Cosmological Parameter Constraints Research Articles

Joint Observations of Late Universe Probes: Cosmological Parameter Constraints from Gravitational Wave and Type Ia Supernova Data

The growing tensions between the early Universe and the late Universe increasingly highlight the importance of developing precise probes for late cosmology. As significant late-Universe probes, Type Ia supernovae (SNe Ia) and gravitational waves (GWs) can provide measurements of relative and absolute distances, respectively. Their complementary nature is likely to break the degeneracies among cosmological parameters, thereby yielding more precise constraints. In this study, we use 43 gravitational-wave sources from the Third LIGO–Virgo–KAGRA Gravitational-Wave Transient Catalog (GWTC-3) and 1590 light curves from Pantheon+ compilation to constrain the dark energy models, as an attempt to achieve precise late-Universe cosmological constraints. For the dark siren GW event, we estimate the corresponding redshift using the binary black hole redshift distribution model. The combination of GW and SNe Ia data could provide the precision on the Hubble constant H 0 and the present matter density Ω m of approximately 16% and 8% for the ΛCDM model. If we consider the equation of state of dark energy w, the combination sample constrains the precision of w to approximately 24%. Although the combination of GWs and SNe Ia observations effectively breaks degeneracies among various cosmological parameters, yielding more stringent constraints, the precision of these constraints still does not meet the stringent standards required by precision cosmology. However, it is reasonable to anticipate that, in the near future, the joint observations of GWs and SNe Ia will become a powerful tool, particularly in the late Universe, for the precise measurement of cosmological parameters.

Detection of gamma-ray burst Amati relation based on Hubble data set and Pantheon+ samples

Using gamma-ray bursts as standard candles for cosmological parameter constraints rely on their empirical luminosity relations and low-redshift calibration. In this paper, we examine the Amati relation and its potential corrections based on the A118 sample of higher-quality gamma-ray bursts, using both Hubble data set and Pantheon+ samples as calibration samples in the redshift range of z<1.965\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$z<1.965$$\\end{document}. In calibrating gamma-ray bursts using these two datasets, we employ Gaussian processes to obtain corresponding Hubble diagrams to avoid the dependence on cosmological models in the calibration process. We first divided the low-redshift sample of GRBs into two bins and examined the Amati relation and its potential modifications. We found that under both calibrations, the Amati relation did not show evidence of redshift evolution (68%\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\%$$\\end{document} confidence level). For the other two Amati relations that include redshift evolution terms, the central values of the redshift evolution coefficients deviated from 0, but due to the limitations of the sample size and the increase in the number of parameters, most of the redshift evolution coefficients were not able to be excluded from 0 at the 1σ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\sigma $$\\end{document} level. Therefore, to assess their situation across the entire redshift range, we employed MCMC to globally fit three types of Amati relations. By computing AIC and BIC, we found that for the GRB A118 sample, the standard Amati relation remains the most fitting empirical luminosity formula, and no potential redshift evolution trend was observed for two different low-redshift calibrating sources.

Are light curve classification metrics good proxies for SN Ia cosmological constraining power?

When selecting a lc classifier for use as part of a photometric supernova Ia (SN Ia) cosmological analysis, it is common to make decisions based on metrics of classification performance, such as the contamination within the photometrically classified SN Ia sample, rather than a measure of cosmological constraining power. If the former is an appropriate proxy for the latter, this practice would save those designing an analysis pipeline from eliminate the computational expense of a full cosmology forecast in the analysis pipeline design process This study tests the assumption that lc classification metrics are an appropriate proxy for cosmology metrics. We emulated photometric SN Ia cosmology lc samples with controlled contamination rates of individual contaminant classes and evaluated each of them under a set of classification metrics. We then derived cosmological parameter constraints from all samples under two common analysis approaches and quantified the impact of contamination by each contaminant class on the resulting cosmological parameter estimates. We observe that cosmology metrics are sensitive to both the contamination rate and the class of the contaminating population, whereas the classification metrics are shown to be insensitive to the latter. Based on these findings, we discourage any exclusive reliance on classification-based metrics for analysis design decisions, which (counterintuitively) include but are not limited to the classifier choice. Instead, we recommend optimising science analysis pipeline design choices using a metric of the information gained about the physical parameters of interest.

Modelling the redshift-space cluster–galaxy correlation function on Mpc scales with emulation of the pairwise velocity distribution

ABSTRACT We present a method for modelling the cluster–galaxy correlation function in redshift space, down to $\sim$ Mpc scales. The method builds upon the so-called galaxy infall kinematics (GIK) model, a parametric model for the pairwise velocities of galaxies with respect to nearby galaxy clusters. We fit the parameters of the GIK model to a suite of simulations run with different cosmologies, and use Gaussian processes to emulate how the GIK parameters depend upon cosmology. This emulator can then be combined with knowledge of the real-space clustering of clusters and galaxies, to predict the cluster–galaxy correlation function in redshift space, $\xi _\mathrm{cg}^s$. Fitting this model to an observed $\xi _\mathrm{cg}^s$ enables the extraction of cosmological parameter constraints, and we present forecasts for a survey like that currently being done by the Dark Energy Spectroscopic Instrument (DESI). We also perform tests of the robustness of our constraints from fitting to mock data extracted from N-body simulations, finding that fitting to scales $\lesssim 3 \, h^{-1}\, \mathrm{Mpc}$ leads to a biased inference on cosmology, due to model mis-specification on these scales. Finally, we discuss what steps will need to be taken in order to apply our method to real data.

Cosmological constraints from the eBOSS Lyman-α forest using the PRIYA simulations

We present new cosmological parameter constraints from the eBOSS Lyman-α forest survey. We use a new theoretical model and likelihood based on the PRIYA simulation suite. PRIYA is the first suite to resolve the Lyman-α forest in a (120 Mpc/h)3 volume, using a multi-fidelity emulation technique. We use PRIYA to predict Lyman-α forest observables with ≲ 1% interpolation error over an 11 dimensional (9 simulated, 2 in post-processing) parameter space. We identify an internal tension within the flux power spectrum data. Once the discrepant data is removed, we find the primeval scalar spectral index measured at a pivot scale of k 0 = 0.78 Mpc-1 to be nP = 1.009+0.027 -0.018 at 68% confidence. This measurement from the Lyman-α forest flux power spectrum alone is in reasonable agreement with Planck, and in tension with earlier eBOSS analyses. The amplitude of matter fluctuations is σ 8 = 0.733+0.026 -0.029 at 68% confidence, in agreement with Dark Energy Survey weak lensing measurements and other small-scale structure probes and in tension with CMB measurements from Planck and ACT. The effective optical depth to Lyman-α photons from our pipeline is in good agreement with earlier high resolution measurements. We find a linear power at z = 3 and k = 0.009 s/km of Δ2 L = 0.302+0.024 -0.027 with a slope n eff = -2.264+0.026 -0.018. Our flux power spectrum only chains prefer a low level of heating during helium reionization. When we add IGM temperature data we find nP = 0.983 ± 0.020 and σ 8 = 0.703+0.023 -0.027. Our chains prefer an early and long helium reionization event, as suggested by measurements from the helium Lyman-α forest. In the near future we will use our pipeline to infer cosmological parameters from the DESI Lyman-α data.

Candl: cosmic microwave background analysis with a differentiable likelihood

We present candl, an automatically differentiable python likelihood for analysing cosmic microwave background power spectrum measurements. candl is powered by JAX, which makes it fast and easy to calculate derivatives of the likelihood. This facilitates, for example, robust Fisher matrices without finite-difference methods. We show the benefits of candl through a series of example calculations, covering forecasting, robustness tests, and gradient-based Markov chain Monte Carlo sampling. These also include optimising the band power bin width to minimise parameter errors of a realistic mock data set. Moreover, we calculate the correlation of parameter constraints from correlated and partially overlapping subsets of the SPT-3G 2018 TT/TE/EE data release. In a traditional analysis framework, these tasks are slow and require careful fine-tuning to obtain stable results. As such, a fully differentiable pipeline allows for a higher level of scrutiny; we argue that this is the paradigm shift required to leverage incoming data from ground-based experiments, which will significantly improve the cosmological parameter constraints from the Planck mission. candl comes with the latest primary and lensing power spectrum data from the South Pole Telescope and Atacama Cosmology Telescope collaborations and will be used as part of the upcoming SPT-3G TT/TE/EE and ϕϕ data releases. Along with the core code, we release a series of auxiliary tools, which simplify common analysis tasks and interface the likelihood with other cosmological software. candl is pip-installable and publicly available on Github.

Accuracy requirements on intrinsic alignments for Stage-IV cosmic shear

In the context of cosmological weak lensing studies, intrinsic alignments (IAs) are one of the most In the context of cosmological weak lensing studies, intrinsic alignments (IAs) are one of the most complicated astrophysical systematic to model, given the poor understanding of the physical processes that cause them. A number of modelling frameworks for IAs have been proposed in the literature, both purely phenomenological or grounded on a perturbative treatment of symmetry-based arguments. However, the accuracy with which any of these approaches is able to describe the impact of IAs on cosmic shear data, particularly on the comparatively small scales () to which this observable is sensitive, is not clear. Here we quantify the level of disagreement between the true underlying intrinsic alignments and the theoretical model used to describe them that can be allowed in the context of cosmic shear analyses with future Stage-IV surveys. We consider various models describing this “IA residual’’, covering both physics-based approaches, as well as completely agnostic prescriptions. The same qualitative results are recovered in all cases explored: for a Stage-IV cosmic shear survey, a mis-modelling of the IA contribution at the ∼10% level produces shifts of ≲0.5σ on the final cosmological parameter constraints. Current and future IA models should therefore aim to achieve this level of accuracy, a prospect that is not unfeasible for models with sufficient flexibility.

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

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

Effects of heterogeneous data sets and time-lag measurement techniques on cosmological parameter constraints from Mg ii and C iv reverberation-mapped quasar data

ABSTRACT Previously, we demonstrated that Mg ii and C iv reverberation-mapped quasars (RM QSOs) are standardizable and that the cosmological parameters inferred using the broad-line region radius–luminosity (R–L) relation are consistent with those determined from better-established cosmological probes. With more data expected from ongoing and future spectroscopic and photometric surveys, it is imperative to examine how new QSO data sets of varied quality, with their own specific luminosity and time-delay distributions, can be best used to determine more restrictive cosmological parameter constraints. In this study, we test the effect of adding 25 OzDES Mg ii RM QSOs as well as 25 lower quality SDSS RM C iv QSOs, which increases the previous sample of RM QSOs by $\sim 36{{\ \rm per\ cent}}$. Although cosmological parameter constraints become tighter for some cosmological models after adding these new QSOs, the new combined data sets have increased differences between R–L parameter values obtained in different cosmological models and thus a lower standardizability for the larger Mg ii + C iv compilation. Different time-delay methodologies, particularly the ICCF and CREAM methods used for inferring time delays of SDSS RM QSOs, slightly affect cosmological and R–L relation parameter values, however, the effect is negligible for (smaller) compilations of robust time-delay detections. Our analysis indicates that increasing the sample size is not sufficient for tightening cosmological constraints and a quality cut is necessary to obtain a standardizable RM QSO sample.

Amalgame: cosmological constraints from the first combined photometric supernova sample

ABSTRACT Future constraints of cosmological parameters from Type Ia supernovae (SNe Ia) will depend on the use of photometric samples, those samples without spectroscopic measurements of the SNe Ia. There is a growing number of analyses that show that photometric samples can be utilized for precision cosmological studies with minimal systematic uncertainties. To investigate this claim, we perform the first analysis that combines two separate photometric samples, SDSS and Pan-STARRS, without including a low-redshift anchor. We evaluate the consistency of the cosmological parameters from these two samples and find they are consistent with each other to under 1σ. From the combined sample, named Amalgame, we measure ΩM = 0.328 ± 0.024 with SN alone in a flat ΛCDM model, and ΩM = 0.330 ± 0.018 and w = $-1.016^{+0.055}_{-0.058}$ when combining with a Planck data prior and a flat wCDM model. These results are consistent with constraints from the Pantheon+ analysis of only spectroscopically confirmed SNe Ia, and show that there are no significant impediments to analyses of purely photometric samples of SNe Ia. The data and results are made available at https://github.com/bap37/AmalgameDR.

Cosmological parameters derived from the final Planck data release (PR4)

We present cosmological parameter constraints using maps from the last Planck data release (PR4). In particular, we detail an upgraded version of the cosmic microwave background likelihood, HiLLiPoP, that is based on angular power spectra and relies on a physical modeling of the foreground residuals in the spectral domain. This new version of the likelihood retains a larger sky fraction (up to 75%) and uses an extended multipole range. Using this likelihood, along with low-ℓ measurements from LoLLiPoP, we derived constraints on ΛCDM parameters that are in good agreement with previous Planck 2018 results, but with smaller uncertainties by 10% to 20%. We demonstrate that the foregrounds can be accurately described in the spectral domain, with a negligible impact on ΛCDM parameters. We also derived constraints on single-parameter extensions to ΛCDM, including AL, ΩK, Neff, and ∑mν. Noteworthy results from this updated analysis include a lensing amplitude value of AL = 1.039 ± 0.052, which is more closely aligned with theoretical expectations within the ΛCDM framework. Additionally, our curvature measurement, ΩK = −0.012 ± 0.010, is now fully consistent with a flat universe and our measurement of S8 is closer to the measurements derived from large-scale structure surveys (at the 1.5σ level). We also added constraints from PR4 lensing, making this combination the most tightly constrained data set currently available from Planck. Additionally, we explored the addition of baryon acoustic oscillation data, which tightens the limits on some particular extensions to the standard cosmology.

Intrinsic alignment from multiple shear estimates: a first application to data and forecasts for stage IV

ABSTRACT Without mitigation, the intrinsic alignment (IA) of galaxies poses a significant threat to achieving unbiased cosmological parameter constraints from precision weak lensing surveys. Here, we apply for the first time to data a method to extract the scale dependence of the IA contribution to galaxy–galaxy lensing, which takes advantage of the difference in alignment signal as measured by shear estimators with different sensitivities to galactic radii. Using data from Year 1 of the Dark Energy Survey, with shear estimators METACALIBRATION and IM3SHAPE, we investigate and address method systematics including non-trivial selection functions, differences in weighting between estimators, and multiplicative bias. We obtain a null detection of IA, which appears qualitatively consistent with existing work. We then forecast the application of this method to Rubin Observatory Legacy Survey of Space and Time (LSST) data and place requirements on a pair of shear estimators for detecting IA and constraining its 1-halo scale dependence. We find that for LSST Year 1, shear estimators should have at least a 40 per cent difference in IA amplitude, and the Pearson correlation coefficient of their shape noise should be at least ρ = 0.50, to ensure a 1σ detection of IA and a constraint on its 1-halo scale dependence with a signal-to-noise ratio greater than 1. For Year 10, a 1σ detection and constraint become possible for 20 per cent differences in alignment amplitude and ρ = 0.50.

Cosmological Parameter Constraints from the SDSS Density and Momentum Power Spectra

We extract the galaxy density and momentum power spectra from a subset of early-type galaxies in the Sloan Digital Sky Survey (SDSS) DR7 main galaxy catalog. Using galaxy distance information inferred from the improved fundamental plane described in Yoon and Park, we reconstruct the peculiar velocities of the galaxies and generate number density and density-weighted velocity fields, from which we extract the galaxy density and momentum power spectra. We compare the measured values to the theoretical expectation of the same statistics, assuming an input Λ cold dark matter (CDM) model and using a third-order perturbative expansion. After validating our analysis pipeline with a series of mock data sets, we apply our methodology to the SDSS data and arrive at constraints and at a mean redshift . Our result is consistent with the Planck cosmological best-fit parameters for the ΛCDM model. The momentum power spectrum is found to be strongly contaminated by small-scale velocity dispersion, which suppresses power by on intermediate scales k ∼ 0.05 h Mpc−1.

KiDS-1000: Cosmology with improved cosmic shear measurements

We present refined cosmological parameter constraints derived from a cosmic shear analysis of the fourth data release of the Kilo-Degree Survey (KiDS-1000). Our main improvements include enhanced galaxy shape measurements made possible by an updated version of thelensfit code and improved shear calibration achieved with a newly developed suite of multi-band image simulations. Additionally, we incorporated recent advancements in cosmological inference from the joint Dark Energy Survey Year 3 and KiDS-1000 cosmic shear analysis. Assuming a spatially flat standard cosmological model, we constrainS8 ≡ σ8(Ωm/0.3)0.5 = 0.776−0.027−0.003+0.029+0.002, where the second set of uncertainties accounts for the systematic uncertainties within the shear calibration. These systematic uncertainties stem from minor deviations from realism in the image simulations and the sensitivity of the shear measurement algorithm to the morphology of the galaxy sample. Despite these changes, our results align with previous KiDS studies and other weak lensing surveys, and we find a ∼2.3σlevel of tension with thePlanckcosmic microwave background constraints onS​8.

Beyond 3×2-point cosmology: the integrated shear and galaxy 3-point correlation functions

We present the integrated 3-point correlation functions (3PCF) involving both the cosmic shear and the galaxy density fields. These are a set of higher-order statistics that describe the modulation of local 2-point correlation functions (2PCF) by large-scale features in the fields, and which are easy to measure from galaxy imaging surveys. Based on previous works on the shear-only integrated 3PCF, we develop the theoretical framework for modelling 5 new statistics involving the galaxy field and its cross-correlations with cosmic shear. Using realistic galaxy and cosmic shear mocks from simulations, we determine the regime of validity of our models based on leading-order standard perturbation theory with an MCMC analysis that recovers unbiased constraints of the amplitude of fluctuations parameter A s and the linear and quadratic galaxy bias parameters b 1 and b 2. Using Fisher matrix forecasts for a DES-Y3-like survey, relative to baseline analyses with conventional 3×2PCFs, we find that the addition of the shear-only integrated 3PCF can improve cosmological parameter constraints by 20–40%. The subsequent addition of the new statistics introduced in this paper can lead to further improvements of 10–20%, even when utilizing only conservatively large scales where the tree-level models are valid. Our results motivate future work on the galaxy and shear integrated 3PCFs, which offer a practical way to extend standard analyses based on 3×2PCFs to systematically probe the non-Gaussian information content of cosmic density fields.

Untying the Growth Index to Relieve the σ8 Discomfort

The matter fluctuation parameter σ8 is, by model construction, degenerate with the growth index γ. Here, we study the effect on the cosmological parameter constraints by treating each independently from one another, considering σ8 as a free and non-derived parameter along with a free γ. We then try to constrain all parameters using three probes that span from deep to local redshifts, namely the CMB spectrum, the growth measurements from redshift space distortions fσ8, and the galaxy cluster counts. We also aim to assess the impact of this relaxation on the σ8 tension between its inferred CMB value in comparison to that obtained from local cluster counts. We also propose a more sophisticated correction, along with the classical one, that takes into account the impact of cosmology on the growth measurements when the parameters are varied in the Monte Carlo process, which consist in adjusting the growth to keep the observed power spectrum, integrated over all angles and scales, as invariant with the background evolution. We found by using the classical correction that untying the two parameters does not shift the maximum likelihood of either σ8 or γ, but it rather enables larger bounds with respect to when σ8 is a derived parameter, and that when considering CMB + fσ8, or when further combining with cluster counts albeit with tighter bounds. Precisely, we obtain σ8=0.809±0.043 and γ=0.613±0.046 in agreement with Planck’s constraint for the former and compatible with ΛCDM for the latter but with bounds wide enough to accommodate both values subject to the tensions. Allowing for massive neutrinos does not change the situation much. On the other hand, considering a tiered correction yields σ8=0.734±0.013 close to ∼1 σ for the inferred local values albeit with a growth index of γ=0.636±0.022 at ∼2 σ from its ΛCDM value. Allowing for massive neutrinos in this case yielded σ8=0.756±0.024, still preferring low values but with much looser constraints on γ=0.549±0.048 and a slight preference for Σmν∼0.19. We conclude that untying σ8 and γ helps in relieving the discomfort on the former between the CMB and local probes, and that careful analysis should be followed when using data products treated in a model-dependent way.

Cosmological constraints with the linear point from the BOSS survey

ABSTRACT The Linear Point (LP), defined as the mid-point between the baryon acoustic oscillation (BAO) peak and the associated left dip of the two-point correlation function (2PCF), ξ(s), is proposed as a new standard ruler which is insensitive to non-linear effects. In this paper, we use a Bayesian sampler to measure the LP and estimate the corresponding statistical uncertainty, and then perform cosmological parameter constraints with LP measurements. Using the Patchy mock catalogues, we find that the measured LPs are consistent with theoretical predictions at 0.6 per cent level. We find constraints with mid-points identified from the rescaled 2PCF (s2ξ) more robust than those from the traditional LP based on ξ, as the BAO peak is not always prominent when scanning the cosmological parameter space, with the cost of 2–4 per cent increase of statistical uncertainty. This problem can also be solved by an additional data set that provides strong parameter constraints. Measuring LP from the reconstructed data slightly increases the systematic error but significantly reduces the statistical error, resulting in more accurate measurements. The 1 σ confidence interval of distance scale constraints from LP measurements are 20–30 per cent larger than those of the corresponding BAO measurements. For the reconstructed Sloan Digital Sky Survey Data Release 12 data, the constraints on H0 and Ωm in a flat-Lambda cold dark matter framework with the LP are generally consistent with those from BAO. When combined with Planck cosmic microwave background data, we obtain $H_0=68.02_{-0.37}^{+0.36}$ ${\rm km}\, {\rm s}^{-1}\, {\rm Mpc}^{-1}$ and $\Omega _{\rm m}=0.3055_{-0.0048}^{+0.0049}$ with the LP.

BEYONDPLANCK

We present posterior sample-based cosmic microwave background (CMB) constraints fromPlanckLFI and WMAP observations as derived through global end-to-end Bayesian processing within the BEYONDPLANCKframework. We first used these samples to study correlations between CMB, foreground, and instrumental parameters. We identified a particularly strong degeneracy between CMB temperature fluctuations and free-free emission on intermediate angular scales (400 ≲ ℓ ≲ 600), mitigated through model reduction, masking, and resampling. We compared our posterior-based CMB results with previousPlanckproducts and found a generally good agreement, however, with notably higher noise due to our exclusion ofPlanckHFI data. We found a best-fit CMB dipole amplitude of 3362.7 ± 1.4 μK, which is in excellent agreement with previousPlanckresults. The quoted dipole uncertainty is derived directly from the sampled posterior distribution and does not involve any ad hoc contributions forPlanckinstrumental systematic effects. Similarly, we find a temperature quadrupole amplitude of $ \sigma^{TT}_2=229\pm97\,\muup{\rm K}^2 $ , which is in good agreement with previous results in terms of the amplitude, but the uncertainty is one order of magnitude greater than the naive diagonal Fisher uncertainty. Concurrently, we find less evidence of a possible alignment between the quadrupole and octopole than previously reported, due to a much larger scatter in the individual quadrupole coefficients that is caused both by marginalizing over a more complete set of systematic effects – as well as by requiring a more conservative analysis mask to mitigate the free-free degeneracy. For higher multipoles, we find that the angular temperature power spectrum is generally in good agreement with bothPlanckand WMAP. At the same time, we note that this is the first time that the sample-based, asymptotically exact Blackwell-Rao estimator has been successfully established for multipoles up toℓ ≤ 600. It now accounts for the majority of the cosmologically important information. Overall, this analysis demonstrates the unique capabilities of the Bayesian approach with respect to end-to-end systematic uncertainty propagation and we believe it can and should play an important role in the analysis of future CMB experiments. Cosmological parameter constraints are presented in a companion paper.

BEYONDPLANCK

We present cosmological parameter constraints estimated using the Bayesian BEYONDPLANCK 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 1σ when considering only temperature multipoles between 30 ≤ ℓ ≤ 600. In cases where there are differences, we note that the BEYONDPLANCK 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 BEYONDPLANCK 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.

Assessing theoretical uncertainties for cosmological constraints from weak lensing surveys

ABSTRACT Weak gravitational lensing is a powerful probe, which is used to constrain the standard cosmological model and its extensions. With the enhanced statistical precision of current and upcoming surveys, high-accuracy predictions for weak lensing statistics are needed to limit the impact of theoretical uncertainties on cosmological parameter constraints. For this purpose, we present a comparison of the theoretical predictions for the non-linear matter and weak lensing power spectra, based on the widely used fitting functions ($\texttt {mead}$ and $\texttt {rev-halofit}$ ), emulators ($\texttt {EuclidEmulator}$ , $\texttt {EuclidEmulator2}$ , $\texttt {BaccoEmulator}$ , and $\texttt {CosmicEmulator}$ ), and N-body simulations (pkdgrav3). We consider the forecasted constraints on the $\Lambda \texttt {CDM}$ and $\texttt {wCDM}$ models from weak lensing for stage III and stage IV surveys. We study the relative bias on the constraints and their dependence on the assumed prescriptions. Assuming a $\Lambda \texttt {CDM}$ cosmology, we find that the relative agreement on the S8 parameter is between 0.2 and 0.3σ for a stage III-like survey between the above predictors. For a stage IV-like survey the agreement becomes 1.4–3.0σ. In the $\texttt {wCDM}$ scenario, we find broader S8 constraints, and agreements of 0.18–0.26σ and 0.7–1.7σ for stage III and stage IV surveys, respectively. The accuracies of the above predictors therefore appear adequate for stage III surveys, whereas the fitting functions would need improvements for future stage IV surveys. Furthermore, we find that, of the fitting functions, $\texttt {mead}$ provides the best agreement with the emulators. We discuss the implication of these findings for the preparation of future weak lensing surveys, and the relative impact of theoretical uncertainties to other systematics.