Johannes Røsok Eskilt

• Eskilt, Johannes Røsok (2026). Cosmic birefringence from a joint analysis of ACT and Planck. Physical Review D. ISSN 2470-0010. 114(4). doi: 10.1103/HCSM-39QW. Full text in Research Archive Show summary

  Dark matter and dark energy could be ultralight pseudoscalar fields that couple to electromagnetism through a Chern-Simons term. This would cause a parity-breaking rotation of the plane of linearly polarized light from the cosmic microwave background, known as cosmic birefringence, which is not predicted by Λ cold dark matter. Recent hints of a nonzero cosmic birefringence angle have been found in both the Planck Data Release 4 and Atacama Cosmology Telescope Data Release 6 datasets independently. This work jointly analyzes the polarized maps of both, leveraging the cross-power spectra between the two telescopes. Taking the reported instrumental priors at face value, the joint analysis yields 𝛽 =0.27⁢7°±0.05⁢7°, which is nonzero with a statistical significance of 4.8⁢𝜎. A robustness test mitigating contamination from dust emission excludes 𝛽 =0° at 3.5⁢𝜎, and retrieving 𝛽 =0° would require both the dust 𝐸⁢𝐵 modeling and instrumental priors to fail simultaneously. However, unresolved systematics in the data must be understood before we can draw strong cosmological conclusions.

• Copi, Craig J.; Samandar, Amirhossein; Starkman, Glenn D.; Duque, Javier Carrón; Akrami, Yashar & Anselmi, Stefano [Show all 16 contributors for this article] (2026). Cosmic topology. Part IIb. Eigenmodes, correlation matrices, and detectability of non-orientable Euclidean manifolds. Journal of Cosmology and Astroparticle Physics (JCAP). 2026(7). doi: 10.1088/1475-7516/2026/07/004. Full text in Research Archive Show summary

  If the Universe has non-trivial spatial topology, observables depend on both the parameters of the spatial manifold and the position and orientation of the observer. In infinite Euclidean space, most cosmological observables arise from the amplitudes of Fourier modes of primordial scalar curvature perturbations. Topological boundary conditions replace the full set of Fourier modes with specific linear combinations of selected Fourier modes as the eigenmodes of the scalar Laplacian. In an earlier work we provided a comprehensive treatment of orientable Euclidean three-manifolds; but a thorough exploration of cosmic topology must include non-orientable three-manifolds as candidates for the geometry of space. In this paper we consider the non-orientable Euclidean topologies E7–E10, E13–E15, and E17, encompassing the full range of manifold parameters and observer positions, generalizing previous treatments. Under the assumption that the amplitudes of primordial scalar curvature eigenmodes are independent random variables, for each topology we obtain the correlation matrices of Fourier-mode amplitudes (of scalar fields linearly related to the scalar curvature) and the correlation matrices of spherical-harmonic coefficients of such fields sampled on a sphere, such as the temperature of the cosmic microwave background (CMB). We evaluate the detectability of these correlations given the cosmic variance of the CMB sky. As for orientable three-manifolds, we find that in manifolds where the distance to our nearest clone is less than about 1.2 times the diameter of the last scattering surface of the CMB, we expect a correlation signal that is larger than cosmic variance noise in the CMB. The parameter space of the non-orientable Euclidean manifolds is quite rich, supporting, for example, complex dependencies of clone distances on those parameters. Our limited selection of manifold parameters — both the values of those we fix, and the choices of which to vary — are therefore exemplary of interesting behaviors (e.g., of how well the manifold can be distinguished from the covering space), but not necessarily representative. Future searches for topology will certainly require a much more thorough exploration of the parameter space to determine what values of the parameters predict statistical correlations that are convincingly attributable to topology.

• Samandar, Amirhossein; Duque, Javier Carrón; Copi, Craig J.; Barandiaran, Mikel Martin; Mihaylov, Deyan P. & Starkman, Glenn D. [Show all 16 contributors for this article] (2025). Cosmic topology. Part IIIb. Eigenmodes and correlation matrices of spin-2 perturbations in orientable Euclidean manifolds. Journal of Cosmology and Astroparticle Physics (JCAP). 2025(08). doi: 10.1088/1475-7516/2025/08/015. Full text in Research Archive Show summary

  We study the eigenmodes of the spin-2 Laplacian in orientable Euclidean manifolds and their implications for the tensor-induced part of the cosmic microwave background (CMB) temperature and polarization anisotropies. We provide analytic expressions for the correlation matrices of Fourier-mode amplitudes and of spherical harmonic coefficients. We demonstrate that non-trivial spatial topology alters the statistical properties of CMB tensor anisotropies, inducing correlations between harmonic coefficients of differing ℓ and m and across every possible pair of temperature and E- and B-modes of polarization. This includes normally forbidden TB and EB correlations. We compute the Kullback-Leibler (KL) divergence between the pure tensor-induced CMB fluctuations in the usual infinite covering space and those in each of the non-trivial manifolds under consideration, varying both the size of the manifolds and the location of the observer. We find that the amount of information about the topology of the Universe contained in tensor-induced anisotropies does not saturate as fast as its scalar counterpart; indeed, the KL divergence continues to grow with the inclusion of higher multipoles up to the largest ℓ we have computed. Our results suggest that CMB polarization measurements from upcoming experiments can provide new avenues for detecting signatures of cosmic topology, motivating a full analysis where scalar and tensor perturbations are combined and noise is included.

• Akrami, Yashar; Anselmi, Stefano; Copi, Craig J.; Eskilt, Johannes Røsok; Jaffe, Andrew H. & Kosowsky, Arthur [Show all 15 contributors for this article] (2024). Promise of Future Searches for Cosmic Topology. Physical Review Letters. ISSN 0031-9007. 132(17). doi: 10.1103/PhysRevLett.132.171501. Full text in Research Archive Show summary

  The shortest distance around the Universe through us is unlikely to be much larger than the horizon diameter if microwave background anomalies are due to cosmic topology. We show that observational constraints from the lack of matched temperature circles in the microwave background leave many possibilities for such topologies. We evaluate the detectability of microwave background multipole correlations for sample cases. Searches for topology signatures in observational data over the large space of possible topologies pose a formidable computational challenge.

• Samandar, Amirhossein; Duque, Javier Carrón; Copi, Craig J.; Barandiaran, Mikel Martin; Mihaylov, Deyan P. & Pereira, Thiago dos Santos [Show all 14 contributors for this article] (2024). Cosmic topology. Part IIIa. Microwave background parity violation without parity-violating microphysics. Journal of Cosmology and Astroparticle Physics (JCAP). 2024(11). doi: 10.1088/1475-7516/2024/11/020. Full text in Research Archive Show summary

  The standard cosmological model, which assumes statistical isotropy and parity invariance, predicts the absence of correlations between even-parity and odd-parity observables of the cosmic microwave background (CMB). Contrary to these predictions, large-angle CMB temperature anomalies generically involve correlations between even-ℓ and odd-ℓ angular power spectrum Cℓ, while recent analyses of CMB polarization have revealed non-zero equal-ℓEB correlations. These findings challenge the conventional understanding, suggesting deviations from statistical isotropy, violations of parity, or both. Cosmic topology, which involves changing only the boundary conditions of space relative to standard cosmology, offers a compelling framework to potentially account for such parity-violating observations. Topology inherently breaks statistical isotropy, and can also break homogeneity and parity, providing a natural paradigm for explaining observations of parity-breaking observables without the need to add parity violation to the underlying microphysics. Our investigation delves into the harmonic space implications of topology for CMB correlations, using as an illustrative example EB correlations generated by tensor perturbations under both parity-preserving and parity-violating scenarios. Consequently, these findings not only challenge the foundational assumptions of the standard cosmological model but also open new avenues for exploring the topological structure of the Universe through CMB observations.

• Tamosiunas, Andrius; Cornet-Gomez, Fernando; Akrami, Yashar; Anselmi, Stefano; Duque, Javier Carron & Copi, Craig J. [Show all 19 contributors for this article] (2024). Cosmic topology. Part IVa. Classification of manifolds using machine learning: a case study with small toroidal universes. Journal of Cosmology and Astroparticle Physics (JCAP). 2024(9). doi: 10.1088/1475-7516/2024/09/057. Full text in Research Archive Show summary

  Non-trivial spatial topology of the Universe may give rise to potentially measurable signatures in the cosmic microwave background. We explore different machine learning approaches to classify harmonic-space realizations of the microwave background in the test case of Euclidean E1 topology (the 3-torus) with a cubic fundamental domain of a size scale significantly smaller than the diameter of the last scattering surface. This is the first step toward developing a machine learning approach to classification of cosmic topology and likelihood-free inference of topological parameters. Different machine learning approaches are capable of classifying the harmonic-space realizations with accuracy greater than 99% if the topology scale is half of the diameter of the last-scattering surface and orientation of the topology is known. For distinguishing random rotations of these sky realizations from realizations of the covering space, the extreme gradient boosting classifier algorithm performs best with an accuracy of 88%. Slightly lower accuracies of 83% to 87% are obtained with the random forest classifier along with one- and two-dimensional convolutional neural networks. The techniques presented here can also accurately classify non-rotated cubic E1 topology realizations with a topology scale slightly larger than the diameter of the last-scattering surface, if enough training data are provided. While information compressing methods like most machine learning approaches cannot exceed the statistical power of a likelihood-based approach that captures all available information, they potentially offer a computationally cheaper alternative. A principle challenge appears to be accounting for arbitrary orientations of a given topology, although this is also a significant hurdle for likelihood-based approaches.

• Eskilt, Johannes Røsok; Akrami, Yashar; Anselmi, Stefano; Copi, Craig J.; Jaffe, Andrew H. & Kosowsky, Arthur [Show all 14 contributors for this article] (2024). Cosmic topology. Part IIa. Eigenmodes, correlation matrices, and detectability of orientable Euclidean manifolds. Journal of Cosmology and Astroparticle Physics (JCAP). 2024(3). doi: 10.1088/1475-7516/2024/03/036. Full text in Research Archive Show summary

  If the Universe has non-trivial spatial topology, observables depend on both the parameters of the spatial manifold and the position and orientation of the observer. In infinite Euclidean space, most cosmological observables arise from the amplitudes of Fourier modes of primordial scalar curvature perturbations. Topological boundary conditions replace the full set of Fourier modes with specific linear combinations of selected Fourier modes as the eigenmodes of the scalar Laplacian. We present formulas for eigenmodes in orientable Euclidean manifolds with the topologies E1–E6, E11, E12, E16, and E18 that encompass the full range of manifold parameters and observer positions, generalizing previous treatments. Under the assumption that the amplitudes of primordial scalar curvature eigenmodes are independent random variables, for each topology we obtain the correlation matrices of Fourier-mode amplitudes (of scalar fields linearly related to the scalar curvature) and the correlation matrices of spherical-harmonic coefficients of such fields sampled on a sphere, such as the temperature of the cosmic microwave background (CMB). We evaluate the detectability of these correlations given the cosmic variance of the observed CMB sky. We find that topologies where the distance to our nearest clone is less than about 1.2 times the diameter of the last scattering surface of the CMB give a correlation signal that is larger than cosmic variance noise in the CMB. This implies that if cosmic topology is the explanation of large-angle anomalies in the CMB, then the distance to our nearest clone is not much larger than the diameter of the last scattering surface. We argue that the topological information is likely to be better preserved in three-dimensional data, such as will eventually be available from large-scale structure surveys.

• Eskilt, Johannes Røsok; Watts, Duncan; Aurvik, Ragnhild; Basyrov, Artem; Bersanelli, Marco & Brilenkov, Maksym [Show all 31 contributors for this article] (2023). Cosmoglobe DR1 results II. Constraints on isotropic cosmic birefringence from reprocessed WMAP and Planck LFI data. Astronomy and Astrophysics (A & A). ISSN 0004-6361. 679. doi: 10.1051/0004-6361/202346829. Full text in Research Archive Show summary

  Cosmic birefringence is a parity-violating effect that might have rotated the plane of the linearly polarized light of the cosmic microwave background (CMB) by an angle β since its emission. This angle has recently been measured to be nonzero at a statistical significance of 3.6 σ in the official Planck PR4 and 9-year WMAP data. In this work, we constrain β using the reprocessed B EYOND P LANCK LFI and C OSMOGLOBE DR1 WMAP polarization maps. These novel maps have both lower systematic residuals and a more complete error description than the corresponding official products. Foreground EB correlations could bias measurements of β , and while thermal dust EB emission has been argued to be statistically nonzero, no evidence for synchrotron EB power has been reported. Unlike the dust-dominated Planck HFI maps, the majority of the LFI and WMAP polarization maps are instead dominated by synchrotron emission. Simultaneously constraining β and the polarization miscalibration angle, α , of each channel, we find a best-fit value of β  = 0.35° ±0.70° with LFI and WMAP data only. When including the Planck HFI PR4 maps, but fitting β separately for dust-dominated, β > 70 GHz , and synchrotron-dominated channels, β ≤70 GHz , we find β ≤70 GHz  = 0.53° ±0.28°. This differs from zero with a statistical significance of 1.9 σ , and the main contribution to this value comes from the LFI 70 GHz channel. While the statistical significances of these results are low on their own, the measurement derived from the LFI and WMAP synchrotron-dominated maps agrees with the previously reported HFI-dominated constraints, despite the very different astrophysical and instrumental systematics involved in all these experiments.

• Brilenkov, Maksym; Fornazier, K.S.F.; Hergt, L.T.; Hoerning, G.A.; Marins, A. & Murokoshi, T. [Show all 51 contributors for this article] (2023). BeyondPlanck: IV. Simulations and validation. Astronomy and Astrophysics (A & A). ISSN 0004-6361. 675. doi: 10.1051/0004-6361/202244958. Full text in Research Archive Show summary

  End-to-end simulations play a key role in the analysis of any high-sensitivity cosmic microwave background (CMB) experiment, providing high-fidelity systematic error propagation capabilities that are unmatched by any other means. In this paper, we address an important issue regarding such simulations, namely, how to define the inputs in terms of sky model and instrument parameters. These may either be taken as a constrained realization derived from the data or as a random realization independent from the data. We refer to these as posterior and prior simulations, respectively. We show that the two options lead to significantly different correlation structures, as prior simulations (contrary to posterior simulations) effectively include cosmic variance, but they exclude realization-specific correlations from non-linear degeneracies. Consequently, they quantify fundamentally different types of uncertainties. We argue that as a result, they also have different and complementary scientific uses, even if this dichotomy is not absolute. In particular, posterior simulations are in general more convenient for parameter estimation studies, while prior simulations are generally more convenient for model testing. Before B EYOND P LANCK , most pipelines used a mix of constrained and random inputs and applied the same hybrid simulations for all applications, even though the statistical justification for this is not always evident. B EYOND P LANCK represents the first end-to-end CMB simulation framework that is able to generate both types of simulations and these new capabilities have brought this topic to the forefront. The B EYOND P LANCK posterior simulations and their uses are described extensively in a suite of companion papers. In this work, we consider one important applications of the corresponding prior simulations, namely, code validation. Specifically, we generated a set of one-year LFI 30 GHz prior simulations with known inputs and we used these to validate the core low-level B EYOND P LANCK algorithms dealing with gain estimation, correlated noise estimation, and mapmaking.

• Eskilt, Johannes Røsok; Herold, Laura; Komatsu, Eiichiro; Murai, Kai; Namikawa, Toshiya & Naokawa, Fumihiro (2023). Constraints on Early Dark Energy from Isotropic Cosmic Birefringence. Physical Review Letters. ISSN 0031-9007. 131(12). doi: 10.1103/PhysRevLett.131.121001. Full text in Research Archive
• Eskilt, Johannes Røsok; Lee, Katherine; Watts, Duncan; Anshul, V.; Aurvik, Ragnhild & Basyrov, Artem [Show all 23 contributors for this article] (2023). COSMOGLOBE: Towards end-to-end CMB cosmological parameter estimation without likelihood approximations. Astronomy and Astrophysics (A & A). ISSN 0004-6361. 678. doi: 10.1051/0004-6361/202347358. Full text in Research Archive Show summary

  We implement support for a cosmological parameter estimation algorithm in Commander and quantify its computational efficiency and cost. For a semi-realistic simulation similar to Planck LFI 70 GHz, we find that the computational cost of producing one single sample is about 20 CPU-hours and that the typical Markov chain correlation length is ∼100 samples. The net effective cost per independent sample is ∼2000 CPU-hours, in comparison with all low-level processing costs of 812 CPU-hours for Planck LFI and WMAP in C OSMOGLOBE Data Release 1. Thus, although technically possible to run already in its current state, future work should aim to reduce the effective cost per independent sample by one order of magnitude to avoid excessive runtimes, for instance through multi-grid preconditioners and/or derivative-based Markov chain sampling schemes. This work demonstrates the computational feasibility of true Bayesian cosmological parameter estimation with end-to-end error propagation for high-precision CMB experiments without likelihood approximations, but it also highlights the need for additional optimizations before it is ready for full production-level analysis.

• Watts, Duncan; Basyrov, Artem; Eskilt, Johannes Røsok; Galloway, Mathew; Gjerløw, Eirik & Hergt, L.T. [Show all 33 contributors for this article] (2023). COSMOGLOBE DR1 results: I. Improved Wilkinson Microwave Anisotropy Probe maps through Bayesian end-to-end analysis. Astronomy and Astrophysics (A & A). ISSN 0004-6361. 679. doi: 10.1051/0004-6361/202346414. Full text in Research Archive Show summary

  We present C OSMOGLOBE Data Release 1, which implements the first joint analysis of WMAP and Planck LFI time-ordered data, processed within a single Bayesian end-to-end framework. This framework directly builds on a similar analysis of the LFI measurements by the B EYOND P LANCK collaboration, and approaches the cosmic microwave background (CMB) analysis challenge through Gibbs sampling of a global posterior distribution, simultaneously accounting for calibration, mapmaking, and component separation. The computational cost of producing one complete WMAP+LFI Gibbs sample is 812 CPU-h, of which 603 CPU-h are spent on WMAP low-level processing; this demonstrates that end-to-end Bayesian analysis of the WMAP data is computationally feasible. We find that our WMAP posterior mean temperature sky maps and CMB temperature power spectrum are largely consistent with the official WMAP9 results. Perhaps the most notable difference is that our CMB dipole amplitude is 3366.2 ± 1.4 μK, which is 11 μK higher than the WMAP9 estimate and 2.5 σ higher than B EYOND P LANCK ; however, it is in perfect agreement with the HFI-dominated Planck PR4 result. In contrast, our WMAP polarization maps differ more notably from the WMAP9 results, and in general exhibit significantly lower large-scale residuals. We attribute this to a better constrained gain and transmission imbalance model. It is particularly noteworthy that the W -band polarization sky map, which was excluded from the official WMAP cosmological analysis, for the first time appears visually consistent with the V -band sky map. Similarly, the long standing discrepancy between the WMAP K -band and LFI 30 GHz maps is finally resolved, and the difference between the two maps appears consistent with instrumental noise at high Galactic latitudes. Relatedly, these updated maps allowed us for the first time to combine WMAP and LFI polarization data into a single coherent model of large-scale polarized synchrotron emission. Still, we identified a few issues that require additional work, including (1) low-level noise modeling; (2) large-scale temperature residuals at the 1–2 μK level; and (3) a strong degeneracy between the absolute K -band calibration and the dipole of the anomalous microwave emission component. We conclude that leveraging the complementary strengths of WMAP and LFI has allowed the mitigation of both experiments’ weaknesses, and resulted in new state-of-the-art WMAP sky maps. All maps and the associated code are made publicly available through the C OSMOGLOBE web page.

• Colombo, L.P.L.; Eskilt, Johannes Røsok; Paradiso, S.; Thommesen, Harald; Andersen, Kristian Joten & Aurvik, Ragnhild [Show all 40 contributors for this article] (2023). BeyondPlanck: XI. Bayesian CMB analysis with sample-based end-to-end error propagation. Astronomy and Astrophysics (A & A). ISSN 0004-6361. 675. doi: 10.1051/0004-6361/202244619. Full text in Research Archive
• Paradiso, S.; Colombo, L.P.L.; Andersen, Kristian Joten; Aurvik, Ragnhild; Banerji, Ranajoy & Basyrov, Artem [Show all 41 contributors for this article] (2023). BeyondPlanck: XII. Cosmological parameter constraints with end-to-end error propagation. Astronomy and Astrophysics (A & A). ISSN 0004-6361. 675. doi: 10.1051/0004-6361/202244060. Full text in Research Archive Show summary

  We present cosmological parameter constraints estimated using the Bayesian B EYOND P LANCK analysis framework. This method supports seamless end-to-end error propagation from raw time-ordered data onto final cosmological parameters. As a first demonstration of the method, we analyzed time-ordered Planck LFI observations, combined with selected external data (WMAP 33–61 GHz, Planck HFI DR4 353 and 857 GHz, and Haslam 408 MHz) in the form of pixelized maps that are used to break critical astrophysical degeneracies. Overall, all the results are generally in good agreement with previously reported values from Planck 2018 and WMAP, with the largest relative difference for any parameter amounting about 1 σ when considering only temperature multipoles between 30 ≤  ℓ  ≤ 600. In cases where there are differences, we note that the B EYOND P LANCK results are generally slightly closer to the high- ℓ HFI-dominated Planck 2018 results than previous analyses, suggesting slightly less tension between low and high multipoles. Using low- ℓ polarization information from LFI and WMAP, we find a best-fit value of τ  = 0.066 ± 0.013, which is higher than the low value of τ  = 0.052 ± 0.008 derived from Planck 2018 and slightly lower than the value of 0.069 ± 0.011 derived from the joint analysis of official LFI and WMAP products. Most importantly, however, we find that the uncertainty derived in the B EYOND P LANCK processing is about 30 % greater than when analyzing the official products, after taking into account the different sky coverage. We argue that this uncertainty is due to a marginalization over a more complete model of instrumental and astrophysical parameters, which results in more reliable and more rigorously defined uncertainties. We find that about 2000 Monte Carlo samples are required to achieve a robust convergence for a low-resolution cosmic microwave background (CMB) covariance matrix with 225 independent modes, and producing these samples takes about eight weeks on a modest computing cluster with 256 cores.

• Gerakakis, S.; Brilenkov, Maksym; Ieronymaki, M.; San, Metin; Watts, Duncan & Andersen, Kristian Joten [Show all 42 contributors for this article] (2023). From BeyondPlanck to Cosmoglobe: Open Science, Reproducibility, and Data Longevity. The Open Journal of Astrophysics. 6. doi: 10.21105/astro.2205.11262. Full text in Research Archive Show summary

  The BeyondPlanck and Cosmoglobe collaborations have implemented the first integrated Bayesian end-to-end analysis pipeline for CMB experiments. The primary long-term motivation for this work is to develop a common analysis platform that supports efficient global joint analysis of complementary radio, microwave, and sub-millimeter experiments. A strict prerequisite for this to succeed is broad participation from the CMB community, and two foundational aspects of the program are therefore reproducibility and Open Science. In this paper, we discuss our efforts toward this aim. We also discuss measures toward facilitating easy code and data distribution, community-based code documentation, user-friendly compilation procedures, etc. This work represents the first publicly released end-to-end CMB analysis pipeline that includes raw data, source code, parameter files, and documentation. We argue that such a complete pipeline release should be a requirement for all major future and publicly-funded CMB experiments, noting that a full public release significantly increases data longevity by ensuring that the data quality can be improved whenever better processing techniques, complementary datasets, or more computing power become available, and thereby also taxpayers’ value for money; providing only raw data and final products is not sufficient to guarantee full reproducibility in the future.

• Watts, Duncan; Galloway, Mathew; Ihle, Håvard Tveit; Andersen, Kristian Joten; Aurvik, Ragnhild & Banerji, Ranajoy [Show all 43 contributors for this article] (2023). From BeyondPlanck to Cosmoglobe: Preliminary WMAP Q-band analysis. Astronomy and Astrophysics (A & A). ISSN 0004-6361. 675. doi: 10.1051/0004-6361/202243410. Full text in Research Archive Show summary

  We present the first application of the C OSMOGLOBE analysis framework by analyzing nine-year WMAP time-ordered observations that uses similar machinery to that of B EYOND P LANCK for the Planck Low Frequency Instrument (LFI). We analyzed only the Q -band (41 GHz) data and report on the low-level analysis process based on uncalibrated time-ordered data to calibrated maps. Most of the existing B EYOND P LANCK pipeline may be reused for WMAP analysis with minimal changes to the existing codebase. The main modification is the implementation of the same preconditioned biconjugate gradient mapmaker used by the WMAP team. Producing a single WMAP Q 1-band sample requires 22 CPU-hrs, which is slightly more than the cost of a Planck 44 GHz sample of 17 CPU-hrs; this demonstrates that a full end-to-end Bayesian processing of the WMAP data is computationally feasible. In general, our recovered maps are very similar to the maps released by the WMAP team, although with two notable differences. In terms of temperature, we find a ∼2 μK quadrupole difference that most likely is caused by different gain modeling, while in polarization we find a distinct 2.5 μK signal that has been previously referred to as poorly measured modes by the WMAP team. In the C OSMOGLOBE processing, this pattern arises from temperature-to-polarization leakage from the coupling between the CMB Solar dipole, transmission imbalance, and sidelobes. No traces of this pattern are found in either the frequency map or TOD residual map, suggesting that the current processing has succeeded in modeling these poorly measured modes within the assumed parametric model by using Planck information to break the sky-synchronous degeneracies inherent in the WMAP scanning strategy.

• Basyrov, Artem; Suur-Uski, A.-S.; Colombo, L.P.L.; Eskilt, Johannes Røsok; Paradiso, S. & Andersen, Kristian Joten [Show all 40 contributors for this article] (2023). BeyondPlanck: X. Planck Low Frequency Instrument frequency maps with sample-based error propagation. Astronomy and Astrophysics (A & A). ISSN 0004-6361. 675. doi: 10.1051/0004-6361/202244819. Full text in Research Archive Show summary

  We present Planck Low Frequency Instrument (LFI) frequency sky maps derived within the B EYOND P LANCK framework. This framework draws samples from a global posterior distribution that includes instrumental, astrophysical, and cosmological parameters, and the main product is an entire ensemble of frequency sky map samples, each of which corresponds to one possible realization of the various modeled instrumental systematic corrections, including correlated noise, time-variable gain, as well as far sidelobe and bandpass corrections. This ensemble allows for computationally convenient end-to-end propagation of low-level instrumental uncertainties into higher-level science products, including astrophysical component maps, angular power spectra, and cosmological parameters. We show that the two dominant sources of LFI instrumental systematic uncertainties are correlated noise and gain fluctuations, and the products presented here support – for the first time – full Bayesian error propagation for these effects at full angular resolution. We compared our posterior mean maps with traditional frequency maps delivered by the Planck Collaboration, and find generally good agreement. The most important quality improvement is due to significantly lower calibration uncertainties in the new processing, as we find a fractional absolute calibration uncertainty at 70 GHz of Δ g 0 / g 0  = 5 × 10 −5 , which is nominally 40 times smaller than that reported by Planck 2018. However, we also note that the original Planck 2018 estimate has a nontrivial statistical interpretation, and this further illustrates the advantage of the new framework in terms of producing self-consistent and well-defined error estimates of all involved quantities without the need of ad hoc uncertainty contributions. We describe how low-resolution data products, including dense pixel-pixel covariance matrices, may be produced from the posterior samples directly, without the need for computationally expensive analytic calculations or simulations. We conclude that posterior-based frequency map sampling provides unique capabilities in terms of low-level systematics modeling and error propagation, and may play an important role for future Cosmic Microwave Background (CMB) B -mode experiments aiming at nanokelvin precision.

• Galloway, Mathew; Reinecke, M.; Andersen, Kristian Joten; Aurvik, Ragnhild; Banerji, Ranajoy & Bersanelli, M. [Show all 41 contributors for this article] (2023). BeyondPlanck: VIII. Efficient sidelobe convolution and corrections through spin harmonics. Astronomy and Astrophysics (A & A). ISSN 0004-6361. 675. doi: 10.1051/0004-6361/202243138. Full text in Research Archive Show summary

  We introduce a new formulation of the Conviqt convolution algorithm in terms of spin harmonics, and apply this to the problem of sidelobe correction for B EYOND P LANCK , the first end-to-end Bayesian Gibbs sampling framework for CMB analysis. We compare our implementation to the previous Planck LevelS implementation, and find good agreement between the two codes in terms of accuracy, but with a speed-up reaching a factor of 3–10, depending on the frequency bandlimits, l max and m max . The new algorithm is significantly simpler to implement and maintain, since all low-level calculations are handled through an external spherical harmonic transform library. We find that our mean sidelobe estimates for Planck LFI are in good agreement with previous efforts. Additionally, we present novel sidelobe rms maps that quantify the uncertainty in the sidelobe corrections due to variations in the sky model.

• Galloway, Mathew; Andersen, Kristian Joten; Aurvik, Ragnhild; Banerji, Ranajoy; Bersanelli, M. & Bertocco, S. [Show all 41 contributors for this article] (2023). BeyondPlanck: III. Commander3. Astronomy and Astrophysics (A & A). ISSN 0004-6361. 675. doi: 10.1051/0004-6361/202243137. Full text in Research Archive Show summary

  We describe the computational infrastructure for end-to-end Bayesian cosmic microwave background (CMB) analysis implemented by the BeyondPlanck Collaboration. The code is called Commander3 . It provides a statistically consistent framework for global analysis of CMB and microwave observations and may be useful for a wide range of legacy, current, and future experiments. The paper has three main goals. Firstly, we provide a high-level overview of the existing code base, aiming to guide readers who wish to extend and adapt the code according to their own needs or re-implement it from scratch in a different programming language. Secondly, we discuss some critical computational challenges that arise within any global CMB analysis framework, for instance in-memory compression of time-ordered data, fast Fourier transform optimization, and parallelization and load-balancing. Thirdly, we quantify the CPU and RAM requirements for the current B EYOND P LANCK analysis, finding that a total of 1.5 TB of RAM is required for efficient analysis and that the total cost of a full Gibbs sample for LFI is 170 CPU-hrs, including both low-level processing and high-level component separation, which is well within the capabilities of current low-cost computing facilities. The existing code base is made publicly available under a GNU General Public Library (GPL) license.

• Keihänen, Elina; Suur-Uski, A.-S.; Andersen, Kristian Joten; Aurvik, Ragnhild; Banerji, Ranajoy & Basyrov, Artem [Show all 42 contributors for this article] (2023). BeyondPlanck: II. CMB mapmaking through Gibbs sampling. Astronomy and Astrophysics (A & A). ISSN 0004-6361. 675. doi: 10.1051/0004-6361/202142799. Full text in Research Archive Show summary

  We present a Gibbs sampling solution to the mapmaking problem for cosmic microwave background (CMB) measurements that builds on existing destriping methodology. Gibbs sampling breaks the computationally heavy destriping problem into two separate steps: noise filtering and map binning. Considered as two separate steps, both are computationally much cheaper than solving the combined problem. This provides a huge performance benefit as compared to traditional methods and it allows us, for the first time, to bring the destriping baseline length to a single sample. Here, we applied the Gibbs procedure to simulated Planck 30 GHz data. We find that gaps in the time-ordered data are handled efficiently by filling them in with simulated noise as part of the Gibbs process. The Gibbs procedure yields a chain of map samples, from which we are able to compute the posterior mean as a best-estimate map. The variation in the chain provides information on the correlated residual noise, without the need to construct a full noise covariance matrix. However, if only a single maximum-likelihood frequency map estimate is required, we find that traditional conjugate gradient solvers converge much faster than a Gibbs sampler in terms of the total number of iterations. The conceptual advantages of the Gibbs sampling approach lies in statistically well-defined error propagation and systematic error correction. This methodology thus forms the conceptual basis for the mapmaking algorithm employed in the B EYOND P LANCK framework, which implements the first end-to-end Bayesian analysis pipeline for CMB observations.

• Andersen, Kristian Joten; Aurvik, Ragnhild; Banerji, Ranajoy; Basyrov, Artem; Bersanelli, M. & Bertocco, S. [Show all 44 contributors for this article] (2023). BeyondPlanck: I. Global Bayesian analysis of the Planck Low Frequency Instrument data. Astronomy and Astrophysics (A & A). ISSN 0004-6361. 675. doi: 10.1051/0004-6361/202244953. Full text in Research Archive Show summary

  We describe the B EYOND P LANCK project in terms of our motivation, methodology, and main products, and provide a guide to a set of companion papers that describe each result in more detail. Building directly on experience from ESA’s Planck mission, we implemented a complete end-to-end Bayesian analysis framework for the Planck Low Frequency Instrument (LFI) observations. The primary product is a full joint posterior distribution P ( ω  ∣  d ), where ω represents the set of all free instrumental (gain, correlated noise, bandpass, etc.), astrophysical (synchrotron, free-free, thermal dust emission, etc.), and cosmological (cosmic microwave background – CMB – map, power spectrum, etc.) parameters. Some notable advantages of this approach compared to a traditional pipeline procedure are seamless end-to-end propagation of uncertainties; accurate modeling of both astrophysical and instrumental effects in the most natural basis for each uncertain quantity; optimized computational costs with little or no need for intermediate human interaction between various analysis steps; and a complete overview of the entire analysis process within one single framework. As a practical demonstration of this framework, we focus in particular on low- ℓ CMB polarization reconstruction with Planck LFI. In this process, we identify several important new effects that have not been accounted for in previous pipelines, including gain over-smoothing and time-variable and non-1/ f correlated noise in the 30 and 44 GHz channels. Modeling and mitigating both previously known and newly discovered systematic effects, we find that all results are consistent with the ΛCDM model, and we constrained the reionization optical depth to τ  = 0.066 ± 0.013, with a low-resolution CMB-based χ 2 probability to exceed of 32%. This uncertainty is about 30% larger than the official pipelines, arising from taking a more complete instrumental model into account. The marginal CMB solar dipole amplitude is 3362.7 ± 1.4 μK, where the error bar was derived directly from the posterior distribution without the need of any ad hoc instrumental corrections. We are currently not aware of any significant unmodeled systematic effects remaining in the Planck LFI data, and, for the first time, the 44 GHz channel is fully exploited in the current analysis. We argue that this framework can play a central role in the analysis of many current and future high-sensitivity CMB experiments, including LiteBIRD, and it will serve as the computational foundation of the emerging community-wide C OSMOGLOBE effort, which aims to combine state-of-the-art radio, microwave, and submillimeter data sets into one global astrophysical model.

• Andersen, Kristian Joten; Herman, Daniel Christopher; Aurvik, Ragnhild; Banerji, Ranajoy; Basyrov, Artem & Bersanelli, M. [Show all 44 contributors for this article] (2023). BeyondPlanck: XIII. Intensity foreground sampling, degeneracies, and priors. Astronomy and Astrophysics (A & A). ISSN 0004-6361. 675. doi: 10.1051/0004-6361/202243186. Full text in Research Archive Show summary

  We present the intensity foreground algorithms and model employed within the B EYOND P LANCK analysis framework. The B EYOND P LANCK analysis is aimed at integrating component separation and instrumental parameter sampling within a global framework, leading to complete end-to-end error propagation in the Planck Low Frequency Instrument (LFI) data analysis. Given the scope of the B EYOND P LANCK analysis, a limited set of data is included in the component separation process, leading to foreground parameter degeneracies. In order to properly constrain the Galactic foreground parameters, we improve upon the previous Commander component separation implementation by adding a suite of algorithmic techniques. These algorithms are designed to improve the stability and computational efficiency for weakly constrained posterior distributions. These are: (1) joint foreground spectral parameter and amplitude sampling, building on ideas from M IRAMARE ; (2) component-based monopole determination; (3) joint spectral parameter and monopole sampling; and (4) application of informative spatial priors for component amplitude maps. We find that the only spectral parameter with a significant signal-to-noise ratio using the current B EYOND P LANCK data set is the peak frequency of the anomalous microwave emission component, for which we find ν p  = 25.3 ± 0.5 GHz; all others must be constrained through external priors. Future works will be aimed at integrating many more data sets into this analysis, both map and time-ordered based, thereby gradually eliminating the currently observed degeneracies in a controlled manner with respect to both instrumental systematic effects and astrophysical degeneracies. When this happens, the simple LFI-oriented data model employed in the current work will need to be generalized to account for both a richer astrophysical model and additional instrumental effects. This work will be organized within the Open Science-based C OSMOGLOBE community effort.

• Petersen, Pip; Akrami, Yashar; Copi, Craig J.; Jaffe, Andrew H.; Kosowsky, Arthur & Starkman, Glenn D. [Show all 11 contributors for this article] (2023). Cosmic topology. Part I. Limits on orientable Euclidean manifolds from circle searches. Journal of Cosmology and Astroparticle Physics (JCAP). 2023(1). doi: 10.1088/1475-7516/2023/01/030. Full text in Research Archive
• Diego-Palazuelos, P.; Martínez-González, E.; Vielva, P.; Barreiro, R.; Tristram, M. & de la Hoz, E. [Show all 14 contributors for this article] (2023). Robustness of cosmic birefringence measurement against Galactic foreground emission and instrumental systematics. Journal of Cosmology and Astroparticle Physics (JCAP). 2023(1). doi: 10.1088/1475-7516/2023/01/044. Full text in Research Archive
• Ihle, Håvard Tveit; Bersanelli, M.; Franceschet, C.; Gjerløw, Eirik; Andersen, Kristian Joten & Aurvik, Ragnhild [Show all 41 contributors for this article] (2023). BeyondPlanck: VI. Noise characterization and modeling. Astronomy and Astrophysics (A & A). ISSN 0004-6361. 675. doi: 10.1051/0004-6361/202243619. Full text in Research Archive Show summary

  We present a Bayesian method for estimating instrumental noise parameters and propagating noise uncertainties within the global BEYONDPLANCK Gibbs sampling framework, which we applied to Planck Low Frequency Instrument (LFI) time-ordered data. Following previous works in the literature, we initially adopted a 1/f model for the noise power spectral density (PSD), but we found the need for an additional lognormal component in the noise model in the 30 and 44 GHz bands. We implemented an optimal Wiener-filter (or constrained realization) gap-filling procedure to account for masked data. We then used this procedure to both estimate the gapless correlated noise in the time-domain, ncorr, and to sample the noise PSD parameters, ξn = {σ0, fknee, α, Ap}. In contrast to previous Planck analyses, we assumed piecewise stationary noise only within each pointing period (PID), and not throughout the full mission, but we adopted the LFI Data Processing Center results as priors on α and fknee. We generally found best-fit correlated noise parameters that are mostly consistent with previous results, with a few notable exceptions. However, a detailed inspection of the time-dependent results has revealed many important findings. First and foremost, we find strong evidence for statistically significant temporal variations in all noise PSD parameters, many of which are directly correlated with satellite housekeeping data. Second, while the simple 1/f model appears to be an excellent fit for the LFI 70 GHz channel, there is evidence for additional correlated noise that is not described by a 1/f model in the 30 and 44 GHz channels, including within the primary science frequency range of 0.1–1 Hz. In general, most 30 and 44 GHz channels exhibit deviations from 1/f at the 2–3σ level in each one-hour pointing period, motivating the addition of the lognormal noise component for these bands. For certain periods of time, we also find evidence of strong common mode noise fluctuations across the entire focal plane. Overall, we conclude that a simple 1/f profile is not adequate for obtaining a full characterization of the Planck LFI noise, even when fitted hour-by-hour, and a more general model is required. These findings have important implications for large-scale CMB polarization reconstruction with the Planck LFI data and the current work is a first attempt at understanding and mitigating these issues.

• Eskilt, Johannes Røsok (2022). Frequency-dependent constraints on cosmic birefringence from the LFI and HFI Planck Data Release 4. Astronomy and Astrophysics (A & A). ISSN 0004-6361. 662. doi: 10.1051/0004-6361/202243269. Full text in Research Archive Show summary

  We present new constraints on the frequency dependence of the cosmic birefringence angle from the Planck Data Release 4 polarization maps. An axion field coupled to electromagnetism predicts a nearly frequency-independent birefringence angle, β ν  =  β , while Faraday rotation from local magnetic fields and Lorentz violating theories predict a cosmic birefringence angle that is proportional to the frequency, ν , to the power of some integer n , β ν  ∝  ν n . In this work, we first sampled β ν individually for each polarized HFI frequency band in addition to the 70 GHz channel from the LFI. We also constrained a power law formula for the birefringence angle, β ν  =  β 0 ( ν / ν 0 ) n , with ν 0  = 150 GHz. For a nearly full-sky measurement, f sky  = 0.93, we find β 0  = 0.26° ±0.11° (68% C.L.) and n  = −0.45 −0.82 +0.61 when we ignore the intrinsic EB correlations of the polarized foreground emission, and β 0  = 0.33° ±0.12° and n  = −0.37 −0.64 +0.49 when we use a filamentary dust model for the foreground EB . Next, we used all the polarized Planck maps, including the 30 and 44 GHz frequency bands. These bands have a negligible foreground contribution from polarized dust emission and we thus treated them separately. Without any modeling of the intrinsic EB of the foreground, we generally find that the inclusion of the 30 and 44 GHz frequency bands raises the measured values of β ν and tightens n . At nearly full-sky, we measure β 0  = 0.29° −0.11° +0.10° and n  = −0.35 −0.47 +0.48 . Assuming no frequency dependence, we measure β  = 0.33° ±0.10°. If our measurements have effectively mitigated the EB of the foreground, our constraints are consistent with a mostly frequency-independent signal of cosmic birefringence.

• Diego-Palazuelos, P.; Eskilt, Johannes Røsok; Minami, Y.; Tristram, M.; Sullivan, R. M. & Banday, A. J. [Show all 15 contributors for this article] (2022). Cosmic Birefringence from the Planck Data Release 4. Physical Review Letters. ISSN 0031-9007. 128(9). doi: 10.1103/PhysRevLett.128.091302. Full text in Research Archive Show summary

  We search for the signature of parity-violating physics in the cosmic microwave background, called cosmic birefringence, using the Planck data release 4. We initially find a birefringence angle of β=0.30°±0.11° (68% C.L.) for nearly full-sky data. The values of β decrease as we enlarge the Galactic mask, which can be interpreted as the effect of polarized foreground emission. Two independent ways to model this effect are used to mitigate the systematic impact on β for different sky fractions. We choose not to assign cosmological significance to the measured value of β until we improve our knowledge of the foreground polarization.

• Eskilt, Johannes Røsok & Komatsu, Eiichiro (2022). Improved constraints on cosmic birefringence from the WMAP and Planck cosmic microwave background polarization data. Physical Review D. ISSN 2470-0010. 106(6). doi: 10.1103/PhysRevD.106.063503. Full text in Research Archive Show summary

  The observed pattern of linear polarization of the cosmic microwave background photons is a sensitive probe of physics violating parity symmetry under inversion of spatial coordinates. A new parity-violating interaction might have rotated the plane of linear polarization by an angle β as the cosmic microwave background photons have been traveling for more than 13 billion years. This effect is known as “cosmic birefringence.” In this paper, we present new measurements of cosmic birefringence from a joint analysis of polarization data from two space missions, Planck and WMAP. This dataset covers a wide range of frequencies from 23 to 353 GHz. We measure β=0.342°+0.094°−0.091° [68% confidence level (CL)] for nearly full-sky data, which excludes β=0 at 99.987% CL. This corresponds to the statistical significance of 3.6σ. There is no evidence for frequency dependence of β. We find a similar result, albeit with a larger uncertainty, when removing the Galactic plane from the analysis.

• Eskilt, Johannes Røsok; Cheghasiahi, Yashar Akrami; Solomon, Adam R. & Vardanyan, Valeri (2022). Cosmological dynamics of multifield dark energy. Physical Review D. ISSN 2470-0010. 106(2). doi: 10.1103/PhysRevD.106.023512. Full text in Research Archive Show summary

  We numerically and analytically explore the background cosmological dynamics of multifield dark energy with highly nongeodesic or “spinning” field-space trajectories. These extensions of standard single-field quintessence possess appealing theoretical features and observable differences from the cosmological standard model. At the level of the cosmological background, we perform a phase-space analysis and identify approximate attractors with late-time acceleration for a wide range of initial conditions. Focusing on two classes of field-space geometry, we derive bounds on parameter space by demanding viable late-time acceleration and the absence of gradient instabilities, as well as from the de Sitter swampland conjecture.

• Eskilt, Johannes Røsok; Amundsen, Morten; Banerjee, Niladri & Linder, Jacob (2019). Long-ranged triplet supercurrent in a single in-plane ferromagnet with spin-orbit coupled contacts to superconductors. Physical review B (PRB). ISSN 2469-9950. 100(22). doi: 10.1103/PhysRevB.100.224519. Full text in Research Archive Show summary

  By converting conventional spin-singlet Cooper pairs to polarized spin-triplet pairs, it is possible to sustain long-ranged spin-polarized supercurrents flowing through strong ferromagnets. Obtaining such a conversion via spin-orbit interactions, rather than magnetic inhomogeneities, has recently been explored in the literature. A challenging aspect with regard to experimental detection has been that in order for Rashba spin-orbit interactions, present, e.g., at interfaces due to inversion symmetry breaking, to generate such long-ranged supercurrents, an out-of-plane component of the magnetization is required. This limits the choice of materials and can induce vortices in the superconducting region complicating the interpretation of measurements. Therefore, it would be desirable to identify a way in which Rashba spin-orbit interactions can induce long-ranged supercurrents for purely in-plane rotations of the magnetization. Here, we show that this is possible in a lateral Josephson junction where two superconducting electrodes are placed in contact with a ferromagnetic film via two thin, heavy normal metals. The magnitude of the supercurrent in such a setup becomes tunable by the in-plane magnetization angle when using only a single magnetic layer. These results could provide a new and simpler way to generate controllable spin-polarized supercurrents than previous experiments which utilized complicated magnetically textured Josephson junctions.

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• Eskilt, Johannes Røsok; Wehus, Ingunn Kathrine; Eriksen, Hans Kristian Kamfjord; Watts, Duncan; Komatsu, Eiichiro & Hansen, Frode Kristian (2023). Signatures of New Physics in the CMB: From Cosmic Topology to Cosmic Birefringence. Universitetet i Oslo. Full text in Research Archive Show summary

  The cosmic microwave background (CMB) is not just the oldest light in the Universe but also the oldest polarized light. By measuring its patterns, we can learn large amounts of information about the origin of the Universe and its content. This work focuses on some of the allowed ''shapes'', or more precisely, topologies of the Universe. We describe their potential patterns in the CMB, showing that the shape of the Universe is likely impossible to be measured in the CMB if its size is too large. We also provide evidence for cosmic birefringence, a potentially new phenomenon that might have rotated the linear polarization of the CMB photons. This work provides evidence for the signal being independent of the energy of the photons, which is consistent with a new fundamental particle called axions. In addition, we show that the signal is unlikely to be attributed to systematic effects or astrophysical foregrounds, and that the rotation must have started after the epoch when the CMB was created. If proven to be real, it would be revolutionary for cosmology and particle physics, and it could shed light on what either dark matter or dark energy is.

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