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Correlations between galaxies and their supermassive black holes (SMBHs) have been observed, but the causal mechanisms remained unclear. The emerging field of causal inference now enables examining these relationships using observational data. This study, using advanced causal discovery techniques and a state-of-the-art dataset, reveals a causal link between galaxy properties and SMBH masses. In elliptical galaxies, bulge properties influence SMBH growth, while in spiral galaxies, SMBHs affect host galaxy properties, potentially through feedback in gas-rich environments. For spiral galaxies, SMBHs progressively quench star formation, whereas in elliptical galaxies, quenching is complete, and the causal connection has reversed. These findings support theoretical models of active galactic nuclei feedback regulating galaxy evolution and suggest further exploration of causal links in astrophysical and cosmological scaling relations., Comment: 34 pages, 20 figures, submitted for peer-review

Diffusion models have emerged as effective distribution estimators in vision, language, and reinforcement learning, but their use as priors in downstream tasks poses an intractable posterior inference problem. This paper studies amortized sampling of the posterior over data, $\mathbf{x}\sim p^{\rm post}(\mathbf{x})\propto p(\mathbf{x})r(\mathbf{x})$, in a model that consists of a diffusion generative model prior $p(\mathbf{x})$ and a black-box constraint or likelihood function $r(\mathbf{x})$. We state and prove the asymptotic correctness of a data-free learning objective, relative trajectory balance, for training a diffusion model that samples from this posterior, a problem that existing methods solve only approximately or in restricted cases. Relative trajectory balance arises from the generative flow network perspective on diffusion models, which allows the use of deep reinforcement learning techniques to improve mode coverage. Experiments illustrate the broad potential of unbiased inference of arbitrary posteriors under diffusion priors: in vision (classifier guidance), language (infilling under a discrete diffusion LLM), and multimodal data (text-to-image generation). Beyond generative modeling, we apply relative trajectory balance to the problem of continuous control with a score-based behavior prior, achieving state-of-the-art results on benchmarks in offline reinforcement learning., Comment: Code: https://github.com/GFNOrg/diffusion-finetuning

Proteins are essential for almost all biological processes and derive their diverse functions from complex 3D structures, which are in turn determined by their amino acid sequences. In this paper, we exploit the rich biological inductive bias of amino acid sequences and introduce FoldFlow-2, a novel sequence-conditioned SE(3)-equivariant flow matching model for protein structure generation. FoldFlow-2 presents substantial new architectural features over the previous FoldFlow family of models including a protein large language model to encode sequence, a new multi-modal fusion trunk that combines structure and sequence representations, and a geometric transformer based decoder. To increase diversity and novelty of generated samples -- crucial for de-novo drug design -- we train FoldFlow-2 at scale on a new dataset that is an order of magnitude larger than PDB datasets of prior works, containing both known proteins in PDB and high-quality synthetic structures achieved through filtering. We further demonstrate the ability to align FoldFlow-2 to arbitrary rewards, e.g. increasing secondary structures diversity, by introducing a Reinforced Finetuning (ReFT) objective. We empirically observe that FoldFlow-2 outperforms previous state-of-the-art protein structure-based generative models, improving over RFDiffusion in terms of unconditional generation across all metrics including designability, diversity, and novelty across all protein lengths, as well as exhibiting generalization on the task of equilibrium conformation sampling. Finally, we demonstrate that a fine-tuned FoldFlow-2 makes progress on challenging conditional design tasks such as designing scaffolds for the VHH nanobody., Comment: preprint

The process of cometary activity continues to pose a challenging question in cometary science. The activity modeling of comet 67P/Churyumov-Gerasimenko, based on data from the Rosetta mission, has significantly enhanced our comprehension of cometary activity. But thermophysical models have difficulties in simultaneously explaining the production rates of various gas species and dust. It has been suggested that different gas species might be responsible for the ejection of refractory material in distinct size ranges. This work focuses on investigating abundance and the ejection mechanisms of large ($\gtrsim$ 1 cm) aggregates from the comet nucleus. We aim to determine their properties and map the distribution of their source regions across the comet surface. This can place constraints on activity models for comets. We examined 189 images acquired at five epochs by the OSIRIS/NAC instrument. Our goal was to identify bright tracks produced by individual aggregates as they traversed the camera field of view. We generated synthetic images based on the output of dynamical simulations involving various types of aggregates. By comparing these synthetic images with the observations, we determine the characteristics of the simulated aggregates that most closely resembled the observations. We identified over 30000 tracks present in the OSIRIS images, derived constraints on the characteristics of the aggregates and mapped their origins on the nucleus surface. The aggregates have an average radius of $\simeq5$ cm, and a bulk density consistent with that of the comet's nucleus. Due to their size, gas drag exerts only a minor influence on their dynamical behavior, so an initial velocity is needed in order to bring them into the camera field of view. The source regions of these aggregates are predominantly located near the boundaries of distinct terrains on the surface., Comment: 19 pages, 15 figures. Accepted for publication in Astronomy & Astrophysics

We present the first $\Lambda$CDM cosmological analysis performed on a galaxy survey using marked power spectra. The marked power spectrum is the two-point function of a marked field, where galaxies are weighted by a function that depends on their local density. The presence of the mark leads these statistics to contain higher-order information of the original galaxy field, making them a good candidate to exploit the non-Gaussian information of a galaxy catalog. In this work we make use of \simbig, a forward modeling framework for galaxy clustering analyses, and perform simulation-based inference using normalizing flows to infer the posterior distribution of the $\Lambda$CDM cosmological parameters. We consider different mark configurations (ways to weight the galaxy field) and deploy them in the \simbig~pipeline to analyze the corresponding marked power spectra measured from a subset of the BOSS galaxy sample. We analyze the redshift-space mark power spectra decomposed in $\ell = 0, 2, 4$ multipoles and include scales up to the non-linear regime. Among the various mark configurations considered, the ones that give the most stringent cosmological constraints produce posterior median and $68\%$ confidence limits on the growth of structure parameters equal to $\Omega_m=0.273^{+0.040}_{-0.030}$ and $\sigma_8=0.777^{+0.077}_{-0.071}$. Compared to a perturbation theory analysis using the power spectrum of the same dataset, the \simbig~marked power spectra constraints on $\sigma_8$ are up to $1.2\times$ tighter, while no improvement is seen for the other cosmological parameters., Comment: 15 pages, 6 figures

Methods. We algorithmically tracked thousands of individual particles through four OSIRIS/NAC image sequences of 67P's near-nucleus coma. We then traced concentrated particle groups back to the nucleus surface, and estimated their potential source regions, size distributions, and projected dynamical parameters. Finally, we compared the observed activity to dust coma simulations. Results. We traced back 409 decimeter-sized particles to four suspected source regions. The regions strongly overlap and are mostly confined to the Khonsu-Atum-Anubis area. The activity may be linked to rugged terrain, and the erosion of fine dust and the ejection of large boulders may be mutually exclusive. Power-law indices fitted to the particle size--frequency distributions range from $3.4 \pm 0.3$ to $3.8 \pm 0.4$. Gas drag fits to the radial particle accelerations provide an estimate for the local gas production rates ($Q_\text{g} = 3.6 \cdot 10^{-5}$ kg s$^{-1}$ m$^{-2}$), which is several times higher than our model predictions based on purely insolation-driven water ice sublimation. Our observational results and our modeling results both reveal that our particles were likely ejected with substantial nonzero initial velocities of around 0.5$-$0.6 m s$^{-1}$. Conclusions. Our findings strongly suggest that the observed ejection of decimeter-sized particles cannot be explained by water ice sublimation and favorable illumination conditions alone. Instead, the local structures and compositions of the source regions likely play a major role. In line with current ejection models of decimeter-sized particles, we deem an overabundance of CO$_2$ ice and its sublimation to be the most probable driver. In addition, because of the significant initial velocities, we suspect the ejection events to be considerably more energetic than gradual liftoffs., Comment: 31 pages, 29 figures

Efficiently generating statistically independent samples from an unnormalized probability distribution, such as equilibrium samples of many-body systems, is a foundational problem in science. In this paper, we propose Iterated Denoising Energy Matching (iDEM), an iterative algorithm that uses a novel stochastic score matching objective leveraging solely the energy function and its gradient -- and no data samples -- to train a diffusion-based sampler. Specifically, iDEM alternates between (I) sampling regions of high model density from a diffusion-based sampler and (II) using these samples in our stochastic matching objective to further improve the sampler. iDEM is scalable to high dimensions as the inner matching objective, is simulation-free, and requires no MCMC samples. Moreover, by leveraging the fast mode mixing behavior of diffusion, iDEM smooths out the energy landscape enabling efficient exploration and learning of an amortized sampler. We evaluate iDEM on a suite of tasks ranging from standard synthetic energy functions to invariant $n$-body particle systems. We show that the proposed approach achieves state-of-the-art performance on all metrics and trains $2-5\times$ faster, which allows it to be the first method to train using energy on the challenging $55$-particle Lennard-Jones system., Comment: Published at ICML 2024. Code for iDEM is available at https://github.com/jarridrb/dem

We study the problem of training diffusion models to sample from a distribution with a given unnormalized density or energy function. We benchmark several diffusion-structured inference methods, including simulation-based variational approaches and off-policy methods (continuous generative flow networks). Our results shed light on the relative advantages of existing algorithms while bringing into question some claims from past work. We also propose a novel exploration strategy for off-policy methods, based on local search in the target space with the use of a replay buffer, and show that it improves the quality of samples on a variety of target distributions. Our code for the sampling methods and benchmarks studied is made public at https://github.com/GFNOrg/gfn-diffusion as a base for future work on diffusion models for amortized inference., Comment: 24 pages; changed title from v2; code: https://github.com/GFNOrg/gfn-diffusion

We propose a comprehensive sample-based method for assessing the quality of generative models. The proposed approach enables the estimation of the probability that two sets of samples are drawn from the same distribution, providing a statistically rigorous method for assessing the performance of a single generative model or the comparison of multiple competing models trained on the same dataset. This comparison can be conducted by dividing the space into non-overlapping regions and comparing the number of data samples in each region. The method only requires samples from the generative model and the test data. It is capable of functioning directly on high-dimensional data, obviating the need for dimensionality reduction. Significantly, the proposed method does not depend on assumptions regarding the density of the true distribution, and it does not rely on training or fitting any auxiliary models. Instead, it focuses on approximating the integral of the density (probability mass) across various sub-regions within the data space., Comment: 14 pages, 13 figures

This paper presents the Learning the Universe Implicit Likelihood Inference (LtU-ILI) pipeline, a codebase for rapid, user-friendly, and cutting-edge machine learning (ML) inference in astrophysics and cosmology. The pipeline includes software for implementing various neural architectures, training schemata, priors, and density estimators in a manner easily adaptable to any research workflow. It includes comprehensive validation metrics to assess posterior estimate coverage, enhancing the reliability of inferred results. Additionally, the pipeline is easily parallelizable and is designed for efficient exploration of modeling hyperparameters. To demonstrate its capabilities, we present real applications across a range of astrophysics and cosmology problems, such as: estimating galaxy cluster masses from X-ray photometry; inferring cosmology from matter power spectra and halo point clouds; characterizing progenitors in gravitational wave signals; capturing physical dust parameters from galaxy colors and luminosities; and establishing properties of semi-analytic models of galaxy formation. We also include exhaustive benchmarking and comparisons of all implemented methods as well as discussions about the challenges and pitfalls of ML inference in astronomical sciences. All code and examples are made publicly available at https://github.com/maho3/ltu-ili., Comment: 22 pages, 10 figures, accepted in the Open Journal of Astrophysics. Code available at https://github.com/maho3/ltu-ili

Extracting the non-Gaussian information of the cosmic large-scale structure (LSS) is vital in unlocking the full potential of the rich datasets from the upcoming stage-IV galaxy surveys. Galaxy skew spectra serve as efficient beyond-two-point statistics, encapsulating essential bispectrum information with computational efficiency akin to power spectrum analysis. This paper presents the first cosmological constraints from analyzing the full set of redshift-space galaxy skew spectra of the data from the SDSS-III BOSS, accessing cosmological information down to nonlinear scales. Employing the ${\rm S{\scriptsize IM}BIG}$ forward modeling framework and simulation-based inference via normalizing flows, we analyze the CMASS-SGC sub-sample, which constitute approximately 10\% of the full BOSS data. Analyzing the scales up to $k_{\rm max}=0.5 \, {\rm Mpc}^{-1}h$, we find that the skew spectra improve the constraints on $\Omega_{\rm m}, \Omega_{\rm b}, h$, and $n_s$ by 34\%, 35\%, 18\%, 10\%, respectively, compared to constraints from previous ${\rm S{\scriptsize IM}BIG}$ power spectrum multipoles analysis, yielding $\Omega_{\rm m}=0.288^{+0.024}_{-0.034}$, $\Omega_{\rm b}= 0.043^{+0.005}_{-0.007}$, $h=0.759^{+0.104}_{-0.050}$, $n_{\rm s} = 0.918^{+0.041}_{-0.090}$ (at 68\% confidence limit). On the other hand, the constraints on $\sigma_8$ are weaker than from the power spectrum. Including the Big Bang Nucleosynthesis (BBN) prior on baryon density reduces the uncertainty on the Hubble parameter further, achieving $h=0.750^{+0.034}_{-0.032}$, which is a 38\% improvement over the constraint from the power spectrum with the same prior. Compared to the ${\rm S{\scriptsize IM}BIG}$ bispectrum (monopole) analysis, skew spectra offer comparable constraints on larger scales ($k_{\rm max}<0.3\, {\rm Mpc}^{-1}h$) for most parameters except for $\sigma_8$., Comment: 23 pages, 12 figures, 2 tables

We present a performant, general-purpose gradient-guided nested sampling algorithm, ${\tt GGNS}$, combining the state of the art in differentiable programming, Hamiltonian slice sampling, clustering, mode separation, dynamic nested sampling, and parallelization. This unique combination allows ${\tt GGNS}$ to scale well with dimensionality and perform competitively on a variety of synthetic and real-world problems. We also show the potential of combining nested sampling with generative flow networks to obtain large amounts of high-quality samples from the posterior distribution. This combination leads to faster mode discovery and more accurate estimates of the partition function., Comment: 10 pages, 5 figures. Code available at https://github.com/Pablo-Lemos/GGNS

Definitive evidence that globular clusters (GCs) host intermediate-mass black holes (IMBHs) is elusive. Machine learning (ML) models trained on GC simulations can in principle predict IMBH host candidates based on observable features. This approach has two limitations: first, an accurate ML model is expected to be a black box due to complexity; second, despite our efforts to realistically simulate GCs, the simulation physics or initial conditions may fail to fully reflect reality. Therefore our training data may be biased, leading to a failure in generalization on observational data. Both the first issue -- explainability/interpretability -- and the second -- out of distribution generalization and fairness -- are active areas of research in ML. Here we employ techniques from these fields to address them: we use the anchors method to explain an XGBoost classifier; we also independently train a natively interpretable model using Certifiably Optimal RulE ListS (CORELS). The resulting model has a clear physical meaning, but loses some performance with respect to XGBoost. We evaluate potential candidates in real data based not only on classifier predictions but also on their similarity to the training data, measured by the likelihood of a kernel density estimation model. This measures the realism of our simulated data and mitigates the risk that our models may produce biased predictions by working in extrapolation. We apply our classifiers to real GCs, obtaining a predicted classification, a measure of the confidence of the prediction, an out-of-distribution flag, a local rule explaining the prediction of XGBoost and a global rule from CORELS., Comment: ApJ accepted

The non-Gaussisan spatial distribution of galaxies traces the large-scale structure of the Universe and therefore constitutes a prime observable to constrain cosmological parameters. We conduct Bayesian inference of the $\Lambda$CDM parameters $\Omega_m$, $\Omega_b$, $h$, $n_s$, and $\sigma_8$ from the BOSS CMASS galaxy sample by combining the wavelet scattering transform (WST) with a simulation-based inference approach enabled by the ${\rm S{\scriptsize IM}BIG}$ forward model. We design a set of reduced WST statistics that leverage symmetries of redshift-space data. Posterior distributions are estimated with a conditional normalizing flow trained on 20,000 simulated ${\rm S{\scriptsize IM}BIG}$ galaxy catalogs with survey realism. We assess the accuracy of the posterior estimates using simulation-based calibration and quantify generalization and robustness to the change of forward model using a suite of 2,000 test simulations. When probing scales down to $k_{\rm max}=0.5~h/\text{Mpc}$, we are able to derive accurate posterior estimates that are robust to the change of forward model for all parameters, except $\sigma_8$. We mitigate the robustness issues with $\sigma_8$ by removing the WST coefficients that probe scales smaller than $k \sim 0.3~h/\text{Mpc}$. Applied to the BOSS CMASS sample, our WST analysis yields seemingly improved constraints obtained from a standard PT-based power spectrum analysis with $k_{\rm max}=0.25~h/\text{Mpc}$ for all parameters except $h$. However, we still raise concerns on these results. The observational predictions significantly vary across different normalizing flow architectures, which we interpret as a form of model misspecification. This highlights a key challenge for forward modeling approaches when using summary statistics that are sensitive to detailed model-specific or observational imprints on galaxy clustering., Comment: 11+5 pages, 8+2 figures, published in Physical Review D

We present the first simulation-based inference (SBI) of cosmological parameters from field-level analysis of galaxy clustering. Standard galaxy clustering analyses rely on analyzing summary statistics, such as the power spectrum, $P_\ell$, with analytic models based on perturbation theory. Consequently, they do not fully exploit the non-linear and non-Gaussian features of the galaxy distribution. To address these limitations, we use the {\sc SimBIG} forward modelling framework to perform SBI using normalizing flows. We apply SimBIG to a subset of the BOSS CMASS galaxy sample using a convolutional neural network with stochastic weight averaging to perform massive data compression of the galaxy field. We infer constraints on $\Omega_m = 0.267^{+0.033}_{-0.029}$ and $\sigma_8=0.762^{+0.036}_{-0.035}$. While our constraints on $\Omega_m$ are in-line with standard $P_\ell$ analyses, those on $\sigma_8$ are $2.65\times$ tighter. Our analysis also provides constraints on the Hubble constant $H_0=64.5 \pm 3.8 \ {\rm km / s / Mpc}$ from galaxy clustering alone. This higher constraining power comes from additional non-Gaussian cosmological information, inaccessible with $P_\ell$. We demonstrate the robustness of our analysis by showcasing our ability to infer unbiased cosmological constraints from a series of test simulations that are constructed using different forward models than the one used in our training dataset. This work not only presents competitive cosmological constraints but also introduces novel methods for leveraging additional cosmological information in upcoming galaxy surveys like DESI, PFS, and Euclid., Comment: 14 pages, 4 figures. A previous version of the paper was published in the ICML 2023 Workshop on Machine Learning for Astrophysics

The 3D distribution of galaxies encodes detailed cosmological information on the expansion and growth history of the Universe. We present the first cosmological constraints that exploit non-Gaussian cosmological information on non-linear scales from galaxy clustering, inaccessible with current standard analyses. We analyze a subset of the BOSS galaxy survey using ${\rm S{\scriptsize IM}BIG}$, a new framework for cosmological inference that leverages high-fidelity simulations and deep generative models. We use two clustering statistics beyond the standard power spectrum: the bispectrum and a convolutional neural network based summary of the galaxy field. We infer constraints on $\Lambda$CDM parameters, $\Omega_b$, $h$, $n_s$, $\Omega_m$, and $\sigma_8$, that are 1.6, 1.5, 1.7, 1.2, and 2.3$\times$ tighter than power spectrum analyses. With this increased precision, we derive constraints on the Hubble constant, $H_0$, and $S_8 = \sigma_8 \sqrt{\Omega_m/0.3}$ that are competitive with other cosmological probes, even with a sample that only spans 10% of the full BOSS volume. Our $H_0$ constraints, imposing the Big Bang Nucleosynthesis prior on the baryon density, are consistent with the early time constraints from the cosmic microwave background (CMB). Meanwhile, our $S_8$ constraints are consistent with weak lensing experiments and similarly lie below CMB constraints. Lastly, we present forecasts to show that future work extending ${\rm S{\scriptsize IM}BIG}$ to upcoming spectroscopic galaxy surveys (DESI, PFS, Euclid) will produce leading $H_0$ and $S_8$ constraints that bridge the gap between early and late time measurements and shed light on current cosmic tensions., Comment: 13 pages, 5 figures, submitted to Nature Astronomy, comments welcome

We present the first cosmological constraints from analyzing higher-order galaxy clustering on non-linear scales. We use ${\rm S{\scriptsize IM}BIG}$, a forward modeling framework for galaxy clustering analyses that employs simulation-based inference to perform highly efficient cosmological inference using normalizing flows. It leverages the predictive power of high-fidelity simulations and robustly extracts cosmological information from regimes inaccessible with current standard analyses. In this work, we apply ${\rm S{\scriptsize IM}BIG}$ to a subset of the BOSS galaxy sample and analyze the redshift-space bispectrum monopole, $B_0(k_1, k_2, k_3)$, to $k_{\rm max}=0.5\,h/{\rm Mpc}$. We achieve 1$\sigma$ constraints of $\Omega_m=0.293^{+0.027}_{-0.027}$ and $\sigma_8= 0.783^{+0.040}_{-0.038}$, which are more than 1.2 and 2.4$\times$ tighter than constraints from standard power spectrum analyses of the same dataset. We also derive 1.4, 1.4, 1.7$\times$ tighter constraints on $\Omega_b$, $h$, $n_s$. This improvement comes from additional cosmological information in higher-order clustering on non-linear scales and, for $\sigma_8$, is equivalent to the gain expected from a standard analysis on a $\sim$4$\times$ larger galaxy sample. Even with our BOSS subsample, which only spans 10% of the full BOSS volume, we derive competitive constraints on the growth of structure: $S_8 = 0.774^{+0.056}_{-0.053}$. Our constraint is consistent with results from both cosmic microwave background and weak lensing. Combined with a $\omega_b$ prior from Big Bang Nucleosynthesis, we also derive a constraint on $H_0=67.6^{+2.2}_{-1.8}\,{\rm km\,s^{-1}\,Mpc^{-1}}$ that is consistent with early universe constraints., Comment: 13 pages, 7 figures, submitted to PRD, comments welcome

Sampling diverse, thermodynamically feasible molecular conformations plays a crucial role in predicting properties of a molecule. In this paper we propose to use GFlowNet for sampling conformations of small molecules from the Boltzmann distribution, as determined by the molecule's energy. The proposed approach can be used in combination with energy estimation methods of different fidelity and discovers a diverse set of low-energy conformations for highly flexible drug-like molecules. We demonstrate that GFlowNet can reproduce molecular potential energy surfaces by sampling proportionally to the Boltzmann distribution.

The cosmic microwave background (CMB) offers a unique window into the early universe, providing insights into cosmological parameters like the Hubble constant. Recent precise measurements of the CMB by experiments like Planck seem to point to a lower value for the Hubble constant compared to some other measurements like those from Type Ia supernovae. This discrepancy, known as the Hubble tension, currently lacks a definitive explanation. In this chapter, we provide an overview of how the Hubble constant is determined from detailed measurements of the CMB power spectrum. We explain the physics underlying key features of the CMB spectrum and their connection to cosmological parameters. We then examine the consistency of Planck's Hubble constant determination, both internally within the data itself and externally with other astrophysical probes. While largely consistent, some anomalies like the lensing amplitude parameter $A_L$ remain unresolved. We also explore various theoretical extensions to the standard ${\Lambda}$CDM cosmological model and assess their potential to resolve the Hubble tension. No clear resolution emerges, indicating significant tensions remain between early and late universe probes within simple extensions to ${\Lambda}$CDM. Upcoming CMB experiments promise improved precision and should provide further insights into this cosmic conundrum. A coherent picture bridging measurements across cosmic time remains an open challenge at the forefront of modern cosmology., Comment: Invited chapter for the edited book "Hubble Constant Tension" (Eds. E. Di Valentino and D. Brout, Springer Singapore, expected in 2024)

Reconstructing the initial conditions of the universe is a key problem in cosmology. Methods based on simulating the forward evolution of the universe have provided a way to infer initial conditions consistent with present-day observations. However, due to the high complexity of the inference problem, these methods either fail to sample a distribution of possible initial density fields or require significant approximations in the simulation model to be tractable, potentially leading to biased results. In this work, we propose the use of score-based generative models to sample realizations of the early universe given present-day observations. We infer the initial density field of full high-resolution dark matter N-body simulations from the present-day density field and verify the quality of produced samples compared to the ground truth based on summary statistics. The proposed method is capable of providing plausible realizations of the early universe density field from the initial conditions posterior distribution marginalized over cosmological parameters and can sample orders of magnitude faster than current state-of-the-art methods., Comment: 8 pages, 7 figures

The CMB is a powerful probe of early-universe physics but is only observed after passing through large-scale structure, which changes the observed spectra in important model-dependent ways. This is of particular concern given recent claims of significant discrepancies with low redshift data sets when a standard $\Lambda$CDM model is assumed. By using empirical measurements of the CMB lensing reconstruction, combined with weak priors on the smoothness of the lensing spectrum, foregrounds, and shape of any additional integrated Sachs-Wolfe effect, we show how the early-universe parameters can be constrained from CMB observations almost independently of the late-time evolution. This provides a way to test new models for early-universe physics, and measure early-universe parameters, independently of late-time cosmology. Using the empirical measurement of lensing keeps the size of the effect of late-time modelling uncertainty under control, leading to only modest increases in error bars of most early-universe parameters compared to assuming a full evolution model. We provide robust constraints on early-$\Lambda$CDM model parameters using the latest Planck PR4 data and show that with future data marginalizing over a single lensing amplitude parameter is sufficient to remove sensitivity to late-time cosmological model only if the spectral shape matches predictions., Comment: 9 pages, 5 figures

Parameter inference, i.e. inferring the posterior distribution of the parameters of a statistical model given some data, is a central problem to many scientific disciplines. Generative models can be used as an alternative to Markov Chain Monte Carlo methods for conducting posterior inference, both in likelihood-based and simulation-based problems. However, assessing the accuracy of posteriors encoded in generative models is not straightforward. In this paper, we introduce `Tests of Accuracy with Random Points' (TARP) coverage testing as a method to estimate coverage probabilities of generative posterior estimators. Our method differs from previously-existing coverage-based methods, which require posterior evaluations. We prove that our approach is necessary and sufficient to show that a posterior estimator is accurate. We demonstrate the method on a variety of synthetic examples, and show that TARP can be used to test the results of posterior inference analyses in high-dimensional spaces. We also show that our method can detect inaccurate inferences in cases where existing methods fail., Comment: 15 pages, Accepted at ICML 2023

Generative flow networks (GFlowNets) are amortized variational inference algorithms that are trained to sample from unnormalized target distributions over compositional objects. A key limitation of GFlowNets until this time has been that they are restricted to discrete spaces. We present a theory for generalized GFlowNets, which encompasses both existing discrete GFlowNets and ones with continuous or hybrid state spaces, and perform experiments with two goals in mind. First, we illustrate critical points of the theory and the importance of various assumptions. Second, we empirically demonstrate how observations about discrete GFlowNets transfer to the continuous case and show strong results compared to non-GFlowNet baselines on several previously studied tasks. This work greatly widens the perspectives for the application of GFlowNets in probabilistic inference and various modeling settings., Comment: ICML 2023; 32 pages; code: https://github.com/saleml/continuous-gfn

We present the first-ever cosmological constraints from a simulation-based inference (SBI) analysis of galaxy clustering from the new ${\rm S{\scriptsize IM}BIG}$ forward modeling framework. ${\rm S{\scriptsize IM}BIG}$ leverages the predictive power of high-fidelity simulations and provides an inference framework that can extract cosmological information on small non-linear scales, inaccessible with standard analyses. In this work, we apply ${\rm S{\scriptsize IM}BIG}$ to the BOSS CMASS galaxy sample and analyze the power spectrum, $P_\ell(k)$, to $k_{\rm max}=0.5\,h/{\rm Mpc}$. We construct 20,000 simulated galaxy samples using our forward model, which is based on high-resolution ${\rm Q{\scriptsize UIJOTE}}$ $N$-body simulations and includes detailed survey realism for a more complete treatment of observational systematics. We then conduct SBI by training normalizing flows using the simulated samples and infer the posterior distribution of $\Lambda$CDM cosmological parameters: $\Omega_m, \Omega_b, h, n_s, \sigma_8$. We derive significant constraints on $\Omega_m$ and $\sigma_8$, which are consistent with previous works. Our constraints on $\sigma_8$ are $27\%$ more precise than standard analyses. This improvement is equivalent to the statistical gain expected from analyzing a galaxy sample that is $\sim60\%$ larger than CMASS with standard methods. It results from additional cosmological information on non-linear scales beyond the limit of current analytic models, $k > 0.25\,h/{\rm Mpc}$. While we focus on $P_\ell$ in this work for validation and comparison to the literature, ${\rm S{\scriptsize IM}BIG}$ provides a framework for analyzing galaxy clustering using any summary statistic. We expect further improvements on cosmological constraints from subsequent ${\rm S{\scriptsize IM}BIG}$ analyses of summary statistics beyond $P_\ell$., Comment: 9 pages, 5 figures

Simulation-Based Inference of Galaxies (${\rm S{\scriptsize IM}BIG}$) is a forward modeling framework for analyzing galaxy clustering using simulation-based inference. In this work, we present the ${\rm S{\scriptsize IM}BIG}$ forward model, which is designed to match the observed SDSS-III BOSS CMASS galaxy sample. The forward model is based on high-resolution ${\rm Q{\scriptsize UIJOTE}}$ $N$-body simulations and a flexible halo occupation model. It includes full survey realism and models observational systematics such as angular masking and fiber collisions. We present the "mock challenge" for validating the accuracy of posteriors inferred from ${\rm S{\scriptsize IM}BIG}$ using a suite of 1,500 test simulations constructed using forward models with a different $N$-body simulation, halo finder, and halo occupation prescription. As a demonstration of ${\rm S{\scriptsize IM}BIG}$, we analyze the power spectrum multipoles out to $k_{\rm max} = 0.5\,h/{\rm Mpc}$ and infer the posterior of $\Lambda$CDM cosmological and halo occupation parameters. Based on the mock challenge, we find that our constraints on $\Omega_m$ and $\sigma_8$ are unbiased, but conservative. Hence, the mock challenge demonstrates that ${\rm S{\scriptsize IM}BIG}$ provides a robust framework for inferring cosmological parameters from galaxy clustering on non-linear scales and a complete framework for handling observational systematics. In subsequent work, we will use ${\rm S{\scriptsize IM}BIG}$ to analyze summary statistics beyond the power spectrum including the bispectrum, marked power spectrum, skew spectrum, wavelet statistics, and field-level statistics., Comment: 28 pages, 6 figures

When Type Ia supernovae are used to infer cosmological parameters, their luminosities are compared to those from a homogeneous cosmology. In this note we propose a test to examine to what degree SN Ia have been observed on lines of sight where the average matter density is \textit{not} representative of the homogeneous background. We apply our test to the Pantheon SN Ia compilation, and find two redshift bins which indicate a moderate bias to over-density at $\sim 2\sigma$. We modify the Tripp estimator to explicitly de-lens SN Ia magnitudes, and show that this reduces scatter of Hubble diagram residuals. Using our revised Tripp estimator, the effect on cosmological parameters from Pantheon in $\Lambda$CDM is however small with a change in mean value from $\Omega_{\rm m} = 0.317 \pm 0.027$ (baseline) to $\Omega_{\rm m} = 0.312 \pm 0.025$ (de-lensed). For the Flat $w$CDM case it is $\Omega_{\rm m} = 0.332 \pm 0.049$ and $w = -1.16 \pm 0.16$ (baseline) versus $\Omega_{\rm m} = 0.316 \pm 0.048$ and $w = -1.12 \pm 0.15$ (de-lensed). We note that the effect of lensing on cosmological parameters may be larger for future high-z surveys., Comment: 4 pages, 3 figures. Accepted by MNRAS

When performing cosmological inference, standard analyses of the Lyman-$\alpha$ (Ly$\alpha$) three-dimensional correlation functions only consider the information carried by the distinct peak produced by baryon acoustic oscillations (BAO). In this work, we address whether this compression is sufficient to capture all the relevant cosmological information carried by these functions. We do this by performing a direct fit to the full shape, including all physical scales without compression, of synthetic Ly$\alpha$ auto-correlation functions and cross-correlations with quasars at effective redshift $z_{\rm{eff}}=2.3$, assuming a DESI-like survey, and providing a comparison to the classic method applied to the same dataset. Our approach leads to a $3.5\%$ constraint on the matter density $\Omega_{\rm{M}}$, which is about three to four times better than what BAO alone can probe. The growth term $f \sigma_{8} (z_{\rm{eff}})$ is constrained to the $10\%$ level, and the spectral index $n_{\rm{s}}$ to $\sim 3-4\%$. We demonstrate that the extra information resulting from our `direct fit' approach, except for the $n_{\rm{s}}$ constraint, can be traced back to the Alcock-Paczy\'nski effect and redshift space distortion information., Comment: Matches version published in MNRAS

Cosmological experiments often employ Bayesian workflows to derive constraints on cosmological and astrophysical parameters from their data. It has been shown that these constraints can be combined across different probes such as Planck and the Dark Energy Survey and that this can be a valuable exercise to improve our understanding of the universe and quantify tension between multiple experiments. However, these experiments are typically plagued by differing systematics, instrumental effects and contaminating signals, which we collectively refer to as `nuisance' components, that have to be modelled alongside target signals of interest. This leads to high dimensional parameter spaces, especially when combining data sets, with > 20 dimensions of which only around 5 correspond to key physical quantities. We present a means by which to combine constraints from different data sets in a computationally efficient manner by generating rapid, reusable and reliable marginal probability density estimators, giving us access to nuisance-free likelihoods. This is possible through the unique combination of nested sampling, which gives us access to Bayesian evidences, and the marginal Bayesian statistics code MARGARINE. Our method is lossless in the signal parameters, resulting in the same posterior distributions as would be found from a full nested sampling run over all nuisance parameters, and typically quicker than evaluating full likelihoods. We demonstrate our approach by applying it to the combination of posteriors from the Dark Energy Survey and Planck., Comment: Published in Phys. Sci. Forum 2022, 5(1), 1; https://doi.org/10.3390/psf2022005001

Simulation-based inference (SBI) is rapidly establishing itself as a standard machine learning technique for analyzing data in cosmological surveys. Despite continual improvements to the quality of density estimation by learned models, applications of such techniques to real data are entirely reliant on the generalization power of neural networks far outside the training distribution, which is mostly unconstrained. Due to the imperfections in scientist-created simulations, and the large computational expense of generating all possible parameter combinations, SBI methods in cosmology are vulnerable to such generalization issues. Here, we discuss the effects of both issues, and show how using a Bayesian neural network framework for training SBI can mitigate biases, and result in more reliable inference outside the training set. We introduce cosmoSWAG, the first application of Stochastic Weight Averaging to cosmology, and apply it to SBI trained for inference on the cosmic microwave background., Comment: 5 pages, 3 figures. Preliminary version accepted at the ML4Astro Machine Learning for Astrophysics Workshop at the Thirty-ninth International Conference on Machine Learning (ICML 2022). Final version published at Machine Learning: Science and Technology

We present an implicit likelihood approach to quantifying cosmological information over discrete catalogue data, assembled as graphs. To do so, we explore cosmological parameter constraints using mock dark matter halo catalogues. We employ Information Maximising Neural Networks (IMNNs) to quantify Fisher information extraction as a function of graph representation. We a) demonstrate the high sensitivity of modular graph structure to the underlying cosmology in the noise-free limit, b) show that graph neural network summaries automatically combine mass and clustering information through comparisons to traditional statistics, c) demonstrate that networks can still extract information when catalogues are subject to noisy survey cuts, and d) illustrate how nonlinear IMNN summaries can be used as asymptotically optimal compressed statistics for Bayesian simulation-based inference. We reduce the area of joint $\Omega_m, \sigma_8$ parameter constraints with small ($\sim$100 object) halo catalogues by a factor of 42 over the two-point correlation function, and demonstrate that the networks automatically combine mass and clustering information. This work utilises a new IMNN implementation over graph data in Jax, which can take advantage of either numerical or auto-differentiability. We also show that graph IMNNs successfully compress simulations away from the fiducial model at which the network is fitted, indicating a promising alternative to n-point statistics in catalogue simulation-based analyses., Comment: 16 pages, 10 figures. Accepted to the Open Journal of Astrophysics. We provide code and a tutorial for the analysis and relevant software at https://github.com/tlmakinen/cosmicGraphs

Marked power spectra are two-point statistics of a marked field obtained by weighting each location with a function that depends on the local density around that point. We consider marked power spectra of the galaxy field in redshift space that up-weight low density regions, and perform a Fisher matrix analysis to assess the information content of this type of statistics using the Molino mock catalogs built upon the Quijote simulations. We identify four different ways to up-weight the galaxy field, and compare the Fisher information contained in their marked power spectra to the one of the standard galaxy power spectrum, when considering monopole and quadrupole of each statistic. Our results show that each of the four marked power spectra can tighten the standard power spectrum constraints on the cosmological parameters $\Omega_{\rm m}$, $\Omega_{\rm b}$, $h$, $n_s$, $M_\nu$ by $15-25\%$ and on $\sigma_8$ by a factor of 2. The same analysis performed by combining the standard and four marked power spectra shows a substantial improvement compared to the power spectrum constraints that is equal to a factor of 6 for $\sigma_8$ and $2.5-3$ for the other parameters. Our constraints may be conservative, since the galaxy number density in the Molino catalogs is much lower than the ones in future galaxy surveys, which will allow them to probe lower density regions of the large-scale structure., Comment: 19 pages, 12 figures

Bayesian analysis has become an indispensable tool across many different cosmological fields including the study of gravitational waves, the Cosmic Microwave Background and the 21-cm signal from the Cosmic Dawn among other phenomena. The method provides a way to fit complex models to data describing key cosmological and astrophysical signals and a whole host of contaminating signals and instrumental effects modelled with `nuisance parameters'. In this paper, we summarise a method that uses Masked Autoregressive Flows and Kernel Density Estimators to learn marginal posterior densities corresponding to core science parameters. We find that the marginal or 'nuisance-free' posteriors and the associated likelihoods have an abundance of applications including; the calculation of previously intractable marginal Kullback-Leibler divergences and marginal Bayesian Model Dimensionalities, likelihood emulation and prior emulation. We demonstrate each application using toy examples, examples from the field of 21-cm cosmology and samples from the Dark Energy Survey. We discuss how marginal summary statistics like the Kullback-Leibler divergences and Bayesian Model Dimensionalities can be used to examine the constraining power of different experiments and how we can perform efficient joint analysis by taking advantage of marginal prior and likelihood emulators. We package our multipurpose code up in the pip-installable code margarine for use in the wider scientific community., Comment: Accepted for MNRAS

The true posterior distribution of a Bayesian neural network is massively multimodal. Whilst most of these modes are functionally equivalent, we demonstrate that there remains a level of real multimodality that manifests in even the simplest neural network setups. It is only by fully marginalising over all posterior modes, using appropriate Bayesian sampling tools, that we can capture the split personalities of the network. The ability of a network trained in this manner to reason between multiple candidate solutions dramatically improves the generalisability of the model, a feature we contend is not consistently captured by alternative approaches to the training of Bayesian neural networks. We provide a concise minimal example of this, which can provide lessons and a future path forward for correctly utilising the explainability and interpretability of Bayesian neural networks., Comment: 10 pages, 5 figures

Extracting non-Gaussian information from the non-linear regime of structure formation is key to fully exploiting the rich data from upcoming cosmological surveys probing the large-scale structure of the universe. However, due to theoretical and computational complexities, this remains one of the main challenges in analyzing observational data. We present a set of summary statistics for cosmological matter fields based on 3D wavelets to tackle this challenge. These statistics are computed as the spatial average of the complex modulus of the 3D wavelet transform raised to a power $q$ and are therefore known as invariant wavelet moments. The 3D wavelets are constructed to be radially band-limited and separable on a spherical polar grid and come in three types: isotropic, oriented, and harmonic. In the Fisher forecast framework, we evaluate the performance of these summary statistics on matter fields from the Quijote suite, where they are shown to reach state-of-the-art parameter constraints on the base $\Lambda$CDM parameters, as well as the sum of neutrino masses. We show that we can improve constraints by a factor 5 to 10 in all parameters with respect to the power spectrum baseline.

Using data from the Pantheon SN Ia compilation and the Sloan Digital Sky Survey (SDSS), we propose an estimator for weak lensing convergence incorporating positional and photometric data of foreground galaxies. The correlation between this and the Hubble diagram residuals of the supernovae has $3.6\sigma$ significance, and is consistent with weak lensing magnification due to dark matter halos centered on galaxies. We additionally constrain the properties of the galactic haloes, such as the mass-to-light ratio $\Gamma$ and radial profile of the halo matter density $\rho(r)$. We derive a new relationship for the additional r.m.s. scatter in magnitudes caused by lensing, finding $\sigma_{\rm lens} = (0.06 \pm 0.017) (d_{\rm C}(z)/ d_{\rm C}(z=1))^{3/2}$ where $d_{\rm C}(z)$ is the comoving distance to redshift $z$. Hence the scatter in apparent magnitudes due lensing will be of the same size as the intrinsic scatter of SN Ia by $z \sim 1.2$. We propose a modification of the distance modulus estimator for SN Ia to incorporate lensing, which can be easily calculated from observational data. We anticipate this will improve the accuracy of cosmological parameter estimation for high-redshift SN Ia data., Comment: Accepted for publication in MNRAS. 18 pages, 13 figures. Minor method update and additional citations

We present an approach for using machine learning to automatically discover the governing equations and hidden properties of real physical systems from observations. We train a "graph neural network" to simulate the dynamics of our solar system's Sun, planets, and large moons from 30 years of trajectory data. We then use symbolic regression to discover an analytical expression for the force law implicitly learned by the neural network, which our results showed is equivalent to Newton's law of gravitation. The key assumptions that were required were translational and rotational equivariance, and Newton's second and third laws of motion. Our approach correctly discovered the form of the symbolic force law. Furthermore, our approach did not require any assumptions about the masses of planets and moons or physical constants. They, too, were accurately inferred through our methods. Though, of course, the classical law of gravitation has been known since Isaac Newton, our result serves as a validation that our method can discover unknown laws and hidden properties from observed data. More broadly this work represents a key step toward realizing the potential of machine learning for accelerating scientific discovery., Comment: 12 pages, 6 figures, under review

Galaxies can be characterized by many internal properties such as stellar mass, gas metallicity, and star-formation rate. We quantify the amount of cosmological and astrophysical information that the internal properties of individual galaxies and their host dark matter halos contain. We train neural networks using hundreds of thousands of galaxies from 2,000 state-of-the-art hydrodynamic simulations with different cosmologies and astrophysical models of the CAMELS project to perform likelihood-free inference on the value of the cosmological and astrophysical parameters. We find that knowing the internal properties of a single galaxy allow our models to infer the value of $\Omega_{\rm m}$, at fixed $\Omega_{\rm b}$, with a $\sim10\%$ precision, while no constraint can be placed on $\sigma_8$. Our results hold for any type of galaxy, central or satellite, massive or dwarf, at all considered redshifts, $z\leq3$, and they incorporate uncertainties in astrophysics as modeled in CAMELS. However, our models are not robust to changes in subgrid physics due to the large intrinsic differences the two considered models imprint on galaxy properties. We find that the stellar mass, stellar metallicity, and maximum circular velocity are among the most important galaxy properties to determine the value of $\Omega_{\rm m}$. We believe that our results can be explained taking into account that changes in the value of $\Omega_{\rm m}$, or potentially $\Omega_{\rm b}/\Omega_{\rm m}$, affect the dark matter content of galaxies. That effect leaves a distinct signature in galaxy properties to the one induced by galactic processes. Our results suggest that the low-dimensional manifold hosting galaxy properties provides a tight direct link between cosmology and astrophysics., Comment: 20+6 pages, 15 figures, data and codes to reproduce the results publicly available at https://github.com/franciscovillaescusa/Cosmo1gal

Since the expansion of the universe was first established by Edwin Hubble and Georges Lemaitre about a century ago, the Hubble constant H0 which measures its rate has been of great interest to astronomers. Besides being interesting in its own right, few properties of the universe can be deduced without it. In the last decade a significant gap has emerged between different methods of measuring it, some anchored in the nearby universe, others at cosmological distances. The SH0ES team has found $H_0 = 73.2 \pm 1.3$ km sec$^{-1}$ Mpc$^{-1}$ locally, whereas the value found for the early universe by the Planck Collaboration is $H_0 = 67.4 \pm 0.5$ km sec$^{-1}$ Mpc$^{-1}$ from measurements of the cosmic microwave background. Is this gap a sign that the well-established $\Lambda$CDM cosmological model is somehow incomplete? Or are there unknown systematics? And more practically, how should humble astronomers pick between competing claims if they need to assume a value for a certain purpose? In this article, we review results and what changes to the cosmological model could be needed to accommodate them all. For astronomers in a hurry, we provide a buyer's guide to the results, and make recommendations., Comment: Accepted for publication in The Astronomy and Astrophysics Review (72 pages, 18 figures)

We study a phenomenological class of models where dark matter converts to dark radiation in the low redshift epoch. This class of models, dubbed DMDR, characterizes the evolution of comoving dark matter density with two extra parameters, and may be able to help alleviate the observed discrepancies between early- and late-time probes of the universe. We investigate how the conversion affects key cosmological observables such as the CMB temperature and matter power spectra. Combining 3x2pt data from Year 1 of the Dark Energy Survey, {\it Planck}-2018 CMB temperature and polarization data, supernovae (SN) Type Ia data from Pantheon, and baryon acoustic oscillation (BAO) data from BOSS DR12, MGS and 6dFGS, we place new constraints on the amount of dark matter that has converted to dark radiation and the rate of this conversion. The fraction of the dark matter that has converted since the beginning of the universe in units of the current amount of dark matter, $\zeta$, is constrained at 68\% confidence level to be $<0.32$ for DES-Y1 3x2pt data, $<0.030$ for CMB+SN+BAO data, and $<0.037$ for the combined dataset. The probability that the DES and CMB+SN+BAO datasets are concordant increases from 4\% for the $\Lambda$CDM model to 8\% (less tension) for DMDR. The tension in $S_8 = \sigma_8 \sqrt{\Omega_{\rm m}/0.3}$ between DES-Y1 3x2pt and CMB+SN+BAO is slightly reduced from $2.3\sigma$ to $1.9\sigma$. We find no reduction in the Hubble tension when the combined data is compared to distance-ladder measurements in the DMDR model. The maximum-posterior goodness-of-fit statistics of DMDR and $\Lambda$CDM model are comparable, indicating no preference for the DMDR cosmology over $\Lambda$CDM., Comment: 23 pages, 11 figures. DES extensions group. Accepted by PRD

We use Density Estimation Likelihood-Free Inference, $\Lambda$ Cold Dark Matter simulations of $\sim 2M$ galaxy pairs, and data from Gaia and the Hubble Space Telescope to infer the sum of the masses of the Milky Way and Andromeda (M31) galaxies, the two main components of the Local Group. This method overcomes most of the approximations of the traditional timing argument, makes the writing of a theoretical likelihood unnecessary, and allows the non-linear modelling of observational errors that take into account correlations in the data and non-Gaussian distributions. We obtain an $M_{200}$ mass estimate $M_{\rm MW+M31} = 4.6^{+2.3}_{-1.8} \times 10^{12} M_{\odot}$ ($68 \%$ C.L.), in agreement with previous estimates both for the sum of the two masses and for the individual masses. This result is not only one of the most reliable estimates of the sum of the two masses to date, but is also an illustration of likelihood-free inference in a problem with only one parameter and only three data points., Comment: 14 pages, 9 figures. Accepted by Physical Review D

The overall cosmological parameter tension between the Atacama Cosmology Telescope 2020 (ACT) and Planck 2018 data within the concordance cosmological model is quantified using the suspiciousness statistic to be 2.6$\sigma$. Between ACT and the South Pole Telescope (SPT) we find a tension of 2.4$\sigma$, and 2.8$\sigma$ between ACT and Planck+SPT combined. While it is unclear whether the tension is caused by statistical fluctuations, systematic effects or new physics, caution should be exercised in combining these cosmic microwave background datasets in the context of the $\Lambda$CDM standard model of the universe., Comment: 6 Pages, 1 figure, 1 table. Prepared for submission to PRL. v2: updated pre-submission with additional analysis and makes clearer the relationship with the ACT DR4 analysis. v3. Additional analysis added for exact suspiciousness calculation. v4. Updates to text and references post PRD review

We propose a principled Bayesian method for quantifying tension between correlated datasets with wide uninformative parameter priors. This is achieved by extending the Suspiciousness statistic, which is insensitive to priors. Our method uses global summary statistics, and as such it can be used as a diagnostic for internal consistency. We show how our approach can be combined with methods that use parameter space and data space to identify the existing internal discrepancies. As an example, we use it to test the internal consistency of the KiDS-450 data in 4 photometric redshift bins, and to recover controlled internal discrepancies in simulated KiDS data. We propose this as a diagnostic of internal consistency for present and future cosmological surveys, and as a tension metric for data sets that have non-negligible correlation, such as LSST and Euclid., Comment: 7 pages, 4 figures

In this work we investigate the systematic uncertainties that arise from the calculation of the peculiar velocity when estimating the Hubble constant ($H_0$) from gravitational wave standard sirens. We study the GW170817 event and the estimation of the peculiar velocity of its host galaxy, NGC 4993, when using Gaussian smoothing over nearby galaxies. NGC 4993 being a relatively nearby galaxy, at $\sim 40 \ {\rm Mpc}$ away, is subject to a significant effect of peculiar velocities. We demonstrate a direct dependence of the estimated peculiar velocity value on the choice of smoothing scale. We show that when not accounting for this systematic, a bias of $\sim 200 \ {\rm km \ s ^{-1}}$ in the peculiar velocity incurs a bias of $\sim 4 \ {\rm km \ s ^{-1} \ Mpc^{-1}}$ on the Hubble constant. We formulate a Bayesian model that accounts for the dependence of the peculiar velocity on the smoothing scale and by marginalising over this parameter we remove the need for a choice of smoothing scale. The proposed model yields $H_0 = 68.6 ^{+14.0}_{-8.5}~{\rm km\ s^{-1}\ Mpc^{-1}}$. We demonstrate that under this model a more robust unbiased estimate of the Hubble constant from nearby GW sources is obtained., Comment: 9 pages, 5 figures

We investigate constraints on the Hubble constant ($H_0$) using Baryon Acoustic Oscillations (BAO) and baryon density measurements from Big Bang Nucleosynthesis (BBN). We start by investigating the tension between galaxy BAO measurements and those using the Lyman-$\alpha$ forest, within a Bayesian framework. Using the latest results from eBOSS DR14 we find that the probability of this tension being statistical is $\simeq6.3\%$ assuming flat $\Lambda$CDM. We measure $H_0 = 67.6\pm1.1$ km s$^{-1}$ Mpc$^{-1}$, with a weak dependence on the BBN prior used, in agreement with results from Planck Cosmic Microwave Background (CMB) results and in strong tension with distance ladder results. Finally, we forecast the future of BAO $+$ BBN measurements of $H_0$, using the Dark Energy Spectroscopic Instrument (DESI). We find that the choice of BBN prior will have a significant impact when considering future BAO measurements from DESI., Comment: 14 pages, 3 figures

We demonstrate a measure for the effective number of parameters constrained by a posterior distribution in the context of cosmology. In the same way that the mean of the Shannon information (i.e. the Kullback-Leibler divergence) provides a measure of the strength of constraint between prior and posterior, we show that the variance of the Shannon information gives a measure of dimensionality of constraint. We examine this quantity in a cosmological context, applying it to likelihoods derived from Cosmic Microwave Background, large scale structure and supernovae data. We show that this measure of Bayesian model dimensionality compares favourably both analytically and numerically in a cosmological context with the existing measure of model complexity used in the literature., Comment: 14 pages, 9 figures. v2: updates post peer-review. v3: typographical correction to equation 35

We provide a new interpretation for the Bayes factor combination used in the Dark Energy Survey (DES) first year analysis to quantify the tension between the DES and Planck datasets. The ratio quantifies a Bayesian confidence in our ability to combine the datasets. This interpretation is prior-dependent, with wider prior widths boosting the confidence. We therefore propose that if there are any reasonable priors which reduce the confidence to below unity, then we cannot assert that the datasets are compatible. Computing the evidence ratios for the DES first year analysis and Planck, given that narrower priors drop the confidence to below unity, we conclude that DES and Planck are, in a Bayesian sense, incompatible under LCDM. Additionally we compute ratios which confirm the consensus that measurements of the acoustic scale by the Baryon Oscillation Spectroscopic Survey (SDSS) are compatible with Planck, whilst direct measurements of the acceleration rate of the Universe by the SHOES collaboration are not. We propose a modification to the Bayes ratio which removes the prior dependency using Kullback-Leibler divergences, and using this statistical test find Planck in strong tension with SHOES, in moderate tension with DES, and in no tension with SDSS. We propose this statistic as the optimal way to compare datasets, ahead of the next DES data releases, as well as future surveys. Finally, as an element of these calculations, we introduce in a cosmological setting the Bayesian model dimensionality, which is a parameterisation-independent measure of the number of parameters that a given dataset constrains., Comment: 16 pages, 9 figures. v2 & v3: updates post peer-review. v4: typographical correction to the reported errors in the log S column of Table II. v5: typographical correction to equation 26

Recent distance ladder determinations of the Hubble constant $H_0$ disagree at about the $3.5\sigma$ level with the value determined from Planck measurements of the cosmic microwave background (CMB) assuming a $\Lambda$CDM cosmology. This discrepancy has prompted speculation that new physics might be required beyond that assumed in the $\Lambda$CDM model. In this paper, we apply the inverse distance ladder to fit a parametric form of $H(z)$ to baryon acoustic oscillation (BAO) and Type Ia supernova data together with priors on the sound horizon at the end of the radiation drag epoch, $r_d$. We apply priors on $r_d$, based on inferences from either Planck or the Wilkinson Microwave Anistropy Probe (WMAP), and demonstrate that these values are consistent with CMB-independent determinations of $r_d$ derived from measurements of the primordial deuterium abundance, BAO and supernova data assuming the $\Lambda$CDM cosmology. The $H(z)$ constraints that we derive are independent of detailed physics within the dark sector at low redshifts, relying only on the validity of the Friedmann-Robertson-Walker (FRW) metric of General Relativity. For each assumed prior on $r_d$, we find consistency with the inferred value of $H_0$ and the Planck $\Lambda$CDM value and corresponding tension with the distance ladder estimate., Comment: 8 pages, 9 figures

In this work we pose the possibility that, at an early stage, the migration of a proto--giant planet caused by the presence of a gaseous circumstellar disk could explain the continuous feeding of small bodies into its orbit. Particularly, we study the probability of capture and permanence in co--orbital resonance of these small bodies, as planets of diverse masses migrate by interaction with the gaseous disk, and the drag induced by this disk dissipates energy from these small objects, making capture more likely. Also, we study the relevance of the circumplanetary disk, a structure formed closely around the planet where the gas density is enhanced, in the process of capture. It is of great interest for us to study the capture of small bodies in 1:1 resonance because it could account for the origin of the Trojan population, which has been proposed \citep{2011Icar..215..669K} as a mechanism of quasi-satellites and irregular satellites capture., Comment: This is a pre-copyedited, author-produced PDF of an article accepted for publication in PSS following peer review; 9 pages, 9 figures

The Kilo-Degree Survey (KiDS) has been used in several recent papers to infer constraints on the amplitude of the matter power spectrum and matter density at low redshift. Some of these analyses have claimed tension with the Planck $\Lambda \mathrm{CDM}$ cosmology at the $\sim 2-3\sigma$ level, perhaps indicative of new physics. However, Planck is consistent with other low redshift probes of the matter power spectrum such as redshift space distortions and the combined galaxy-mass and galaxy-galaxy power spectra. Here we perform consistency tests of the KiDS data, finding internal tensions for various cuts of the data at $\sim 2.2 - 3.5\sigma$ significance. Until these internal tensions are understood, we argue that it is premature to claim evidence for new physics from KiDS. We review the consistency between KiDS and other weak lensing measurements of $S_8$, highlighting the importance of intrinsic alignments for precision cosmology., Comment: Comments: 8 pages, 5 figures. Accepted for publication in MNRAS