.8% precision, S 8 σ 8 ( Ω m / 0.3 ) 0.5 = 0.840 ± 0.028 , and the Hubble constantH0= (68.3 ± 1.1) km s−1Mpc−1at 1.6% precision. A joint constraint with Planck CMB lensing yieldsσ8= 0.812 ± 0.013, S 8 σ 8 ( Ω m / 0.3 ) 0.5 = 0.831 ± 0.023 , andH0= (68.1 ± 1.0) km s−1Mpc−1. These measurements agree with ΛCDM extrapolations from the CMB anisotropies measured by Planck. We revisit constraints from the KiDS, DES, and HSC galaxy surveys with a uniform set of assumptions and find thatS8from all three are lower than that from ACT+Planck lensing by levels ranging from 1.7σto 2.1σ. This motivates further measurements and comparison, not just between the CMB anisotropies and galaxy lensing but also between CMB lensing probingz∼ 0.5–5 on mostly linear scales and galaxy lensing atz∼ 0.5 on smaller scales. We combine with CMB anisotropies to constrain extensions of ΛCDM, limiting neutrino masses to ∑mν< 0.13 eV (95% c.l.), for example. We describe the mass map and related data products that will enable a wide array of cross-correlation science. Our results provide independent confirmation that the universe is spatially flat, conforms with general relativity, and is described remarkably well by the ΛCDM model, while paving a promising path for neutrino physics with lensing from upcoming ground-based CMB surveys. 
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