arXiv subjects

William Giarè

Publications and source records attributed to William Giarè.

At least 19 recordsLinked to original sources

arXiv2026

Unifying Early and Late Dark Energy: Dynamical Requirements and Obstructions

We investigate whether early- and late-time dark energy could arise from a single scalar field. Adopting a bottom-up perspective, we first identify the sequence of dynamical regimes that any unified scenario must traverse to account for both an early dark energy phase relevant for pre-recombination solutions of the Hubble tension and the late-time acceleration of the Universe. We derive the corresponding requirements on the scalar energy density and equation of state. We then adopt a complementary top-down perspective and translate these requirements into constraints on the phase-space structure of minimally coupled scalar fields with tracking-like dynamics. We show that satisfying all requirements necessitates a potential with three distinct slopes, arranged in a steep-steeper-shallow hierarchy. This conclusion remains unchanged in the presence of conformal couplings to dark matter. These results place strong constraints on attempts to construct unified models of early- and late-time dark energy. We discuss implications for model-building.

astro-ph.CO↗

arXiv2026

Intertwined Constraints in Extended Cosmologies: Dark Energy, Curvature, Neutrinos, and Inflation

We present a systematic reassessment of cosmological constraints beyond $Λ$CDM by progressively relaxing the assumptions underlying Dark Energy (DE), Curvature, Neutrinos, and Inflation. Using the latest CMB data together with DESI BAO and different SN catalogues, we show that the preference for dynamical DE persists across all the extended cosmologies considered. $Ω_k$ remains compatible with flatness, despite a mild $2.2σ$ preference for $Ω_k>0$ that is substantially degraded in dynamical DE extensions. Constraints on $N_{\rm eff}$ are broadly consistent with $N_{\rm eff}=3.04$, while cosmological upper limits on the total neutrino mass vary substantially across the cosmologies explored, ranging from $\sum m_ν\lesssim 0.06$ eV to $\lesssim 0.2$ eV. We quantify both the preference for the mass ordering and the apparent tension between cosmology and oscillation experiments, showing that they are strongly framework dependent. We find no evidence for inflationary tensor modes, with $r\lesssim 0.035$. Constraints on the spectral index $n_s$ show significant model dependence. Allowing for the scalar runnings produces a mild shift toward $α_s>0$ and $β_s>0$ that can reabsorb the preference for larger $n_s$ found in small-scale CMB data, although both $α_s$ and $β_s$ remain consistent with zero at $\sim 1.5σ$. We highlight the implications for slow-roll inflation and benchmark models. None of the extensions considered here can resolve the $H_0$ tension. We discuss the implications for $Ω_m$ and $S_8$. Overall, dynamical DE is the only significant deviation from $Λ$CDM and has the strongest impact on the inferred conclusions in the other sectors of the model.

astro-ph.CO↗

arXiv2026

Robust Preference for Dark Sector Interactions

Recent DESI baryon acoustic oscillation data reveal deviations from $Λ$CDM cosmology, conventionally attributed to dynamical dark energy (DE). We demonstrate that these deviations are equally, if not better, explained by interactions between dark matter and dark energy (IDE), without requiring a time-varying DE equation of state. Using a unified framework, we analyze two IDE models - coupled quintessence and coupled fluid - against the latest CMB (Planck, ACT, SPT), DESI BAO, and SN (including DES-Dovekie recalibrated) data. Both IDE scenarios show robust evidence for non-vanishing interactions at the 3-5$σ$ level, with marginalized constraints significantly deviating from the $Λ$CDM limit. This preference persists even under DES-Dovekie SN recalibration, which weakens dynamical DE evidence. Crucially, for the same number of free parameters, IDE models provide fits to low- and high-redshift data that match or exceed the performance of the CPL dynamical DE parametrization. Our results establish IDE as a physically motivated alternative to dynamical DE, highlighting the necessity of future cosmological perturbation measurements (e.g., weak lensing, galaxy clustering) to distinguish between these paradigms.

astro-ph.CO↗

arXiv2026

Slow-rolling down the curvature: a reassessment of the Planck constraints on $ϕ^2$ inflation in a closed universe

We revisit the Cosmic Microwave Background (CMB) constraints on the spatial curvature of the Universe, assessing how they change when the curvature parameter and the primordial inflationary scalar spectrum are treated consistently within theoretically motivated frameworks. Instead of relying on the phenomenological parametrisation commonly used to capture curvature effects at the largest scales, we present a case study based on closed quadratic inflation, where the primordial spectrum is derived in full generality and in a gauge-invariant manner. Within this framework, we analyze both the $\texttt{plik}$ PR3 and $\texttt{CamSpec}$ PR4 Planck CMB likelihoods and find that the constraints on $Ω_{\mathcal{K}}$ shift towards spatial flatness. In $\texttt{plik}$ the preference for $Ω_{\mathcal{K}}<0$ decreases from $\gtrsim 3.5σ$ to $\sim 2.5σ$, while in $\texttt{CamSpec}$ it reduces to $\sim 2σ$. At large angular scales ($\ell < 10$), our model explains the low-$\ell$ power suppression anomaly, notably improving the fit to the quadrupole. However, the reduced preference for highly negative values of $Ω_{\mathcal{K}}$ only partially accounts for the lensing anomaly at high multipoles, worsening the fit to the $\texttt{plik}$ spectrum at small scales. By contrast, in the $\texttt{CamSpec}$ PR4 spectrum, where the lensing anomaly is less pronounced, the model yields an overall improvement. Our analysis highlights a key conceptual point: closed-inflation models tie the curvature parameter to the inflationary dynamics and the primordial spectrum, enforcing consistency conditions that do not necessarily allow for the large deviations from flatness seen in phenomenological parametrisations. In the case of quadratic inflation, these restrictions reduce the apparent evidence for negative curvature reported by earlier analyses, while allowing for a mildly closed geometry.

astro-ph.CO↗

arXiv2026

Gamma-Ray Bursts as an Independent High-Redshift Probe of Dark Energy

Testing the $Λ$CDM model requires cosmological probes spanning the wide redshift interval between Type Ia Supernovae (SNe Ia, $z\lesssim2.9$) and the Cosmic Microwave Background (CMB, $z\approx1100$). Gamma-Ray Bursts (GRBs), observed up to redshift $z=9.2$, offer the opportunity to explore this regime. Here, we investigate how many GRBs are needed to become a useful cosmological probe capable of independently testing deviations from $Λ$CDM suggested by the recent DESI BAO observations. We develop forecasts based on the two-dimensional X-ray and optical Dainotti relations, between the luminosity at the end of the plateau phase and its rest-frame duration. Using simulated GRB samples constructed from the observed population, we evaluate the constraining power of GRBs on cosmological parameters within the $w$CDM and $w_0w_a$CDM models, both independently and in combination with CMB observations. Our results show that GRB samples containing several tens to hundreds of well-characterized plateau can already approach the precision currently achieved by CMB measurements on the Dark Energy (DE) equation-of-state parameter $w$. Particularly, a sample of $\sim66$ optical GRBs can reach a precision $σ_w \approx 0.47$, comparable to that obtained from Planck within the $w$CDM framework. Such sample sizes are already attainable through Machine Learning techniques that double the number of GRBs using inferred redshifts. These forecasts indicate that future GRB observations, when combined with next-generation transient missions and improved statistical techniques, will provide an independent high-redshift probe of cosmic expansion and will play an important role in testing the robustness of potential Dynamical DE signals suggested by other cosmological datasets.

astro-ph.CO↗

arXiv2026

A solution to the S8 tension through neutrino-dark matter interactions

Neutrinos and dark matter (DM) are two of the least understood components of the Universe, yet both play crucial roles in cosmic evolution. Clues about their fundamental properties may emerge from discrepancies in cosmological measurements across different epochs of cosmic history. Possible interactions between them could leave distinctive imprints on cosmological observables, offering a rare window into dark sector physics beyond the standard $Λ$CDM framework. We present compelling evidence that DM-neutrino interactions can resolve the persistent structure growth parameter discrepancy, $S_8 = σ_8\,\sqrt{Ω_m/0.3}$, between early and late universe observations. By incorporating cosmic shear measurements from current Weak Lensing surveys, we demonstrate that an interaction strength of $u \sim 10^{-4}$ not only provides a coherent explanation for the high-multipole observations from the Atacama Cosmology Telescope (\texttt{ACT}), but also alleviates the $S_8$ discrepancy. Combining early universe constraints with \texttt{DES Y3 cosmic shear} data yields a nearly $3σ$ preference for non-zero DM neutrino interactions. This strengthens previous observational claims and provides a clear path toward a significant breakthrough in cosmological research. Our findings challenge the standard $Λ$CDM paradigm and highlight the potential of future large-scale structure surveys, which can rigorously test this interaction and unveil the fundamental properties of DM.

astro-ph.CO↗

arXiv2025

Cosmographic Footprints of Dynamical Dark Energy

We introduce a novel cosmographic framework to trace the late-time kinematics of the Universe without assuming any underlying dynamics. The method relies on generalized Padé-$(2,1)$ expansions around arbitrary pivot redshifts, which, compared to state-of-the-art calculations, reduce truncation errors by up to two orders of magnitude at high redshift and yield more precise constraints by defining cosmographic parameters exactly where the data lie. This avoids extrapolations, mitigates degeneracies, and enables a clean disentangling of their effects. Using the latest low-redshift datasets, we center the generalized expansion in multiple bins across $z\in[0,1]$ and obtain precise constraints on the redshift evolution of cosmographic parameters. We find that all key parameters deviate from their $Λ$CDM predictions in a redshift-dependent way that can be naturally explained within dynamical Dark Energy scenarios. The deceleration parameter $q(z)$ follows a redshift evolution consistent with the Chevallier-Polarski-Linder (CPL) parameterization, while the generalized $Om(z)$ diagnostic shows deviations of up to $\sim4σ$ from the constant $Λ$CDM expectation, closely matching the CPL predictions. Taken together, these results point to footprints of dynamical Dark Energy in the kinematics of the Universe at $z\lesssim 1$.

astro-ph.CO↗

arXiv2025

Neutrino mass tension or suppressed growth rate of matter perturbations?

Assuming a minimal $Λ$CDM cosmology with three massive neutrinos, the joint analysis of Planck cosmic microwave background data, DESI baryon acoustic oscillations, and distance moduli measurements of Type Ia supernovae from the Pantheon+ sample sets an upper bound on the total neutrino mass, $\sum m_ν\lesssim 0.06$-$0.07$ eV, that lies barely above the lower limit from oscillation experiments. These constraints are mainly driven by mild differences in the inferred values of the matter density parameter across different probes that can be alleviated by introducing additional background-level degrees of freedom (e.g., by dynamical dark energy models). However, in this work we explore an alternative possibility. Since both $Ω_\mathrm{m}$ and massive neutrinos critically influence the growth of cosmic structures, we test whether the neutrino mass tension may originate from the way matter clusters, rather than from a breakdown of the $Λ$CDM expansion history. To this end, we introduce the growth index $γ$, which characterizes the rate at which matter perturbations grow. Deviations from the standard $Λ$CDM value ($γ\simeq 0.55$) can capture a broad class of models, including non-minimal dark sector physics and modified gravity. We show that allowing $γ$ to vary significantly relaxes the neutrino mass bounds to $\sum m_ν\lesssim 0.13$-$0.2$ eV, removing any tension with terrestrial constraints without altering the inferred value of $Ω_\mathrm{m}$. However, this comes at the cost of departing from standard growth predictions: to have $\sum m_ν\gtrsim 0.06$ eV one needs $γ> 0.55$, and we find a consistent preference for $γ> 0.55$ at the level of $\sim 2σ$. This preference increases to $\sim 2.5$-$3σ$ when a physically motivated prior $\sum m_ν\ge 0.06$ eV from oscillation experiments is imposed.

astro-ph.CO↗

arXiv2025

Model-Independent Test of Prerecombination New Physics: Measuring the Sound Horizon with Gravitational Wave Standard Sirens and the Baryon Acoustic Oscillation Angular Scale

In a broad class of cosmological models where spacetime is described by a pseudo-Riemannian manifold, photons propagate along null geodesics, and their number is conserved, upcoming Gravitational Wave (GW) observations can be combined with measurements of the Baryon Acoustic Oscillation (BAO) angular scale to provide model-independent estimates of the sound horizon at the baryon-drag epoch. By focusing on the accuracy expected from forthcoming surveys such as LISA GW standard sirens and DESI or Euclid angular BAO measurements, we forecast a relative precision of $σ_{r_{\rm d}} /r_{\rm d} \sim 1.5\%$ within the redshift range $z \lesssim 1$. This approach will offer a unique model-independent measure of a fundamental scale characterizing the early universe, which is competitive with model-dependent values inferred within specific theoretical frameworks. These measurements can serve as a consistency test for $Λ$CDM, potentially clarifying the nature of the Hubble tension and confirming or ruling out new physics prior to recombination with a statistical significance of $\sim 4σ$.

astro-ph.CO↗

arXiv2025

The CosmoVerse White Paper: Addressing observational tensions in cosmology with systematics and fundamental physics

The standard model of cosmology has provided a good phenomenological description of a wide range of observations both at astrophysical and cosmological scales for several decades. This concordance model is constructed by a universal cosmological constant and supported by a matter sector described by the standard model of particle physics and a cold dark matter contribution, as well as very early-time inflationary physics, and underpinned by gravitation through general relativity. There have always been open questions about the soundness of the foundations of the standard model. However, recent years have shown that there may also be questions from the observational sector with the emergence of differences between certain cosmological probes. In this White Paper, we identify the key objectives that need to be addressed over the coming decade together with the core science projects that aim to meet these challenges. These discordances primarily rest on the divergence in the measurement of core cosmological parameters with varying levels of statistical confidence. These possible statistical tensions may be partially accounted for by systematics in various measurements or cosmological probes but there is also a growing indication of potential new physics beyond the standard model. After reviewing the principal probes used in the measurement of cosmological parameters, as well as potential systematics, we discuss the most promising array of potential new physics that may be observable in upcoming surveys. We also discuss the growing set of novel data analysis approaches that go beyond traditional methods to test physical models. [Abridged]

astro-ph.CO↗

arXiv2025

Dark Energy Crosses the Line: Quantifying and Testing the Evidence for Phantom Crossing

Combinations of the most recent CMB, BAO, and SNeIa datasets, when analyzed using the CPL parametrization, $w(a) = w_0 + (1 - a) w_a$, exclude $Λ$CDM at $\gtrsim\!3σ$ in favor of a dark energy equation of state (EoS) parameter that crosses the phantom divide. We confirm this behavior and show that it persists when DESI BAO data are replaced by SH0ES $H_0$ measurements, despite the known tension between these probes in the presence of CMB data. In both cases, the constraints favor a transition from an early-time phantom-like phase to a late-time quintessence-like phase, with the crossing occurring at different redshifts depending on the dataset combination. The probability that a phantom divide line (PDL) crossing does not occur within the expansion history is excluded at significance levels ranging between $3.1σ$-$5.2σ$. To investigate whether the apparent PDL crossing is a genuine feature preferred by the data or an artifact of the linear form of the CPL parametrization, we isolate the PDL crossing feature by introducing two modified versions of CPL that explicitly forbid it: CPL${}_{>a_\mathrm{c}}$ and CPL${}_{<a_\mathrm{c}}$. These models are physically motivated in that they phenomenologically capture the behavior of thawing and freezing scalar field scenarios. While previous studies have primarily considered thawing quintessence as a non-crossing alternative, we find that a freezing phantom-like model is the only one capable of performing comparably to CPL -- and only in a few cases. Nevertheless, across all dataset combinations considered, the standard CPL model consistently provides the best fit, strongly indicating that the data genuinely favor a PDL crossing.

astro-ph.CO↗

arXiv2025

Dynamical Dark Energy Beyond Planck? Constraints from multiple CMB probes, DESI BAO and Type-Ia Supernovae

The latest Baryon Acoustic Oscillation (BAO) measurements from the Dark Energy Spectroscopic Instrument (DESI) collaboration, when combined with Planck satellite Cosmic Microwave Background (CMB) data and Type Ia Supernovae, suggest a preference for Dynamical Dark Energy (DDE) at a significance level ranging from $2.8σ$ to $4.2σ$. In this work, I test whether, and to what extent, this preference is supported by CMB experiments other than Planck. I analyze the latest Atacama Cosmology Telescope (ACT) and South Pole Telescope (SPT) temperature, polarization, and lensing spectra at small scales, eventually combining them with Planck or WMAP 9-year observations at large angular scales. My analysis shows that ACT and WMAP data, when combined with DESI BAO and Pantheon-plus Supernovae, yield independent constraints with a precision comparable to Planck. Notably, in this case, the cosmological constant value is recovered within two standard deviations. A preference for DDE reappears when Pantheon-plus is replaced with distance moduli measurements from the Dark Energy Survey Supernova program (DESy5). However, it remains less pronounced compared to the Planck-based results. When considering SPT data, no clear preference for DDE is found in combinations involving Pantheon-plus Supernovae, and the preference is significantly weaker in combinations involving DESy5. Overall, CMB experiments other than Planck generally weaken the evidence for DDE. I argue that the subsets of Planck data that strengthen the shift toward DDE are the temperature and E-mode polarization anisotropy measurements at large angular scales $\ell \lesssim 30$.

astro-ph.CO↗

arXiv2025

Inflation in non-local hybrid metric-Palatini gravity

Within the framework of hybrid metric-Palatini gravity, we incorporate non-localities introduced via the inverse of the d'Alembert operators acting on the scalar curvature. We analyse the dynamical structure of the theory and, adopting a scalar-tensor perspective, assess the stability conditions to ensure the absence of ghost instabilities. Focusing on a special class of well-defined hybrid actions -- where local and non-local contributions are carried by distinct types of curvature -- we investigate the feasibility of inflation within the resulting Einstein-frame multi-field scenario. We examine how the non-minimal kinetic couplings between the fields, reflecting the non-local structure of the original frame, influence the number of e-folds and the field trajectories. To clarify the physical interpretation of our results, we draw analogies with benchmark single-field inflation scenarios that include spectator fields.

hep-th↗

arXiv2025

Planck-PR4 anisotropy spectra show (better) consistency with General Relativity

We present the results from a series of analyses on two parametric tests of gravity that modify the growth of linear, sub-horizon matter perturbations in the $Λ$CDM model. The first test, known as the $(μ,Σ)$ framework, modifies the Poisson and lensing equations from General Relativity (GR). The second test introduces the growth index $γ$, which directly affects the time evolution of matter density perturbations. Our study is motivated by results from the analysis of the Planck-PR3 2018 spectra, which indicate a preference for $Σ_0 \neq 0$ and $γ_0 > 0.55$, both of which deviate from the $Λ$CDM predictions at a significance level of $\sim 2.5σ$. To clarify the nature of these anomalous results and understand how the lensing anomaly fits into the picture, we analyze the most recent Planck-PR4 spectra extracted from the updated \texttt{NPIPE} maps. Overall, the Planck-PR4 data show better consistency with GR. The updated likelihood \texttt{Camspec} provides constraints on $Σ_0$ and $γ_0$ that are consistent with GR within $1.5σ$ and $2σ$, respectively. The updated likelihoods \texttt{HiLLiPoP} and \texttt{LoLLiPoP} show even closer agreement, with all parameter values consistent with a $Λ$CDM cosmology within $1σ$. This enhanced consistency is closely correlated with the lensing anomaly. Across the different likelihoods, the tendency of $Σ_0$ and $γ_0$ to drift towards non-standard values matches the observed preference for $A_L > 1$, both of which are significantly reduced or disappear within the Planck-PR4 data.

astro-ph.CO↗

arXiv2025

Resilience and implications of adiabatic CMB cooling

We investigate potential deviations from the standard adiabatic evolution of the cosmic microwave background (CMB) temperature, $T_{\rm CMB}(z)$, using the latest Sunyaev-Zeldovich (SZ) effect measurements and molecular line excitation data, covering a combined redshift range of $0 < z \lesssim 6$. We follow different approaches. First, we reconstruct the redshift evolution of $T_{\rm CMB}(z)$ in a model-independent way using Gaussian Process regression. The tightest constraints come from SZ measurements at $z < 1$, while molecular line data at $z > 3$ yield broader uncertainties. By combining both datasets, we find good consistency with the standard evolution across the full analysed redshift range, inferring a present-day CMB monopole temperature of $T_0 = 2.744 \pm 0.019$ K. Next, we test for deviations from the standard scaling by adopting the parameterisation $T_{\rm CMB}(z) = T_0(1+z)^{1-β}$, where $β$ quantifies departures from adiabaticity, with $β= 0$ corresponding to the standard scenario. In this framework, we use Gaussian Process reconstruction to test the consistency of $β= 0$ across the full redshift range and perform $χ^2$ minimisation techniques to determine the best-fit values of $T_0$ and $β$. In both cases, we find good consistency with the standard temperature-redshift relation. The $χ^2$-minimisation analysis yields best-fit values of $β= -0.0106 \pm 0.0124$ and $T_0 = 2.7276 \pm 0.0095$ K, in excellent agreement with both $β= 0$ and independent direct measurements of $T_0$ from FIRAS and ARCADE. We discuss the implications of our findings, which offer strong empirical support for the standard cosmological prediction and place tight constraints on a wide range of alternative scenarios of interest in the context of cosmological tensions and fundamental physics.

astro-ph.CO↗

arXiv2025

Implications of distance duality violation for the $H_0$ tension and evolving dark energy

We investigate whether a violation of the distance duality relation (DDR), $D_L(z) = (1+z)^2 D_A(z)$, connecting the angular diameter and luminosity distances, can explain the Hubble tension and alter the evidence for dynamical dark energy in recent cosmological observations. We constrain five phenomenological parameterisations of DDR violation using Baryon Acoustic Oscillation measurements from the DESI survey calibrated with the sound horizon derived from \textit{Planck} Cosmic Microwave Background data and the Pantheon+ Type Ia supernova (SNIa) catalogue calibrated with the supernova absolute magnitude from S$H_0$ES. We find that two toy models can resolve the tension: a constant offset in the DDR (equivalent to a shift in the calibration of the SNIa data), $D_L(z)/D_A(z)\simeq 0.925(1+z)^2$, which leaves the hint for evolving dark energy unaffected; or a change in the power-law redshift-dependence of the DDR, restricted to $z\lesssim 1$, $D_L(z)/D_A(z)\simeq(1+z)^{1.866}$, together with a {\it constant} phantom dark energy equation of state $w\sim -1.155$. The Bayesian evidence slightly favours the latter model. Our phenomenological approach motivates the investigation of physical models of DDR violation as a novel way to explain the Hubble tension.

astro-ph.CO↗

arXiv2025

An overview of what current data can (and cannot yet) say about evolving dark energy

Recent measurements of Baryon Acoustic Oscillations (BAO) and distance moduli from Type Ia supernovae suggest a preference for Dynamical Dark Energy (DDE) scenarios characterized by a time-varying equation of state (EoS). This focused review assesses its robustness across independent measurements and surveys. Using the Chevallier-Polarski-Linder (CPL) parametrization to describe the evolution of the DE EoS, we analyze over 35 dataset combinations, incorporating Planck Cosmic Microwave Background (CMB) anisotropies, three independent Type Ia supernova (SN) catalogs (PantheonPlus, Union3, DESY5), BAO measurements from DESI and SDSS, and expansion rate measurements $H(z)$ inferred from the relative ages of massive, passively evolving galaxies at early cosmic times known as Cosmic Chronometers (CC). This review has two main objectives: first, to evaluate the statistical significance of the DDE preference across different dataset combinations, which incorporate varying sources of information. Specifically, we consider cases where only low-redshift probes are used in different combinations, others where individual low-redshift probes are analyzed together with CMB data, and finally, scenarios where high- and low-redshift probes are included in all possible independent combinations. Second, we provide a reader-friendly synthesis of what the latest cosmological and astrophysical probes can (and cannot yet) reveal about DDE. Overall, our findings highlight that combinations that \textit{simultaneously} include PantheonPlus SN and SDSS BAO significantly weaken the preference for DDE. However, intriguing hints supporting DDE emerge in combinations that do not include DESI-BAO measurements: SDSS-BAO combined with SN from Union3 and DESY5 (with and without CMB) support the preference for DDE.

astro-ph.CO↗

arXiv2025

Neutrino masses and mixing: Entering the era of subpercent precision

We perform an updated global analysis of the known and unknown parameters of the standard $3ν$ framework as of 2025. The known oscillation parameters include three mixing angles $(θ_{12},\,θ_{23},\,θ_{13})$ and two squared mass gaps, chosen as $δm^2=m^2_2-m^2_1>0$ and $Δm^2=m^2_3-{\textstyle\frac{1}{2}}(m^2_1+m^2_2)$, where $α=\mathrm{sign}(Δm^2)$ distinguishes normal ordering (NO, $α=+1$) from inverted ordering (IO, $α=-1$). With respect to our previous 2021 update, the combination of oscillation data leads to appreciably reduced uncertainties for $θ_{23}$, $θ_{13}$ and $|Δm^2|$. In particular, $|Δm^2|$ is the first $3ν$ parameter to enter the domain of subpercent precision (0.8\% at $1σ$). We underline some issues about systematics, that might affect this error estimate. Concerning oscillation unknowns, we find a relatively weak preference for NO versus IO (at $2.2σ$), for CP violation versus conservation in NO (1.3$σ$) and for the first $θ_{23}$ octant versus the second in NO ($1.1σ$). We discuss the status and qualitative prospects of the mass ordering hint in the plane $(δm^2,\,Δm^2_{ee})$, where $Δm^2_{ee}=|Δm^2|+{\textstyle\frac{1}{2}}α(\cos^2θ_{12}-\sin^2θ_{12})δm^2$, to be measured by the JUNO experiment with subpercent precision. We also discuss upper bounds on nonoscillation observables. We report $m_β<0.50$~eV and $m_{ββ}<0.086$~eV ($2σ$). Concerning the sum of neutrino masses $Σ$, we discuss representative combinations of data, with or without augmenting the $Λ$CDM model with extra parameters accounting for possible systematics or new physics. The resulting $2σ$ upper limits are roughly spread around the bound $Σ< 0.2$~eV within a factor of three. [Abridged]

hep-ph↗