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The Hubble tension between direct measurements of the expansion rate and the prediction of the $\Lambda$CDM cosmological model calibrated on the Cosmic Microwave Background (CMB), is a strong motivation to explore alternative cosmological models. A popular class of such models includes an additional component of dark energy relevant in the early Universe, which solves the Hubble tension. These Early Dark Energy (EDE) models however typically worsen the $S_8$ tension between measurements of weak gravitational lensing and the $\Lambda$CDM expectation. Here, we show how combining EDE with scale-dependent primordial non-Gaussianities (sPNG) can in principle solve both tensions at once. Such sPNG are related to non-trivial inflationary physics, and observationally affect the non-linear regime of structure formation while leaving the linear regime mostly untouched. Depending on the amplitude of the sPNG, such models can either yield back the $\Lambda$CDM expectation for the PS in the non-linear regime, and hence an $S_8$ parameter compatible with $\Lambda$CDM, or can even reconcile the value of $S_8$ from weak-lensing measurements with the CMB, while solving the Hubble tension in all cases. In such models, both tensions would then be entirely related to pre-CMB physics of the early Universe., Comment: 17 pages, 3 figures, 2 tables, comments welcome :)

We describe the vision, user interface, governing equations, and numerical methods that underpin new ocean modeling software called ``Oceananigans''. Oceananigans is being developed by the Climate Modeling Alliance as part of a larger project to build a trainable climate model with quantifiable uncertainty. We argue that Oceananigans status as a popular, capable modeling system realizes a vision for accelerating progress in Earth system modeling that balances demands for model accuracy and performance, needed for state-of-the-art science, against accessibility, which is needed to accelerate development. This vision combines three cooperative elements: (i) a relatively simple finite volume algorithm (ii) optimized for high-resolution simulations on GPUs which is (iii) exposed behind an expressive, high-level user interface (using the Julia programming language in our case). We offer evidence for the vision's potential by illustrating the creative potential of our user interface, showcasing Oceananigans physics with example simulations that range from simple classroom problems to a realistic global ocean simulation spanning all scales of oceanic fluid motion, and describing advances in parameterization, numerical methods, and computational efficiency.

We characterize exactness of a countable group $\Gamma$ in terms of invariant random equivalence relations (IREs) on $\Gamma$. Specifically, we show that $\Gamma$ is exact if and only if every weak limit of finite IREs is an amenable IRE. In particular, for exact groups this implies amenability of the restricted rerooting relation associated to the ideal Bernoulli Voronoi tessellation, the discrete analog of the ideal Poisson Voronoi tesselation., Comment: 20 pages

Sudden violations of the slow-roll regime during inflation, a natural prediction of many UV-complete inflationary models, give rise to sharp features in the primordial power spectrum. At large scales, these features provide a unique window into the physics of inflation, with constraints primarily derived from Cosmic Microwave Background observations of linearly evolved primordial fluctuations. However, on smaller scales, it is less clear whether primordial features would survive the late-time nonlinear cosmological evolution, as they are expected to be washed out by mode coupling. In this paper, we run dedicated N-body simulations to tackle this question. We demonstrate that, while oscillatory-like patterns are erased over time by nonlinearities, signatures of primordial sharp features can persist through the nonlinear regime of structure formation. Those take the form of a localised power enhancement or decrease in the matter power spectrum, whose amplitude and position can in principle be used to recover the scale of the primordial feature, and an oscillatory pattern in the halo mass function. While these findings highlight the power for constraining inflationary physics at small scales, they also show the challenges posed by potential degeneracies with other physical processes relevant in the nonlinear regime of structure formation such as non-cold dark matter candidates. Our results open new avenues for probing inflationary physics in large scale structures and galactic physics and emphasise the need for refined theoretical tools to robustly constrain primordial features., Comment: 17 pages, 9 figures, 3 tables

We investigate a cosmological model inspired by hybrid inflation, where two scalar fields representing dark energy (DE) and dark matter (DM) interact through a coupling that is proportional to the DE scalar field $1/\phi$. The strength of the coupling is governed solely by the initial condition of the scalar field, $\phi_i$, which parametrises deviations from the standard $\Lambda$CDM model. In this model, the scalar field tracks the behaviour of DM during matter-domination until it transitions to DE while the DM component decays quicker than standard CDM during matter-domination, and is therefore different from some interacting DM-DE models which behaves like phantom dark energy. Using \textit{Planck} 2018 CMB data, DESI BAO measurements and Pantheon+ supernova observations, we find that the model allows for an increase in $H_0$ that can help reduce the Hubble tension. In addition, we find that higher values of the coupling parameter are correlated with lower values of $\omega_m$, and a mild decrease of the weak-lensing parameter $S_8$, potentially relevant to address the $S_8$ tension. Bayesian model comparison, however, reveals inconclusive results for most datasets, unless S$H_0$ES data are included, in which case a moderate evidence in favour of the hybrid model is found., Comment: V1: 17 pages, 9 figures, 6 tables

We prove that measure-class-preserving non-amenable treeable equivalence relations of type III, meaning not preserving any equivalent $\sigma$-finite measure, are induced by free actions of non-abelian free groups of any given number of generators, including infinitely generated free groups, with the additional property that no ends of the induced Schreier graph are vanishing. This is done using a characterization of type III due to Hopf for transformations and Dang-Ngoc-Nghiem in general. This highlights the difference between the type III setting and the measure-preserving setting.

Early dark energy, an additional component of dark energy active in the decade of redshift before recombination, has emerged as one of the most effective models at reducing the $H_0$ tension between direct measurement of the Hubble parameter $H_0$ in the late-universe and the $\Lambda$CDM prediction when calibrated on Planck. However, it requires a slight increase in the dark matter density $\omega_{\rm cdm}$ and primordial tilt $n_s$ that worsens the $S_8$ tension between measurements of weak gravitational lensing at low redshifts and the Planck/$\Lambda$CDM prediction. Using a phenomenological fluid model, we investigate whether the inclusion of a drag term between dark matter and early dark energy can compensate for the effect of the increase in power at small-scales, such that both $H_0$ and $S_8$ tensions are simultaneously alleviated. We find that this works if the drag term is dynamically relevant in the post-recombination universe. However, a drag term active before or just around the time at which the early dark energy contribution to the energy density is maximum is significantly constrained due to its impact on the matter perturbations before recombination, and the subsequent modifications to the cosmic microwave background power spectra., Comment: 10 + 7 pages, 8 figures. Comments welcome!

We investigate the sensitivity of the 21cm power spectrum from cosmic dawn and the epoch of reionization to models of free-streaming dark radiation (parameterized through $N_{\rm eff}$) and interacting dark radiation-dark matter models (DM-DR). The latter models have gained attention for their potential in addressing recent cosmological tensions and structure formation challenges. We perform a Fisher matrix analysis under different assumptions regarding the astrophysical modeling, and forecast the sensitivity of HERA observations, combined with CMB data from Planck and the Simons Observatory (SO), to $N_{\rm eff}$ and DM-DR interaction modeled using the ETHOS framework assuming a constant scattering rate between the two components. Most importantly, we find that 21cm observations can improve the sensitivity to the DM-DR interaction rate by up to four order of magnitude compared to Planck and SO. Conversely, in the limit of low interaction rate (which asymptotically matches $N_{\rm eff}$), CMB data dominates the constraining power, but the inclusion of HERA data can provide a $\sim 20\%$ improvement in sensitivity over CMB data alone. Moreover, we find that HERA observations will be able to probe a region of the DM-DR interaction parameter space which is promising to explain the weak lensing amplitude `$S_8$' tension. Our results demonstrate the complementarity of 21cm and CMB data in exploring dark sector interactions., Comment: Version 2 - 25+15pages, 11 figures. Comments welcome!

The evolution of artificial intelligence (AI) presents an unprecedented opportunity for Historically Black Colleges and Universities (HBCUs) to lead in an era characterized by rapid technological advancement and societal transformation. This report explores the integral role HBCUs--with their history of academic excellence and commitment to inclusivity--can play in steering the AI revolution, ensuring that the Black community remains at the forefront of educational, economic, and social progress. Institutional leaders, faculty and instructors, and instructional support staff can benefit from the findings of this report, which is presented in the following sections: (1) Why AI Matters and the Unique Role of HBCUs in the AI Revolution; (2) An AI Policy and Practice Framework for Institutional Development; (3) AI and Curricular Innovation; (4) The Importance of Industry Partnerships and Student Development; and (5) AI at HBCUs: A Path to the Future. [This report was created in collaboration with the Thurgood Marshall College Fund.]

Cold New Early Dark Energy (Cold NEDE) addresses the Hubble tension through a triggered vacuum phase transition in the dark sector. In this paper, we constrain a phenomenological fluid model using recent cosmic microwave background likelihoods based on Planck NPIPE data alongside baryonic acoustic oscillations (BAO) and supernovae data from Pantheon+. Exploiting the enhanced constraining power of the datasets, we introduce and study an extended version of the NEDE fluid model in which the equation of state parameter $w_\mathrm{NEDE}$, characterizing the post-phase transition fluid, is allowed to evolve with non-vanishing derivatives ${d}w_\mathrm{NEDE}/d\ln a$ and ${d^2}w_\mathrm{NEDE}/{d}(\ln a)^2$. Our results indicate that data is compatible with a rather simple time dependence that could arise from a mixture of radiation and a stiff fluid. With the updated datasets, the base and extended models still show a significant reduction of the DMAP tension from $6.3 \sigma$ in $\Lambda$CDM down to $3.5\sigma$ with a small simultaneous reduction of the $S_8$ tension, slightly improving over recent findings for the axion-like early dark energy model. Finally, we also provide a first test of the model against new BAO data from the Dark Energy Spectroscopic Instrument (DESI) survey. Replacing the previous BAO constraints in our analysis with the new ones, the tension is further reduced to $2.6 \sigma$, reaffirming the Cold NEDE model as a promising solution to the Hubble tension., Comment: 21 pages, 5 figures; v2: added DESI constraints and profile likelihoods

The `cosmic calibration tension' is a $> 5\sigma$ discrepancy between the cosmological distance ladder built from baryonic acoustic oscillations (BAO) calibrated by the Planck/$\Lambda$CDM sound horizon ($r_s$) and Type Ia supernovae (SN1a) calibrated instead with the S$H_0$ES absolute magnitude, assuming the distance-duality relationship (DDR) holds. In this work, we emphasize the consequences of this tension beyond the value of the Hubble constant $H_0$, and the implications for physics beyond $\Lambda$CDM. Of utmost importance, it implies a larger physical matter density $\omega_m\equiv \Omega_m h^2$, as both the fractional matter density $\Omega_m$ and $h\equiv H_0/100$ km/s/Mpc are well constrained from late-time data. New physics in the pre-recombination era must thus be able to decrease $r_s$ while either reducing the value of $\Omega_m$, or increasing the value of $\omega_m$. Assuming a $\Lambda$CDM-like primordial power spectrum, this necessarily results in an increase in the clustering amplitude $\sigma_8$. Deviations from $\Lambda$CDM in the late-time expansion history cannot resolve the calibrator tension but can help relax the required shifts to the matter density and $\sigma_8$: it is in that sense that a combination of early and late-time new physics may help alleviate the tension. More precisely, models that modify the pre-recombination expansion history can accommodate the increase in $\omega_m$ without the need for additional modifications. It is those models which only affect recombination that require additional deviations at late-times to be successful. Hence, the `cosmic calibration tension' points either to a targeted modification of the pre-recombination expansion history, or to a broader change affecting multiple cosmic epochs., Comment: 12+6pages, 12 figures. Comments welcome!

Cosmological neutrino mass bounds are becoming increasingly stringent. The latest limit within $\Lambda$CDM from Planck 2018+ACT lensing+DESI is $\sum m_\nu < 0.072\,{\rm eV}$ at 95\% CL, very close to the minimum possible sum of neutrino masses ($\sum m_\nu > 0.06\,{\rm eV}$), hinting at vanishing or even ``negative'' cosmological neutrino masses. In this context, it is urgent to carefully evaluate the origin of these cosmological constraints. In this paper, we investigate the robustness of these results in three ways: i) we check the role of potential anomalies in Planck CMB and DESI BAO data; ii) we compare the results for frequentist and Bayesian techniques, as very close to physical boundaries subtleties in the derivation and interpretation of constraints can arise; iii) we investigate how deviations from $\Lambda$CDM, potentially alleviating these anomalies, can alter the constraints. From a profile likelihood analysis, we derive constraints in agreement at the $\sim 10\%$ level with Bayesian posteriors. We find that the weak preference for negative neutrino masses is mostly present for Planck 18 data, affected by the well-known `lensing anomaly'. It disappears when the new Planck 2020 HiLLiPoP is used, leading to significantly weaker constraints. Additionally, the pull towards negative masses in DESI data stems from the $z=0.7$ bin, which contains a BAO measurement in $\sim 3\sigma$ tension with Planck expectations. Without this bin, and in combination with HiLLiPoP, the bound relaxes to $\sum m_\nu < 0.11\,{\rm eV}$ at 95\% CL. The recent preference for dynamical dark energy alleviates this tension and further weakens the bound. As we are at the dawn of a neutrino mass discovery from cosmology, it will be very exciting to see if this trend is confirmed by future data., Comment: 17 pages + Appendices. Matches version accepted for publication in PRD

The Near-InfraRed Planet Searcher or NIRPS is a precision radial velocity spectrograph developed through collaborative efforts among laboratories in Switzerland, Canada, Brazil, France, Portugal and Spain. NIRPS extends to the 0.98-1.8 $\mu$m domain of the pioneering HARPS instrument at the La Silla 3.6-m telescope in Chile and it has achieved unparalleled precision, measuring stellar radial velocities in the infrared with accuracy better than 1 m/s. NIRPS can be used either stand-alone or simultaneously with HARPS. Commissioned in late 2022 and early 2023, NIRPS embarked on a 5-year Guaranteed Time Observation (GTO) program in April 2023, spanning 720 observing nights. This program focuses on planetary systems around M dwarfs, encompassing both the immediate solar vicinity and transit follow-ups, alongside transit and emission spectroscopy observations. We highlight NIRPS's current performances and the insights gained during its deployment at the telescope. The lessons learned and successes achieved contribute to the ongoing advancement of precision radial velocity measurements and high spectral fidelity, further solidifying NIRPS' role in the forefront of the field of exoplanets., Comment: Proceeding at the SPIE Astronomical Telescopes + Instrumentation conference [Yokohama,Japan; June 2024]

Motivated by the quantum description of gauge theories, we study the cosmological effects of relaxing the Hamiltonian and momentum constraints in general relativity and Gauss' law in electromagnetism. We show that the unconstrained theories have new source terms that mimic a pressureless dust and a charge density that only follows geodesics. The source terms may be the simplest explanation for dark matter and generically predict a charged component. We comment that discovery of such terms would rule out inflation and be a direct probe of the initial conditions of the universe., Comment: 6 pages

In 2020, Calderoni, Marker, Motto Ros and Shani asked what the Borel complexity of the isomorphism relation of Archimedean orders on $\mathbb{Q}^n$ is. We answer this question by proving that the isomorphism relation of Archimedean orders on $\mathbb{Z}^n$ is not hyperfinite when $n \geq 3$ and not treeable when $n \geq 4$. As a corollary, we get that the isomorphism relation of Archimedean orders on $\mathbb{Q}^n$ is not hyperfinite when $n \geq 3$ and not treeable when $n \geq 4$.

Quantum computers hold the promise of solving certain problems that lie beyond the reach of conventional computers. Establishing this capability, especially for impactful and meaningful problems, remains a central challenge. One such problem is the simulation of nonequilibrium dynamics of a magnetic spin system quenched through a quantum phase transition. State-of-the-art classical simulations demand resources that grow exponentially with system size. Here we show that superconducting quantum annealing processors can rapidly generate samples in close agreement with solutions of the Schr\"odinger equation. We demonstrate area-law scaling of entanglement in the model quench in two-, three- and infinite-dimensional spin glasses, supporting the observed stretched-exponential scaling of effort for classical approaches. We assess approximate methods based on tensor networks and neural networks and conclude that no known approach can achieve the same accuracy as the quantum annealer within a reasonable timeframe. Thus quantum annealers can answer questions of practical importance that classical computers cannot.

Frequentist profile likelihoods have seen a resurgence in cosmology, offering an alternative to Bayesian methods as they can circumvent the impact of prior-volume effects. This paper presents Procoli, a fast and accessible package to obtain profile likelihoods in cosmology, available on GitHub and PyPI. Procoli seamlessly integrates with MontePython, incorporating all its available data likelihoods, as well as any modified versions of CLASS. This paper provides a comprehensive overview of the Procoli code, detailing the simulated-annealing optimizer at its core and the sequential computation of the profile. An an example, we use the early dark energy model which is afflicted by prior-volume effects to illustrate the code's features. We validate its optimizer with mock data, and compare optimization techniques for both the global minimum and the profile. Procoli further enables splitting profiles into their component contributions from individual experiments, offering nuanced insights into the data and model. As a valuable addition to the cosmologist's toolkit, Procoli supplements existing Bayesian codes, contributing to more robust parameter constraints in cosmological studies., Comment: 14 pages (9 pages of text), 10 figures. For the associated code, please see https://github.com/tkarwal/procoli/

We find that combined Planck cosmic microwave background, baryon acoustic oscillations and supernovae data analyzed under $\Lambda$CDM are in 4.9$\sigma$ tension with eBOSS Ly$\alpha$ forest in inference of the linear matter power spectrum at wavenumber $\sim 1 h\,\mathrm{Mpc}^{-1}$ and redshift = 3. Model extensions can alleviate this tension: running in the tilt of the primordial power spectrum ($\alpha_\mathrm{s} \sim -0.01$); a fraction $\sim (1 - 5)\%$ of ultra-light axion dark matter (DM) with particle mass $\sim 10^{-25}$ eV or warm DM with mass $\sim 10$ eV. The new DESI survey, coupled with high-accuracy modeling, will help distinguish the source of this discrepancy., Comment: 16 pages, 9 figures. Minor changes to match published letter

Quantum Error Mitigation (QEM) presents a promising near-term approach to reduce error when estimating expectation values in quantum computing. Here, we introduce QEM techniques tailored for quantum annealing, using Zero-Noise Extrapolation (ZNE). We implement ZNE through zero-temperature extrapolation as well as energy-time rescaling. We conduct experimental investigations into the quantum critical dynamics of a transverse-field Ising spin chain, demonstrating the successful mitigation of thermal noise through both of these techniques. Moreover, we show that energy-time rescaling effectively mitigates control errors in the coherent regime where the effect of thermal noise is minimal. Our ZNE results agree with exact calculations of the coherent evolution over a range of annealing times that exceeds the coherent annealing range by almost an order of magnitude., Comment: 10 pages, 5 figures

Axion-like early dark energy (EDE) as an extension to $\Lambda$CDM has been proposed as a possible solution to the 'Hubble tension'. We revisit this model using a new cosmic microwave background (CMB) temperature and polarization likelihood constructed from the {\it Planck} NPIPE data release. In a Bayesian analysis, we find that the maximum fractional contribution of EDE to the total energy density is $f_{\rm EDE} < 0.061$ (without SH0ES) over the redshift range $z\in[10^3,10^4]$ and that the Hubble constant is constrained to lie within the range $ 66.9 < H_0 < 69.5$ km/s/Mpc (both at 95 \% C.L.). The data therefore favour a model close to $\Lambda$CDM, leaving a residual tension of $3.7\sigma$ with the SH$0$ES Cepheid-based measurement of $H_0$. A comparison with the likelihood profile shows that our conclusions are robust to prior-volume effects. Our new CMB likelihood provides no evidence in favour of a significant EDE component., Comment: 4 pages, 3 figures, comments welcome

The two-planet transiting system LHS 1140 has been extensively observed since its discovery in 2017, notably with $Spitzer$, HST, TESS, and ESPRESSO, placing strong constraints on the parameters of the M4.5 host star and its small temperate exoplanets, LHS 1140 b and c. Here, we reanalyse the ESPRESSO observations of LHS 1140 with the novel line-by-line framework designed to fully exploit the radial velocity content of a stellar spectrum while being resilient to outlier measurements. The improved radial velocities, combined with updated stellar parameters, consolidate our knowledge on the mass of LHS 1140 b (5.60$\pm$0.19 M$_{\oplus}$) and LHS 1140 c (1.91$\pm$0.06 M$_{\oplus}$) with unprecedented precision of 3%. Transits from $Spitzer$, HST, and TESS are jointly analysed for the first time, allowing us to refine the planetary radii of b (1.730$\pm$0.025 R$_{\oplus}$) and c (1.272$\pm$0.026 R$_{\oplus}$). Stellar abundance measurements of refractory elements (Fe, Mg and Si) obtained with NIRPS are used to constrain the internal structure of LHS 1140 b. This planet is unlikely to be a rocky super-Earth as previously reported, but rather a mini-Neptune with a $\sim$0.1% H/He envelope by mass or a water world with a water-mass fraction between 9 and 19% depending on the atmospheric composition and relative abundance of Fe and Mg. While the mini-Neptune case would not be habitable, a water-abundant LHS 1140 b potentially has habitable surface conditions according to 3D global climate models, suggesting liquid water at the substellar point for atmospheres with relatively low CO$_2$ concentration, from Earth-like to a few bars., Comment: 31 pages, 18 figures, accepted for publication in ApJL

Previous studies based on Bayesian methods have shown that the constraints on cosmological parameters from the Baryonic Oscillation Spectroscopic Survey (BOSS) full-shape data using the Effective Field Theory of Large Scale Structure (EFTofLSS) depend on the choice of prior on the EFT nuisance parameters. In this work, we explore this prior dependence by adopting a frequentist approach based on the profile likelihood method, which is inherently independent of priors, considering data from BOSS, eBOSS and Planck. We find that the priors on the EFT parameters in the Bayesian inference are informative and that prior volume effects are important. This is reflected in shifts of the posterior mean compared to the maximum likelihood estimate by up to 1.0 {\sigma} (1.6 {\sigma}) and in a widening of intervals informed from frequentist compared to Bayesian intervals by factors of up to 1.9 (1.6) for BOSS (eBOSS) in the baseline configuration, while the constraints from Planck are unchanged. Our frequentist confidence intervals give no indication of a tension between BOSS/eBOSS and Planck. However, we find that the profile likelihood prefers extreme values of the EFT parameters, highlighting the importance of combining Bayesian and frequentist approaches for a fully nuanced cosmological inference. We show that the improved statistical power of future data will reconcile the constraints from frequentist and Bayesian inference using the EFTofLSS., Comment: 20 pages, 8 figures, 6 tables

The SPT-3G 2018 TT/TE/EE cosmic microwave background (CMB) data set (temperature and polarization) is used to place constraints on an axion-like model of early dark energy (EDE). These data do not favor axion-like EDE and place an upper limit on the maximum fraction of the total energy density $f_{\rm EDE}< 0.172$ (at the 95% confidence level, CL). This is in contrast with ACT DR4 which gives $f_{\rm EDE}=0.150^{+0.050}_{-0.078}$. When combining CMB measurements with measurements of the baryon acoustic oscillations and luminosity distance to Type Ia supernovae, we show that the tension with the S$H_0$ES measurement of the Hubble parameter goes up from 2.6$\sigma$ with Planck to 2.9$\sigma$ with Planck+SPT-3G 2018. The additional inclusion of ACT DR4 data leads to a reduction of the tension to $1.6\sigma$, but the discrepancy between ACT DR4 and Planck+SPT-3G 2018 casts some doubt on the statistical consistency of this joint analysis. The importance of improved measurements of the CMB at both intermediate and small scales (in particular the shape of the damping tail) as well as the interplay between temperature and polarization measurements in constraining EDE are discussed. Upcoming ground-based measurements of the CMB will play a crucial role in determining whether EDE remains a viable model to address the Hubble tension., Comment: 15 pages, 10 figures, comments welcome!

In this work, we explore the possibility that Early Dark Energy (EDE) is dynamical in nature and study its effect on cosmological observables. We introduce a parameterization of the equation of state allowing for an equation of state $w$ differing considerably from cosmological constant (cc, $w={-1}$) and vary both the initial $w_i$ as well final $w_f$ equation of state of the EDE fluid. This idea is motivated by the fact that in many models of EDE, the scalar field may have some kinetic energy when it starts to behave like EDE before the CMB decoupling. We find that the present data have a mild preference for non-cc early dark energy $( w_i= -0.78)$ using Planck+BAO+Pantheon+S$H_0$ES data sets, leading to $\Delta \chi^2_{\rm min}$ improvement of -2.5 at the expense of one more parameter. However, $w_i$ is only weakly constrained, with $w_i < -0.56$ at $1\sigma$. We argue that allowing for $w_i\neq -1$ can play a role in decreasing the $\sigma_8$ parameter. Yet, in practice the decrease is only $\sim0.4\sigma$ and $\sigma_8$ is still larger than weak lensing measurements. We conclude that while promising, a dynamical EDE cannot resolve both $H_0$ and $\sigma_8$ tensions simultaneously., Comment: 8 figures, Comments are most welcome

We prove several results showing that every locally finite Borel graph whose large-scale geometry is "tree-like" induces a treeable equivalence relation. In particular, our hypotheses hold if each component of the original graph either has bounded tree-width or is quasi-isometric to a tree, answering a question of Tucker-Drob. In the latter case, we moreover show that there exists a Borel quasi-isometry to a Borel forest, under the additional assumption of (componentwise) bounded degree. We also extend these results on quasi-treeings to Borel proper metric spaces. In fact, our most general result shows treeability of countable Borel equivalence relations equipped with an abstract wallspace structure on each class obeying some local finiteness conditions, which we call a proper walling. The proof is based on the Stone duality between proper wallings and median graphs, i.e., CAT(0) cube complexes. Finally, we strengthen the conclusion of treeability in these results to hyperfiniteness in the case where the original graph has one (selected) end per component, generalizing the same result for trees due to Dougherty--Jackson--Kechris., Comment: 42 pages; added section 6.B on one selected end

We consider a model of early modified gravity (EMG) that was recently proposed as a candidate to resolve the Hubble tension. The model consists in a scalar field $\sigma$ with a non-minimal coupling (NMC) to the Ricci curvature of the form $F(\sigma) = M_{\mathrm{pl}}^2+\xi\sigma^2$ and an effective mass induced by a quartic potential $V(\sigma) = \lambda \sigma^4/4$. We present the first analyses of the EMG model in light of the latest ACT DR4 and SPT-3G data in combination with full Planck data, and find a $\gtrsim 2\sigma$ preference for a non-zero EMG contribution from a combination of primary CMB data alone, mostly driven by ACT DR4 data. This is different from popular 'Early Dark Energy' models, which are detected only when the high-$\ell$ information from Planck temperature is removed. We find that the NMC plays a key role in controlling the evolution of density perturbations that is favored by the data over the minimally coupled case. Including measurements of supernovae luminosity distance from Pantheon+, baryonic acoustic oscillations and growth factor from BOSS, and CMB lensing of Planck leaves the preference unaffected. In the EMG model, the tension with S$H_0$ES is alleviated from $\sim 6\sigma$ to $\sim 3\sigma$. Further adding S$H_0$ES data rise the detection of the EMG model above $5\sigma$., Comment: 25 pages, 9 figures, 5 tables. Added minor corrections. v2 matches the published JCAP version. Comments welcome!