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Retrospective Search for Strongly Lensed Supernovae in the DESI Legacy Imaging Surveys

The introduction of deep wide-field surveys in recent years and the adoption of machine-learning techniques have led to the discoveries of $\mathcal{O}$(10 4 ) strong gravitational lensing systems and candidates. However, the discovery of multiply-lensed transients remains a rarity. Lensed transients and especially lensed supernovae are invaluable tools to cosmology because they allow us to constrain cosmological parameters via lens modeling and the measurements of their time delays. In this paper, we develop a pipeline to perform a targeted lensed transient search. We apply this pipeline to 5807 strong lenses and candidates, which were identified in the literature, in the DESI Legacy Imaging Surveys Data Release 9 (DR9) footprint. For each system, we analyze every exposure in all of the observed bands (DECam g, r, and z). Our pipeline finds, groups, and ranks detections that are in sufficient proximity temporally and spatially. After the first round of inspection, for promising candidate systems, we further examine the newly available DR10 data (with additional i and Y bands). Here we present our targeted lensed supernova search pipeline and seven new lensed supernova candidates, including a very likely lensed supernova—probably a Type Ia—in a system with an Einstein radius of ~1$^{"}_{.}$5.

79 ASTRONOMY AND ASTROPHYSICS↗

Cosmological consequences of first-order general-relativistic viscous fluid dynamics

In this work, we investigate the out-of-equilibrium dynamics of viscous fluids in a spatially flat Friedmann-LemaîtreRobertson-Walker cosmology using the most general causal and stable viscous energy-momentum tensor defined at first order in spacetime derivatives. In this new framework a pressureless viscous fluid having equilibrium energy density ρ can evolve to an asymptotic future solution in which the Hubble parameter approaches a constant while ρ → 0, even in the absence of a cosmological constant (i.e., Λ = 0). Thus, while viscous effects in this model drive an accelerated expansion of the universe, the equilibrium energy density itself vanishes, leaving behind only the acceleration. This behavior emerges as a consequence of causality in first-order theories of relativistic fluid dynamics and it is fully consistent with Einstein’s equations.

79 ASTRONOMY AND ASTROPHYSICS↗

Cosmological constraints from H ii starburst galaxy apparent magnitude and other cosmological measurements

ABSTRACT We use H ii starburst galaxy apparent magnitude measurements to constrain cosmological parameters in six cosmological models. A joint analysis of H ii galaxy, quasar angular size, baryon acoustic oscillations peak length scale, and Hubble parameter measurements result in relatively model-independent and restrictive estimates of the current values of the non-relativistic matter density parameter $\Omega _{\rm m_0}$ and the Hubble constant H0. These estimates favour a 2.0–3.4σ (depending on cosmological model) lower H0 than what is measured from the local expansion rate. The combined data are consistent with dark energy being a cosmological constant and with flat spatial hypersurfaces, but do not strongly rule out mild dark energy dynamics or slightly non-flat spatial geometries.

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TDCOSMO - XVI. Measurement of the Hubble constant from the lensed quasar WGD 2038–4008

Time-delay cosmography is a powerful technique to constrain cosmological parameters, particularly the Hubble constant (H0). The TDCOSMO Collaboration is performing an ongoing analysis of lensed quasars to constrain cosmology using this method. In this work, we obtain constraints from the lensed quasar WGD 2038−4008 using new time-delay measurements and previous mass models by TDCOSMO. This is the first TDCOSMO lens to incorporate multiple lens modeling codes and the full time-delay covariance matrix into the cosmological inference. The models are fixed before the time delay is measured, and the analysis is performed blinded with respect to the cosmological parameters to prevent unconscious experimenter bias. We obtain DΔ t = 1.68−0.38+0.40 Gpc using two families of mass models, a power-law describing the total mass distribution, and a composite model of baryons and dark matter, although the composite model is disfavored due to kinematics constraints. In a flat ΛCDM cosmology, we constrain the Hubble constant to be H0 = 65−14+23 km s−1 Mpc−1. The dominant source of uncertainty comes from the time delays, due to the low variability of the quasar. Future long-term monitoring, especially in the era of the Vera C. Rubin Observatory’s Legacy Survey of Space and Time, could catch stronger quasar variability and further reduce the uncertainties. This system will be incorporated into an upcoming hierarchical analysis of the entire TDCOSMO sample, and improved time delays and spatially-resolved stellar kinematics could strengthen the constraints from this system in the future.Key words: gravitational lensing: strong / cosmological parameters / distance scale⋆ Corresponding author; kcwong19@gmail.com.⋆⋆ NHFP Einstein fellow.

79 ASTRONOMY AND ASTROPHYSICS↗

Planck 2018 results. VI. Cosmological parameters

In this paper, we present cosmological parameter results from the final full-mission Planck measurements of the cosmic microwave background (CMB) anisotropies, combining information from the temperature and polarization maps and the lensing reconstruction. Compared to the 2015 results, improved measurements of large-scale polarization allow the reionization optical depth to be measured with higher precision, leading to significant gains in the precision of other correlated parameters. Improved modelling of the small-scale polarization leads to more robust constraints on many parameters, with residual modelling uncertainties estimated to affect them only at the 0.5 σ level. We find good consistency with the standard spatially-flat 6-parameter ΛCDM cosmology having a power-law spectrum of adiabatic scalar perturbations (denoted “base ΛCDM” in this paper), from polarization, temperature, and lensing, separately and in combination. A combined analysis gives dark matter density Ω c h 2 = 0.120 ± 0.001, baryon density Ω b h 2 = 0.0224 ± 0.0001, scalar spectral index n s = 0.965 ± 0.004, and optical depth τ = 0.054 ± 0.007 (in this abstract we quote 68% confidence regions on measured parameters and 95% on upper limits). The angular acoustic scale is measured to 0.03% precision, with 100 θ * = 1.0411 ± 0.0003. These results are only weakly dependent on the cosmological model and remain stable, with somewhat increased errors, in many commonly considered extensions. Assuming the base-ΛCDM cosmology, the inferred (model-dependent) late-Universe parameters are: Hubble constant H 0 = (67.4 ± 0.5) km s –1 Mpc –1 ; matter density parameter Ω m = 0.315 ± 0.007; and matter fluctuation amplitude σ 8 = 0.811 ± 0.006. We find no compelling evidence for extensions to the base-ΛCDM model. Combining with baryon acoustic oscillation (BAO) measurements (and considering single-parameter extensions) we constrain the effective extra relativistic degrees of freedom to be N eff = 2.99 ± 0.17, in agreement with the Standard Model prediction N eff = 3.046, and find that the neutrino mass is tightly constrained to Σ m ν < 0.12 eV. The CMB spectra continue to prefer higher lensing amplitudes than predicted in base ΛCDM at over 2 σ , which pulls some parameters that affect the lensing amplitude away from the ΛCDM model; however, this is not supported by the lensing reconstruction or (in models that also change the background geometry) BAO data. The joint constraint with BAO measurements on spatial curvature is consistent with a flat universe, Ω K = 0.001 ± 0.002. Also combining with Type Ia supernovae (SNe), the dark-energy equation of state parameter is measured to be w 0 = –1.03 ± 0.03, consistent with a cosmological constant. We find no evidence for deviations from a purely power-law primordial spectrum, and combining with data from BAO, BICEP2, and Keck Array data, we place a limit on the tensor-to-scalar ratio r 0.002 < 0.06. Standard big-bang nucleosynthesis predictions for the helium and deuterium abundances for the base-ΛCDM cosmology are in excellent agreement with observations. The Planck base-ΛCDM results are in good agreement with BAO, SNe, and some galaxy lensing observations, but in slight tension with the Dark Energy Survey’s combined-probe results including galaxy clustering (which prefers lower fluctuation amplitudes or matter density parameters), and in significant, 3.6 σ , tension with local measurements of the Hubble constant (which prefer a higher value). Simple model extensions that can partially resolve these tensions are not favoured by the Planck data.

79 ASTRONOMY AND ASTROPHYSICS↗

Using Pantheon and DES supernova, baryon acoustic oscillation, and Hubble parameter data to constrain the Hubble constant, dark energy dynamics, and spatial curvature

ABSTRACT We use Pantheon Type Ia supernova (SN Ia) apparent magnitude, DES-3 yr binned SN Ia apparent magnitude, Hubble parameter, and baryon acoustic oscillation measurements to constrain six spatially flat and non-flat cosmological models. These sets of data provide mutually consistent cosmological constraints in the six cosmological models we study. A joint analysis of these data sets provides model-independent estimates of the Hubble constant, $H_0=68.8\pm 1.8\ \rm {km \, s^{-1} \ Mpc^{-1}}$, and the non-relativistic matter density parameter, $\Omega _{\rm m_0}=0.294\pm 0.020$. Although the joint constraints prefer mild dark energy dynamics and a little spatial curvature, they do not rule out dark energy being a cosmological constant and flat spatial hypersurfaces. We also add quasar angular size and H ii starburst galaxy measurements to the combined data set and find more restrictive constraints.

79 ASTRONOMY AND ASTROPHYSICS↗

Joint Analysis of X-Ray and Sunyaev-Zel'Dovich Observations of Galaxy Clusters Using an Analytic Model of the Intracluster Medium

We perform a joint analysis of X-ray and Sunyaev-Zel'dovich effect data using an analytic model that describes the gas properties of galaxy clusters. The joint analysis allows the measurement of the cluster gas mass fraction profile and Hubble constant independent of cosmological parameters. Weak cosmological priors are used to calculate the overdensity radius within which the gas mass fractions are reported. Such an analysis can provide direct constraints on the evolution of the cluster gas mass fraction with redshift. We validate the model and the joint analysis on high signal-to-noise data from the Chandra X-ray Observatory and the Sunyaev-Zel'dovich Array for two clusters, A2631 and A2204.

Galaxies↗

Cosmological constraints from the DESI DR1 joint power spectrum and bispectrum analysis

We derive cosmological parameter constraints from the Dark Energy Spectroscopic Instrument (DESI) Data Release 1 (DR1) galaxy clustering data, based on a joint full-shape analysis of the power spectrum multipoles and the bispectrum monopole using the ShapeFit framework. This is the follow-up of our previous work, in which we obtained for the first time constraints on the ShapeFit parameters using the bispectrum of DESI DR1. Here we present the first ShapeFit cosmological inference results using the bispectrum of DESI DR1. We recover values for the matter density parameter and Hubble constant of respectively $Ω_m=0.310\pm0.012$ and $H_0=[68.92\pm0.97]\,\mathrm{km\, s^{-1} Mpc^{-1}}$, consistent with previous results from the full DESI DR1 dataset that did not use the bispectrum signal. The inclusion of the bispectrum significantly tightens the constraints on the amplitude of fluctuations, reducing the error-bars in $\ln(A_s\times10^{10})$ by approximately 20%, compared to using the power spectrum alone. We also explore extended cosmological models by performing fits for the evolving dark energy equation of state $w_0w_a$, and the sum of neutrino masses $\sum m_ν$. In these cases, we obtain constraints slightly larger than the ones from previous works from the DESI collaboration, due to not combining the full-shape results with other probes in all tracers. We find no strong evidence of deviations from standard $Λ$CDM, with the dark energy equation-of-state remaining within 2$σ$ from a cosmological constant $Λ$, and the neutrino mass being consistent with the normal hierarchy, $\sum m_ν<0.1\,[eV]$ at 95% confidence limit. These constraints are broadly consistent with other DESI DR1 analyses, thus validating the robustness of the ShapeFit compression approach and the inclusion of the bispectrum for cosmological inference.

Novell-Masot, S. [ICC, Barcelona U.; Geneva U., De↗

Cosmological constraints from the DESI DR1 joint power spectrum and bispectrum analysis

We derive cosmological parameter constraints from the Dark Energy Spectroscopic Instrument (DESI) Data Release 1 (DR1) galaxy clustering data, based on a joint full-shape analysis of the power spectrum multipoles and the bispectrum monopole using the ShapeFit framework. This is the follow-up of our previous work, in which we obtained for the first time constraints on the ShapeFit parameters using the bispectrum of DESI DR1. Here we present the first ShapeFit cosmological inference results using the bispectrum of DESI DR1. We recover values for the matter density parameter and Hubble constant of respectively $Ω_m=0.310\pm0.012$ and $H_0=[68.92\pm0.97]\,\mathrm{km\, s^{-1} Mpc^{-1}}$, consistent with previous results from the full DESI DR1 dataset that did not use the bispectrum signal. The inclusion of the bispectrum significantly tightens the constraints on the amplitude of fluctuations, reducing the error-bars in $\ln(A_s\times10^{10})$ by approximately 20%, compared to using the power spectrum alone. We also explore extended cosmological models by performing fits for the evolving dark energy equation of state $w_0w_a$, and the sum of neutrino masses $\sum m_ν$. In these cases, we obtain constraints slightly larger than the ones from previous works from the DESI collaboration, due to not combining the full-shape results with other probes in all tracers. We find no strong evidence of deviations from standard $Λ$CDM, with the dark energy equation-of-state remaining within 2$σ$ from a cosmological constant $Λ$, and the neutrino mass being consistent with the normal hierarchy, $\sum m_ν<0.1\,[eV]$ at 95% confidence limit. These constraints are broadly consistent with other DESI DR1 analyses, thus validating the robustness of the ShapeFit compression approach and the inclusion of the bispectrum for cosmological inference.

Novell-Masot, S. [ICC, Barcelona U.; Geneva U., De↗

Scale covariance and G-varying cosmology. IV - The log N-log S relation

The traditional radio counts N(S) and radio source models are studied within the framework of the scale-covariant cosmology developed to investigate whether the relative strength of the gravitational and electromagnetic constants is a function of cosmological epoch. It is found that a gravitational constant G varying as the inverse of t, where t is the epoch in atomic units, is consistent with all the data analyzed. For a wide class of models the present cosmology allows a finer discrimination of the deceleration parameter than does standard theory. The results, when combined with those of previous papers, namely, those from radio and optical flux and angular-diameter data analysis, favor an open universe.

Canuto, V. M.↗

The Dark Energy Survey: Cosmology Results with ∼1500 New High-redshift Type Ia Supernovae Using the Full 5 yr Data Set

Abstract We present cosmological constraints from the sample of Type Ia supernovae (SNe Ia) discovered and measured during the full 5 yr of the Dark Energy Survey (DES) SN program. In contrast to most previous cosmological samples, in which SNe are classified based on their spectra, we classify the DES SNe using a machine learning algorithm applied to their light curves in four photometric bands. Spectroscopic redshifts are acquired from a dedicated follow-up survey of the host galaxies. After accounting for the likelihood of each SN being an SN Ia, we find 1635 DES SNe in the redshift range 0.10 < z < 1.13 that pass quality selection criteria sufficient to constrain cosmological parameters. This quintuples the number of high-quality z > 0.5 SNe compared to the previous leading compilation of Pantheon+ and results in the tightest cosmological constraints achieved by any SN data set to date. To derive cosmological constraints, we combine the DES SN data with a high-quality external low-redshift sample consisting of 194 SNe Ia spanning 0.025 < z < 0.10. Using SN data alone and including systematic uncertainties, we find Ω M = 0.352 ± 0.017 in flat ΛCDM. SN data alone now require acceleration ( q 0 < 0 in ΛCDM) with over 5 σ confidence. We find ( Ω M , w ) = ( 0.264 − 0.096 + 0.074 , − 0.80 − 0.16 + 0.14 ) in flat w CDM. For flat w 0 w a CDM, we find ( Ω M , w 0 , w a ) = ( 0.495 − 0.043 + 0.033 , − 0.36 − 0.30 + 0.36 , − 8.8 − 4.5 + 3.7 ) , consistent with a constant equation of state to within ∼2 σ . Including Planck cosmic microwave background, Sloan Digital Sky Survey baryon acoustic oscillation, and DES 3 × 2pt data gives (Ω M , w ) = (0.321 ± 0.007, −0.941 ± 0.026). In all cases, dark energy is consistent with a cosmological constant to within ∼2 σ . Systematic errors on cosmological parameters are subdominant compared to statistical errors; these results thus pave the way for future photometrically classified SN analyses.

79 ASTRONOMY AND ASTROPHYSICS↗

Cosmological constraints from higher redshift gamma-ray burst, H ii starburst galaxy, and quasar (and other) data

ABSTRACT We use higher redshift gamma-ray burst (GRB), H ii starburst galaxy (H iiG), and quasar angular size (QSO-AS) measurements to constrain six spatially flat and non-flat cosmological models. These three sets of cosmological constraints are mutually consistent. Cosmological constraints from a joint analysis of these data sets are largely consistent with currently accelerating cosmological expansion and with cosmological constraints derived from a combined analysis of Hubble parameter (H(z)) and baryon acoustic oscillation (BAO, with Planck-determined baryonic matter density) measurements. A joint analysis of the H(z) + BAO + QSO-AS + H iiG + GRB data provides fairly model-independent determinations of the non-relativistic matter density parameter $\Omega _{\rm m_0}=0.313\pm 0.013$ and the Hubble constant $H_0=69.3\pm 1.2\, \rm {km \, s^{-1} \, Mpc^{-1}}$. These data are consistent with the dark energy being a cosmological constant and with spatial hypersurfaces being flat, but they do not rule out mild dark energy dynamics or a little spatial curvature. We also investigate the effect of including quasar flux measurements in the mix and find no novel conclusions.

79 ASTRONOMY AND ASTROPHYSICS↗

Uncovering New Physics in the Cosmic Microwave Background: Developing Novel Theoretical Models and Machine-Learning-Powered Constraints

The search for evidence of new physics via its signatures in the cosmos is a cornerstone goal of the Office of High Energy Physics in the DOE Office of Science. Indeed, the current concordance cosmological model provides intriguing hints for beyond-the-standard-model (BSM) physics, such as dark matter and dark energy. Recently, a potential breakdown has appeared in this model, which could be initial evidence toward a further important revision in our fundamental theoretical understanding of cosmology. This breakdown is reflected in disagreements between inferences of the current expansion rate of the universe, H 0 (the Hubble constant), based on indirect, cosmological data (e.g., from the early universe) and based on direct, local measurements. Despite significant effort, a compelling new concordance cosmological model has yet to be found; achieving significant progress on this front was the first major focus of the project. Theoretical considerations indicate that if the observational discrepancies are not due to systematic errors, they strongly suggest new physics operating in the redshift range just prior to recombination, when cosmic microwave background (CMB) photons last scattered. Crucially, almost all such models produce unique signatures in the CMB temperature and polarization power spectra, which will be measured with unprecedented precision by ongoing and upcoming experiments, including the DOE-supported CMB-S4 project. However, these subtle hints of new physics must be uncovered from beneath a swath of Galactic and extragalactic foreground contamination. Current CMB analysis methods, although powerful, do not optimally infer the CMB power spectrum in the presence of non-Gaussian foregrounds. There is thus scope for theoretical improvement in this foundational challenge of cosmological inference, which formed the second major focus of the project. The primary objectives of the project were two-fold: (1) to develop new theoretical models in cosmology that can restore concordance amongst the full suite of cosmological data sets, thereby potentially providing evidence of novel BSM physics; (2) to develop new theoretical machinery to enable significant sensitivity improvements in searches for new physics in cosmology, particularly via the CMB power spectrum. The two objectives are intertwined, as the analysis methodology improvements in (2) will enable the tightest possible constraints on the signatures of new physics predicted by the novel scenarios in (1). The theoretical approaches to restore concordance focused on models involving novel scalar field dynamics in the pre-recombination universe (the “early dark energy” scenario and modifications thereof), as well as couplings between this field and other components in the standard cosmological model, such as dark matter. We also studied a model featuring a generalization of the decaying dark matter scenario, in which a sub-component of dark matter converts into dark radiation at late times in cosmic history. While these ideas are mostly driven by phenomenological considerations, this tactic has proven extremely successful in cosmology throughout the past few decades, including in the early history of evidence for dark matter and dark energy. The new theoretical machinery envisioned in (2) is undergirded by developments in signal processing and machine learning, which will enable improvements in CMB power spectrum estimation in the presence of non-Gaussian foreground contaminants. In turn, this will yield optimal sensitivity in searches for new physics in the CMB, by maximizing the cosmological information that is extracted from this observable. The most ambitious outcome of this work would be the construction of a new cosmological model that restores concordance amongst data sets. Although the individual models studied here did not fully achieve that goal, significant progress in narrowing down the model space was made, as described below. Moreover, the outcome of the methodological improvements in (2) will significantly impact a wide range of theoretical cosmology, by enabling the tightest possible constraints on any model that leaves novel signatures in the CMB temperature and polarization power spectra.

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Theoretical frameworks for testing relativistic gravity. 5: Post-Newtonian limit of Rosen's theory

The post-Newtonian limit of Rosen's theory of gravity is evaluated and is shown to be identical to that of general relativity, except for the PPN parameter alpha sub 2, which is related to the difference in propagation speeds for gravitational and electromagnetic waves. Both the value of alpha sub 2 and the value of the Newtonian gravitational constant depend on the present cosmological structure of the Universe. If the cosmological structure has a specific but presumably special form, the Newtonian gravitational constant assumes its current value, alpha sub 2 is zero, the post-Newtonian limit of Rosen's theory is identical to that of general relativity--and standard solar system experiments cannot distinguish between the two theories.

Lee, D. L.↗

Theoretical frameworks for testing relativistic gravity. V - Post-Newtonian limit of Rosen's theory

The post-Newtonian limit of Rosen's theory of gravity is evaluated and is shown to be identical to that of general relativity, except for the post-Newtonian parameter alpha sub 2 (which is related to the difference in propagation speeds for gravitational and electromagnetic waves). Both the value of alpha sub 2 and the value of the Newtonian gravitational constant depend on the present cosmological structure of the Universe. If the cosmological structure has a specific (but presumably special) form, the Newtonian gravitational constant assumes its current value, alpha sub 2 is zero, the post-Newtonian limit of Rosen's theory is identical to that of general relativity - and standard solar system experiments cannot distinguish between the two theories.

Lee, D. L.↗

Fully covariant cosmology and its astrophysical implications

We present a cosmological model with good physical properties which is invariant not only under changes of the space and time coordinates but also under changes of an extra (Kaluza-Klein) coordinate related to rest mass. In frames where the latter is chosen to be constant we recover standard cosmology. In frames where it is chosen to be variable we obtain new astrophysical effects and gain insight into the nature of the big bang.

Wesson, Paul S.↗

The Atacama Cosmology Telescope: DR6 constraints on extended cosmological models

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 the Planck mission. To break geometric degeneracies, we include ACT and Planck CMB lensing data and baryon acoustic oscillation data from DESI Year-1. To test the dependence of our results on non-ACT data, we also explore combinations replacing Planck with WMAP and DESI with BOSS, and further add supernovae measurements from Pantheon+ for models that affect the late-time expansion history. We verify the near-scale-invariance (running of the spectral index dn s /d ln k = 0.0062 ± 0.0052) and adiabaticity of the primordial perturbations. Neutrino properties are consistent with Standard Model predictions: we find no evidence for new light, relativistic species that are free-streaming (N eff = 2.86 ± 0.13, which combined with astrophysical measurements of primordial helium and deuterium abundances becomes N eff = 2.89 ± 0.11), for non-zero neutrino masses (∑m ν < 0.089 eV at 95% CL), or for neutrino self-interactions. We also find no evidence for self-interacting dark radiation (N idr < 0.134), or for early-universe variation of fundamental constants, including the fine-structure constant (α EM /α EM,0 = 1.0043 ± 0.0017) and the electron mass (m e /m e,0 = 1.0063 ± 0.0056). Our data are consistent with standard big bang nucleosynthesis (we find Y p = 0.2312 ± 0.0092), the COBE/FIRAS-inferred CMB temperature (we find T CMB = 2.698 ± 0.016 K), a dark matter component that is collisionless and with only a small fraction allowed as axion-like particles, a cosmological constant (w = -0.986 ± 0.025), and the late-time growth rate predicted by general relativity (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 find H 0 = 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.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗