Dr Harry Desmond

Abstract:

Abstract Statistical methodology is rarely considered significant in distance-ladder studies or a potential contributor to the Hubble tension. We suggest it should be, highlighting two appreciable issues. First, astronomical distances are inferred latent parameters, requiring a prior. We show that the (often implicit) uniform priors on distance moduli common to Bayesian distance-ladder analyses bias distances low due to objects being uniformly distributed in volume, which biases the Hubble constant high. Frequentist χ2 methods are unbiased for volume- or redshift-limited samples only if the redshift uncertainty (including peculiar velocities) vanishes, though simulation-based calibration can correct the bias. Second, in a Bayesian framework, selection effects introduce additional posterior factors describing the probability of objects entering the sample under the model. These partly counteract the volume prior, depending on the nature of the selection. After detailed analytic and mock-based studies, we quantify the volume-prior effect in the CosmicFlows-4 and SH0ES samples. Both use frequentist methods, so the effect appears as a potential estimator bias rather than a missing prior. The implied Hubble constant shifts are significant but must not be applied naïvely—principled selection modelling is also required, as we investigate explicitly for CosmicFlows-4. Both effects should already be captured by the SH0ES pipeline’s simulation-based bias corrections. Our work highlights the crucial need to model both distances and selection accurately, either directly in a Bayesian forward model, or via post-hoc simulation-based corrections with realistic source and selection distributions. Such modelling requires samples with known, homogeneous selection criteria, which future surveys should prioritise.

Abstract:

Dark matter haloes are typically characterized by radial density profiles with fixed forms motivated by simulations (e.g. Navarro-Frenk-White [NFW]). However, simulation predictions depend on uncertain dark matter physics and baryonic modelling. Here, we present a method to constrain halo density profiles directly from observations using Exhaustive Symbolic Regression (ESR), a technique that searches the space of analytic expressions for the function that best balances accuracy and simplicity for a given dataset. We test the approach on mock weak lensing excess surface density (ESD) data of synthetic clusters with NFW profiles. Motivated by real data, we assign each ESD data point a constant fractional uncertainty and vary this uncertainty and the number of clusters to probe how data precision and sample size affect model selection. For fractional errors around 5%, ESR recovers the NFW profile even from samples as small as approximately 20 clusters. At higher uncertainties representative of current surveys, simpler functions are favoured over NFW, though it remains competitive. This preference arises because weak lensing errors are smallest in the outskirts, causing the fits to be dominated by the outer profile. ESR therefore provides a robust, simulation-independent framework both for testing mass models and determining which features of a halo's density profile are genuinely constrained by the data. This article is part of the discussion meeting issue 'Symbolic regression in the physical sciences'.

Abstract:

Physics seeks to uncover the laws of Nature and express them through mathematical equations . Despite the vast diversity of natural phenomena, physical equations exhibit structural regularities that set them apart from arbitrary mathematical expressions. While principles such as dimensional analysis have long guided the formulation of physical models, the exploration of more subtle statistical patterns within the equations of physics remains an open question. Here, by analysing four corpora of physics equations and applying advanced implicit-likelihood techniques, we find that the frequency of mathematical operators follows an exponential decay law, in contrast to Zipf's power law for word frequencies in natural languages. This reveals a statistical meta-law of physics, possibly reflecting a combination of communication efficiency and constraints imposed by Nature itself. The meta-law offers practical benefits for symbolic regression by drastically narrowing down the space of physically plausible expressions. More broadly, it may inform the development of language models that can generate coherent mathematical representations, advancing the automation of physical law discovery. This article is part of the discussion meeting issue 'Symbolic regression in the physical sciences'.

Abstract:

We test whether (Formula presented.) symmetric teleparallel gravity theories can solve the Hubble tension consistently with DESI DR2 BAO. We consider three (Formula presented.) functional forms: logarithmic, exponential, and hyperbolic tangent. We extend these models by allowing a cosmological constant, and compare to phenomenological models with a flexible exponential, hyperbolic secant, and polynomial decay addition to the standard (Formula presented.) CDM (Formula presented.). We test these models against DESI DR2 BAO, CMB (Planck 2018 + SPT-3G + ACT DR6), local (Formula presented.), and Cosmic Chronometer data. The logarithmic and hyperbolic tangent (Formula presented.) models do not provide an adequate solution, but the exponential model does. Furthermore, it slightly reduces the (Formula presented.) parameter space tension between CMB and BAO datasets to (Formula presented.), down from (Formula presented.) for (Formula presented.) CDM. Although (Formula presented.) CDM faces only (Formula presented.) tension in DESI data space, the (Formula presented.) higher tension in parameter space suggests a real anomaly. The models assisted by the cosmological constant perform slightly better still, at the cost of undermined theoretical motivation. They also perform poorly once local (Formula presented.) measurements are included. The phenomenological models fit all data reasonably well, yet the best-fitting models predict isotropically averaged BAO distances exceeding the DESI DR2 measurements at all redshifts. This highlights the difficulties of finding a theoretically motivated solution to the Hubble tension while remaining consistent with BAO data.